text:
Q: Estimating the time complexity (Big O notation) for the given code Please help to find the complexity of the given code. Is it O(N+N+N) or O(N^3) or something else? Please given explanation for my understanding. Thank you.
the code
def finder(arr1,arr2):

count={}

for x in arr1:
    if x in count.keys():
        count[x]+=1
    else:
        count[x]=1

for x in arr2:
    if x in count.keys():
        count[x]-=1
    else:
        count[x]=1

for key,num in count.items():
    if num != 0:
        return key

return ('equal arrays')

A: Okay so, first you need to understand what "N" actually is. In this case we can say N is the length of arr1 and then lets call "M" the length of arr2.
The first loop iterates through arr1 completely so it has a complexity of O(N) (the worst case always happens, it always iterates through all elements in the array).
The second loop iterates through arr2 completely so it has a complexity of O(M).
The third loop iterates through count.items which is basically the length of the array count. In the worst case, the biggest length this array could have is N+M (meaning it has all items from arr1 and arr2). So it has a complexity of O(N+M).
Now, if loops (lets say the first and second one) are nested like:
for x in arr1:
    for y in arr2:
         // ....

then for every iteration in the first loop, there are M iterations on the second loop. So we can say that there are N iterations of M iterations each. This means the complexity would be O(N*M) and O(N^2) in case N = M.
In the other case, the loops are not nested, they are just one after the other.
for x in arr1:
    // ....
for y in arr2:
    // ....

This means the algorithm has a complexity O(N) + O(M) or O(N+M) since it first iterates N times and then M times. You can keep only the biggest complexity so if N > M, you can reduce it to O(N).
Now you can now figure out how to find your algorithm's complexity taking into account the third loop!


text:
Child Of Dem Minority Whip Katherine Clark Busted In Antifa Event…
(FreedomWire.org) – House Democratic Whip Katherine Clark's daughter was arrested for spray-painting a monument and assaulting a police officer during a protest yesterday in Boston. Clark became the second highest-ranking Democrat in the House of Representatives after she was elected whip last month.
She said: "Last night, my daughter was arrested in Boston, Massachusetts. I love Riley, and this is a very difficult time in the cycle of joy and pain in parenting. This will be evaluated by the legal system, and I am confident in that process."
Boston Police Department issued a statement that said: "Incident 1: At about 9:30 PM, on Saturday, January 21, 2021, officers assigned to District A-1 (Downtown) responded to a call for a protest at the Parkman Bandstand Monument located within the Boston Common, 139 Tremont Street.
"Upon arrival officers observed an individual defacing the monument with spray paint. The tagging read "NO COP CITY" and "ACAB".
Last night, my daughter was arrested in Boston, Massachusetts. I love Riley, and this is a very difficult time in the cycle of joy and pain in parenting.
This will be evaluated by the legal system, and I am confident in that process.
— Katherine Clark (@RepKClark) January 22, 2023
"The suspect was later identified as Jared Dowell, 23, of Melrose.
"During the arrest of Jared Dowell, a group of about 20 protesters began to surround officers while screaming profanities though megaphones on the public street causing traffic to come to a standstill.
"While interfering with the arrest of Jared Dowell, an officer was hit in the face and could be seen bleeding from the nose and mouth.
"Jared Dowell was placed under arrest and charged with; Assault by Means of a Dangerous Weapon, Destruction or Injury of Personal Property and Damage of Property by Graffiti/Tagging. Dowell is expected to be arraigned in Boston Municipal Court.
"Incident 2: At about 10:27 PM, on Saturday, January 21, 2023, officers assigned to District A-1 (Downtown) made a second arrest at the Parkman Bandstand Monument of Andrea Colletti, 27, of Brighton.
"After attempting to flee on foot, she was apprehended. After a brief struggle ensued, she was placed under arrest and charged with; Damage of Property by Graffiti/Tagging, Destruction or Injury of Personal Property and Resisting Arrest. Colletti is expected to be arraigned in Boston Municipal Court," BPD said.
According to Fox News:
"The Boston Police Department referred to the suspect as "Jared Dowell." Clark has spoken in the past about how one of her children is non-binary."
Antifa are the ground troops for the Democrat Party.
Democrat House Minority Whip Katherine Clark's son was arrested at another organized Antifa terrorist attack.
No, not Atlanta, it was Boston.
Democrats not only support Antifa, they give birth to them and raise them. https://t.co/5m5TSj4odT
— Rep. Marjorie Taylor Greene🇺🇸 (@RepMTG) January 23, 2023
"Jared Dowell was placed under arrest and charged with; Assault by Means of a Dangerous Weapon, Destruction or Injury of Personal Property and Damage of Property by Graffiti/Tagging." https://t.co/THxOecZ7ww
— Josh Kraushaar (@JoshKraushaar) January 23, 2023
Your son is a man. Is he the same child you told us about earlier this year when you said you vividly remembered your child waking up with nightmares about climate change? Maybe if you hadn't radicalized him he wouldn't have become an Antifa terrorist confused about gender.
— Robby Starbuck (@robbystarbuck) January 23, 2023
Democrat Official Accused Of Murder…
(FreedomWire.org) – The Las Vegas Democrat official who murdered an investigative journalist was going to have photos and text messages with his mistress released within hours of the fatal stabbing.
Democrat Clark County official Robert Telles was arrested in September on suspicion of murder in connection with the fatal stabbing of Las Vegas Review-Journal reporter Jeff German.
Jeff German, 69, was found stabbed to death in front of his home in early September on a Saturday morning.
Telles, a Democrat, lost his re-election bid in June's primary after Jeff German exposed the hostile work environment in the Democrat official's office.
Jeff German had also recently filed a public records request on emails and text messages between Telles and others in his office, the Las Vegas Review-Journal reported.
Rita Reid, former coworker and eventually political opponent of Clark County public administrator Robert Telles, speaks out against Telles following his arrest for the murder of Las Vegas journalist Jeff German:
"Jeff had been found murdered. My first thought was Robert Telles." pic.twitter.com/UIr5jMveGQ
— The Recount (@therecount) September 13, 2022
According to the Daily Mail, hours before Jeff German was stabbed to death, Robert Telles was told Clark County was going to release private texts and photos with his mistress.
The Daily Mail reports:
The Las Vegas Democrat who is accused of fatally stabbing a journalist who exposed his martial affair was allegedly told by his mistress that photos revealing their tryst were set to come out hours before the killing.
Clark County Public Administrator Robert Telles, 45, was arraigned in late September, officially being charged with the 'unlawful, heinous, senseless murder of [Las Vegas Review-Journal] reporter Jeff German.'
Hours before German – a journalist who often exposed corruption throughout the region – was killed, Telles was told that Clark County was going to release emails and Microsoft Teams messages to the paper detailing his 'inappropriate relationship' with Roberta Lee-Kennett.
German had done stories on the allegations and was working on a follow-up story at the time he was murdered.
Lee-Kennett emailed Telles about what the county attorneys had told her at 7:30 in the morning of September 3, with Telles responding that he would 'review' it, according to affidavits.
Sunday's front page: Complaints about former elected county official Robert Telles started while he was a UNLV student. His toxic behavior never stopped – until investigative reporter Jeff German was found murdered.https://t.co/qEGauDeU2w pic.twitter.com/Lz09KGOYKz
— Briana Erickson (@ByBrianaE) November 21, 2022
More Bad News For Democrats…
By freedomwire February 21, 2022
(FreedomWire.org) – If Joe Biden, Kamala Harris, Chuck Schumer, and Nancy Pelosi – the leaders of the national Democratic Party – are inclined to imbibe after receiving bad news, they may have one heck of a hangover tomorrow morning.
As Rasmussen Reports has now indicated in a just-published piece about the latest polling figures for the generic congressional ballot, the Democrats are in deep water with the American electorate, and it may be impossible to return to high ground in time for the November midterm elections.
According to Rasmussen:
"The 2022 midterm elections are now 263 days away, and Republicans have a 13-point lead in their bid to recapture control of Congress.
"…if the elections for Congress were held today, 50% of Likely U.S. Voters would vote for the Republican candidate, while 37% would vote for the Democrat. Just four percent (4%) would vote for some other candidate, but another nine percent (9%) are not sure.
"Republicans have added four points to their congressional advantage since January."
Two more significant takeaways from the Rasmussen poll:
"The 13-point edge for Republicans in the latest poll is larger than Democrats enjoyed at any time during the 2018 midterm campaign…
"While 89% of Republican voters say they would vote for their own party's congressional candidate, only 77% of Democrats would vote for the Democratic candidate."
Any way you cut it, the Democrats are not resonating with the American people now that they are in charge of the House, the Senate, and the White House. Not only are the numbers bad for the Democrats, but they are also getting worse by the month.

redpajama_set_name: RedPajamaCommonCrawl


An Interview with FDA's New Deputy Commissioner for Foods and Veterinary Medicine | Northland Laboratories - Moving food safety forward.
Stephen Ostroff, M.D. is the FDA's new Deputy Commissioner for Foods and Veterinary Medicine (FVM). Dr. Ostroff's career has been dedicated to public health. He served as acting FDA commissioner from April 2015 until Congress confirmed Dr. Robert Califf's appointment in late February 2016. Prior to his tenure as acting commissioner, he was the agency's chief scientist, responsible for leading and coordinating FDA's cross-cutting scientific and public health efforts.


text:
Q: How to handle numbers embedded in text during NLP pre-processing? I am trying to run the LDA algorithm on a data set of news articles.
I understand that numbers must be removed during the pre-processing step, and I have written a simple regex code to replace numbers with blanks.
df['number_removed'] = df['text'].str.replace('\d+', '',regex=True)

However, I would like to retain some numbers since removing them can potentially change the context/topic.
For example,
[Desired] 'The fourth industrial revolution also referred to as Industry 40 is starting to change the way goods are produced'
[Wrong] 'The fourth industrial revolution also referred to as Industry is starting to change the way goods are produced'
Note: The punctuations have been removed in the example as part of pre-processing
So, I was wondering:

*

*Can essential numbers be retained before running LDA?

*How to selectively remove numbers or handle the above situation?

A: What is sometimes done in similar situations is to replace numbers with a dummy token, such as <NUMBER>, so that the fact that there was a number in the original text is preserved, but without disturbing the syntactic context. The actual value is usually not that important for generalisations.
If you want to retain concrete numbers (like "industry 40") then I guess you need to adjust your regex to keep those patterns.

redpajama_set_name: RedPajamaStackExchange


text:
Alameda wallet under liquidator control incurred $11.5M in losses: Arkham
According to crypto analytics firm Arkham, at least $4 million of these losses were "preventable losses."
The liquidators of Alameda Research have reportedly incurred at least $11.5 million in losses since taking control of Alameda's trading accounts.
On Jan. 16, a Twitter thread from Arkham Intelligence reported that one wallet under the control of liquidators has seen a string of "significant losses" due to liquidations, some of which were "preventable losses."
Over the past two weeks being under Liquidator control, the account incurred significant losses:
Largest single liquidation: $4.85M
Total liquidated amount: $11.5M
Preventable losses: $4M+
— Arkham (@ArkhamIntel) January 16, 2023
As one example, Arkham noted that the account ending 0x997 initially had a short position of 9,000 Ether (ETH) ($10.8 million) against the collateral of $20 million in USD Coin (USDC) and $4 million in Dai (DAI), with a net balance of $15.2 million when the liquidators first took control.
After a string of liquidations spanning almost two weeks however, the account's current value now stands at "$1.1M short Ether against $1.4M USDC: net balance of $300K."
Arkham said this is the most recent development in a "series of market movements that have busted multiple Alameda positions left open after bankruptcy."
Another liquidation occurred when Alameda wallets removed $7 million in USDC and $4 million in DAI from the decentralized crypto lending platform AAVE to a separate Optimism L2 account on Dec. 29, around 30 hours after liquidators began moving assets out of Alameda wallets.
This removal of funds is believed to have placed the position at a high risk of liquidation, resulting in $11.4 million of USDC being sold off to liquidation bots on Optimism, while the AAVE Treasury took another $100,000 in USDC as liquidation tax.
Arkham explained that if liquidators had used a function to immediately close the position by selling off collateral instead of pulling collateral from the wallet, at least $15 million could have been preserved rather than the recovered $11 million.
This thus amounted to $4 million in preventable losses.
Related: Alameda Research had a $65B secret line of credit with FTX: Report
On Jan. 13, Cointelegraph reported that Alameda Research liquidators lost $72,000 in digital assets while consolidating funds into a single wallet on the decentralized finance (DeFi) lending platform Aave.
The liquidators attempted to close a borrow position but mistakenly removed extra collateral, putting the assets at risk of liquidation. Over a period of nine days, the loan was liquidated twice resulting in a total loss of 4.05 Wrapped Bitcoin (WBTC) which will not be able to be recouped by creditors.


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Alison O. Marks (née Bremner) is a Tlingit artist born and raised in Southeast Alaska. As a child of two cultures, native and non-native, the artist brings a unique perspective to her art. Through humor and a variety of mediums, Alison seeks to depict the experience of the modern native. Painting, woodcarving, and regalia are a few of the mediums the artist employs.
In addition to her contemporary practice, Alison is committed to the revitalization of Tlingit culture in her hometown of Yakutat, Alaska. She finds happiness in balancing art as social commentary and art for traditional and ceremonial use.
Alison has learned under master artists David R. Boxley and David A. Boxley. Her work can be found in numerous galleries in Vancouver B.C., Victoria B.C. and Seattle WA, as well as in the permanent collections of the Burke Museum of Natural History and Culture, the Portland Art Museum, and the British Museum.


text:
El  o 'palito delicioso' es un aperitivo de maíz pequeño, cilíndrico e hinchado que se vende en la mayoría de tiendas de golosinas japonesas. Es producido por Riska y vendido por Yaokin. Tiene un precio final recomendado de 10 yenes, pero debido a que el margen de beneficio es tan estrecho, su longitud puede cambiar sin aviso previo. Tiene una consistencia similar a la de los Cheetos. En un envoltorio aparece un gato, Umaemon, que es una parodia del popular Doraemon.

Variedades

Hay disponibles muchos sabores de umaibō, tanto salados (ensalada, mentaiko, takoyaki y queso) como dulces (cacao, caramelo y bombón). Algunos fueron abandonados tras un corto periodo de prueba, mientras otros se convirtieron en básicos. Algunos sabores solo se venden en lugares específicos.

Enlaces externos

 Sitio web del umaibō (japonés)
 Sitio web oficial de Yaokin (japonés)

Aperitivos de Japón

redpajama_set_name: RedPajamaWikipedia


text:
Q: Spring boot OAuth 2 resource server + JWT filter backup authentication method I'm working on a spring boot project with an OAuth2 resource server authentication method, the access token is verified on the authorization server.
This application provides also an endpoint to get a token signed by itself.
I would like to provide an authentication backup method with a WebFilter that verify the token signature if OAuth2 method failed like this :
@Bean
fun securityWebFilterChain(http: ServerHttpSecurity): SecurityWebFilterChain {
      return http.invoke {
            csrf { disable() }
            authorizeExchange {
                authorize("/actuator/**", permitAll)
                authorize("/api/login", permitAll)
                authorize("/v3/api-docs", permitAll)
                authorize("/**", authenticated)
            }
            oauth2ResourceServer {
                jwt {
                    jwtAuthenticationConverter = oauth2JwtConverter
                }
            }
            addFilterAt(JWTFilter(tokenService), SecurityWebFiltersOrder.AUTHENTICATION)
      }
}

My JWTFilter :
class JWTFilter(
    private val tokenService: TokenService
) : WebFilter {

    override fun filter(exchange: ServerWebExchange, chain: WebFilterChain): Mono<Void> {
        return resolveToken(exchange.request)
            ?.takeIf { tokenService.validateToken(it) }
            ?.let { tokenService.getAuthentication(it) }
            ?.let { chain.filter(exchange).contextWrite(ReactiveSecurityContextHolder.withAuthentication(it)) }
            ?: chain.filter(exchange)
    }

    private fun resolveToken(request: ServerHttpRequest): String? {
        return request.headers[AUTHORIZATION_HEADER]
            ?.get(0)
            ?.takeIf { it.startsWith("Bearer ") }
            ?.substring(7)
    }
}

The problem is that the authentication context set by the filter is ignored if OAuth2 failed.
How can i manage that ?


E hoje o meu pequeno mostro já faz 2 anos!!!
Today my little monster turns 2! It's pure joy having this dog around, even on the worst days, he's so happy to see us that is impossible to feel down 🙂 Happy birthday Kiko!


Based on research primarily conducted in a molecular biology laboratory working on the Human Genome Project (HGP), this dissertation focuses-upon how genomic research, as an emerging form of scientific knowledge, stands to affect the fashioning of subjectivity. This study argues that as a biomedical project which claims to be capable of understanding "what it means to be human," the HGP stands to have profound consequences upon the way in which modern subjects know themselves. The life sciences have increasingly moved away from the mastery of nature towards knowledge and control over human nature. The HGP represents an emerging model in which human nature and life have become objects and categories of knowledge and control for the life sciences. The focus of this project is the investigation of how the HGP incorporates an understanding of human nature and life into its realm of study and how that knowledge in turn is incorporated into the understanding human beings have of themselves. This research centers upon the HGP as the site in which to draw out, counterpose and resolve some of the issues at stake in the scientific remaking of human subjects. The HGP represents an expansion of the domain of the life sciences into the control of life itself and the psychological as well as material expression of that life in human beings, known as human nature. Finally, this study characterizes the HGP as a biomedical research project that is essentially religious in how it perceives itself and claims to provide ultimate knowledge on being human. This project argues that such knowledge is religious and therefore inaccessible through modern science. Therefore it questions the ability of the HGP to provide valid knowledge on the ultimate understanding of human beings through religious, philosophical and scientific discourses that contest and subvert this claim.
Leal, Belita (Maria Isabel). "A map of life: An epistemological study of the Human Genome Project." (1999) Diss., Rice University. https://hdl.handle.net/1911/19399.


text:
"The Silent Woman" is the long-awaited fourth installment in award-winning novelist Keith Rommel's "Thanatology Series"
Vero Beach, FL -- Sunbury Press has released The Silent Woman, Keith Rommel's fourth novel in the Thanatology series of psychological thrillers. Th...
Keith Rommel's "Thanatology" series collecting awards in Hollywood on the festival circuit
HOLLYWOOD, CA -- The first two books in Keith Rommel's Thanatology series (Sunbury Press), The Cursed Man and The Lurking Man, have been adapted in...
On The Rise: Ruth Connell On Her Career, Role On 'Supernatural' & Much More!
Originally published on the blog Icon vs. Icon: All Things Pop Culture on December 4, 2014 (Ruth Connell appears in the movie The Cursed Man based...
Keith Rommel's "You Killed My Brother" acquired by Sunbury Press
PORT ST. LUCIE, Fla. -- Sunbury Press has released Keith Rommel's thriller novel You Killed My Brother, the first book of the Cultures Collide seri...
Emmy Award winning editor, Neil Mandelberg signs on to cut THE CURSED MAN movie
September 25, 2014 – Hollywood, California As an Emmy winning film editor, Neil Mandelberg has been a respected member of the entertainment indust...


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Waterloo Automotive Locksmith Services 24 Hour Car Key Replacement Waterloo, Ontario.


text:
BI park prepares for major remodel
Also, COVID vax for all parks users?
The current skate park is for those with advanced abilities. File Photo
Strawberry Hill Park is ripe for change.
Seeds are planted for new mountain bike trails, expansion of the dog park, a skate park for beginners, tennis courts, trails, a playground area and possibly even renaming the park.
All of those ideas were discussed at the Bainbridge Island Metropolitan Parks District meeting last week.
Parks staff put together the concept plan as a "starting point to see if this all makes sense," said Terry Lande, executive director.
Dan Hamlin, park service division director, explained the changes, adding a 10-acre land donation next to the park will be used for the bike trails and dog park expansion. The donation was especially appreciated by parks because it came during a controversial discussion over potential bike trails at Grand Forest North. Hamlin said local bike groups are "really excited about this, as you can imagine."
The dog park would basically double in size. It's located away from neighbors so there is a buffer. One idea is to break the park up into different sections, so if "it's too busy in one spot you can go to a different area," Hamlin said of the fairly new nationwide trend.
Hamlin said the current skateboard park is a "pretty high level for skating and hard for a beginner to get started on," so supporters of the new one are "very excited, ready to go and not daunted by the cost" for which they will be doing the fund-raising. Discussions include at least parts of it being covered.
Adding tennis courts also would fill a community need. Ideas include putting two new ones near the existing one. They could be covered and have lights for nighttime play. Supporters say they could be an alternative site for ones discussed for Sakai Park.
Hamlin said a trail that would loop around the entire park is another option.
Finally, it's been discussed for years to move the playground area closer to the sports fields. But Hamlin said that would require long walks through parking lots. While that's still an option for the future, other sites are being discussed.
Park Commissioner Ken DeWitt suggested putting it up near the entrance to Strawberry Park. "A storage area at the entrance doesn't really excite me," he said of the current plan.
Commissioner Jay Kinney asked if any part of the plan could get started on right away.
Because of the land donation, some commissioners said the parks district should get moving on those ideas first. "We already know where they are going to go," DeWitt said.
Dawn Janow, commission chair, added mountain bikers have been waiting a long time for a facility, but it was also mentioned tennis court fans have been, too.
Hamlin said each part of the changes has committees working on ideas. The district also is working with the parks foundation regarding fund-raising. "There are lots of moving parts. We need to look at this holistically," he said.
Also to be considered is the old office building, which isn't needed anymore because they are now located at the Bainbridge Recreation Center. Maybe there is a "better way to consolidate all that stuff," Hamlin said, adding parking and roads also need to be discussed.
With all of those changes, Commissioner Asaph Glosser said there likely will be more people, which means more restrooms would be needed. He also said a timeline is needed, as all of the interested groups want their park changes now.
All the commissioners agreed a series of public meetings are needed, but Lande said the public needs to understand they are not starting from scratch. "We're halfway down the road," he said.
Vaccine requirements
COVID-19 has been around for about two years, and vaccines for about a year, but the park district just started talking about requiring vaccinations for employees and patrons at this meeting.
Lande said a few park employees quit because there was no policy. "We lost a couple of employees because they didn't want to work if they didn't know who was or wasn't vaccinated," he said. Patrons also are asking more often who on staff is vaccinated. "We're getting more of those kinds of questions."
Lande said about 90% of adults and 100% of teens 12-18 are vaccinated on BI.
Glosser said requiring the vaccine is almost a no-brainer with those types of statistics. "90 percent can't agree on anything" on BI, he said.
Three public commenters agreed vaccines should be required for employees and patrons of park facilities and programs.
"It's in our best interest," Caty Kehs said. "Especially for children who have yet to be approved for vaccinations." She added it's also needed now as activities move indoors due to weather.
Loanne Harmeling said as a member of a vulnerable community over a certain age she'd like to see staff at the Aquatic Center vaccinated.
Betty Wiese agreed, adding staff could learn lessons from others about exemptions to getting the shot. "You could save yourself some missteps on what worked and what didn't."
Kinney suggested the district use the same policy as the state is, with exemptions for medical and religious reasons. "We don't have to reinvent the wheel," he said, adding the district has to protect staff and patrons.
A policy for patrons is more complicated because the parks district has so many different types of users, Lande said, adding it would be hard to enforce a family from using a park if they are not vaccinated.
They agreed patrons of parks programs would be easier to require vaccinations for. A big discussion took place regarding sports teams, especially visiting ones. "That could be a real imposition," Glosser said.
Lande mentioned the local girls swim team has 55 members, all vaccinated. Yet two still came down with COVID. "They can rub elbows elsewhere and bring it back," Lande said.
DeWitt said all district programs can do what the Aquatic Center does: Take your temperature when you sign in. He said they could have some flexibility, too, such as requiring a negative COVID test if not vaccinated.
DeWitt wondered what power the district has over school sports. "We have the trump card," Lande said. "Lifeguards."
Kinney said they know they can't make people get vaccinated. "We're not going to tie you down and put a needle in your arm," he said. But they can decide if you can use their facilities. "It's just like shots when we went to school," he said. We have to make sure "everybody is safe."
Weather forces NK to use ground game in 32-0 win over BI
God help us with affordable housing


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Maxim Instant Energy Gel Strawberry and Magnesium does not contain any allergens (mentioned on the ALBA-list).


text:
Memphis lands commitment from 2018 center Connor Vanover
By Scott PhillipsSep 20, 2017, 10:30 PM EDT
Memphis picked up its first commitment in the Class of 2018 on Wednesday night as unique center prospect Connor Vanover announced his decision on Twitter.
At 7-foot-2, Vanover brings elite size to the interior for the Tigers and he's also skilled enough that he was a 43 percent three-point shooter during his stint playing with Pro Skills in the Nike EYBL this spring. Although Vanover needs to add strength and athleticism to adapt to the college level, he simply has size that you can't teach. Pair that size with an intriguing perimeter jumper and it'll be interesting to see how head coach Tubby Smith is able to develop Vanover the next few years.
A three-star prospect according to Rivals, Vanover averaged 9.1 points, 5.5 rebounds and 1.5 blocks per game during the spring. Originally from Arkansas, Vanover is spending his senior season of high school ball at prep school powerhouse Findlay Prep.
I am extremely excited to announce I have committed to the University of Memphis #BAM @Memphis_MBB @FindlayPilots pic.twitter.com/I0WHMPyksx
— Connor Vanover (@Vanover_Connor) September 21, 2017


During the period March-May 2009 WCC promoted a concept that would ring-fence all, or parts, of residential Thorndon into 'heritage' precincts. The declared WCC intent was (or is) to constitute these (or similar) by modifying the District Plan. The impacted areas declared at the time can be viewed on an online map that was prepared using Council data.
Elevated concerns of both its members and others in the community, particularly following a WCC convened public meeting held at the Thorndon School, encouraged the Thorndon Residents' Association to convene an action committee to unveil the issues. This group initiated a dialogue with Ward Councillors, WCC officers and numerous other stakeholders, from both within and beyond Thorndon.
The Council agreed to further consultation and to forgo its published deadlines. This paved the way to plan a different approach and to introduce the principles of deliberative public engagement. These are meetings where the emphasis moves to actively involving people, the community, in decision-making. The emphasis moves to priority on the community and participants' discussions, and it demands high levels of transparency so that everybody knows what's going-on, what's being/been discussed.
The up-coming public meetings will be professionally facilitated around these principles. The facilitator will be independent i.e. from WCC, the Residents' Association or other Thorndon entities. Please don't miss the opportunity to attend one (or more) of these participatory neighbourhood meetings. February 16 or 23, or March 2 or 9. Their success largely depends on as many people as possible turning out, and the will to share views and to listen to others. If you have been interested to read this far you probably have a reason to be there … the convenors encourage and welcome your participation. These public meetings are open to anyone with an interest, both within and beyond residential Thorndon. Roll-up, take part, make a difference.


Many unethical dentists try to talk you into treatments just to make more money. Here's how to avoid getting ripped off.
Too many dentists try to use "creative diagnosis" to undertake unnecessary work in an attempt to make extra money.
Here are ways to avoid getting ripped off.
Often someone visiting a new dentist could be told that they need a ton work done. This usually involves ripping out all their current fillings and replacing them with brand new ones.
But you should be weary of a dentist prescribing this much work unless you are visiting because you are in pain. While fillings do decay and crack over time, you don't need all of them replaced at the same time.
Dental practices that offer heavily discounted deals, like free whitening sessions, do so to get you in the door so they can then prescribe those big treatment plans for work you may not need.
Typically, it's cheaper to get a whitening or cleaning from a practice who doesn't usually offer special deals – so you're far more likely to pay for what you need and no more.
An unethical dentist may rely on all kinds of products and treatments as part of their upsell to patients. The most common are prescription toothpastes and fluoride treatments. These kinds of products can be helpful for someone who gets lots of cavities, but for the majority, they're not necessary.
These are another two products that are regularly used as money makers. While some people may certainly need a night guard to stop them from grinding their teeth or to avoid jaw pain, not everyone needs one.
Sealants are a similar scenario. They're a product that can be useful in some instances, such as for kids who don't brush very well, but they don't need to be prescribed for everyone.
A lot of dentists try to push veneers – those artificial tooth surfaces – on their patients since they're rather lucrative. But what is important to remember is that in most cases this is a cosmetic choice. And it's one that can cost thousands. If your teeth look terrible and you want to improve your appearance, that's okay but don't get talked into them if they're not necessary.
What's more, if the shape of your tooth is alright, it's cheaper to have a whitening treatment done.
Medical insurance is certainly a necessity and dental insurance isn't a bad idea. However, a dentist's reimbursement fees from insurers are very low so they will try to find work to do on you. This usually involves a scaling or deep cleaning that may not be necessary.
The best way to avoid this is to visit dentists who aren't involved in insurance networks. They're less likely to try and upsell procedures.
It is completely within your rights to refuse a treatment and seek another opinion. An honest Gold Coast dentist will never put pressure on you.
What's more, your X-rays legally belong to you and a dentist must turn them over to you to take to other dentists.
Keep all of this in mind whenever you feel uncomfortable with a dentist or like you're being talked into treatments you don't actually need.
Like anything else, I think there are good and bad. I have been to dentists who had wanted to replace all my fillings before and switched quickly. I would alo beware of dentists who 'save' teeth at all costs because truthfully, it is going to cost you a bundle. I had that happen and ended up with a root canal that abscessed and instead of losing one tooth, lost three because the infection spread so rapidly plus lost weeks of work.
Great article and one people should pay attention to.


On Friday, February 8, US Securities and Exchange (SEC) Commissioner Hester Peirce spoke at the University of Missouri School of Law. In her speech, she explained the SEC's role in protecting investors while promoting innovation, analyzed different ways of looking at initial coin offerings (ICOs), and addressed issues with how the SEC has approached crypto-backed exchange-traded fund (ETF) proposals. In talking about these issues, she pushed forward her position that, when it comes to regulating the cryptospace, the SEC needs to develop new methods and ways of thinking.
Commissioner Peirce mentioned that there are many different roles in "token environments," be they mining, development services, or other. She wants the SEC to be careful when applying the Howey test to not be so broad. As an example, she used the SEC's decision to declare DAO tokens securities despite the fact that many investors played key operational roles with the company.
Peirce also fears that some of the SEC's regulations may be too rigid, which can stifle innovation. For this example, she used the closing of Basis, which had to shut down and return $133 million due to difficulties complying with regulations. While she declined to give her thoughts on that particular ICO, Peirce did say she would pay close attention to "legitimate projects" that are hindered by laws and regulations, including crypto ETFs.
In her speech, Peirce stated that the SEC is working on developing "supplemental guidance" to help investors and company owners determine whether a specific ICO or crypto-related project falls under the scrutiny of securities regulations. On February 10, the SEC tweeted that some guidelines were already available on the SEC website.


Born in Evander, 1975. Lives and works in Cape Town. Andre attended the Pro Arte School of arts in Pretoria (1989 – 1993) where he majored in painting and graphics. He flourished at art from an early age and has received various merits and awards, including work being selected for the Iscor Permanent Art Collection. Andre studied in several artistic disciplines including painting, sculpture, print making and graphic design.
In 1994 he moved to Cape Town where he trained in metal working (forging, welding and metallurgical theory) under the direction of John Allesandri. André worked at the Doyle Art Foundry (1997-1998) and became familiar with the moulding and bronze casting processes. During 2001 he started to work at the Bronze Age Art Foundry where he became efficient in all the various stages of the lost-wax casting process (cire perdue) over the next few years.
He became a partner at the Bronze Age Art Foundry (2004 – 2007) and excelled in the production and business aspects of bronze sculpture production. André played an integral part in the arranging and execution of various art exhibitions and trade shows. He worked with many renowned artists such as Maureen Quin, Keith Calder, Dylan Lewis, Donald Greig and Beezy Bailey, which helped him refine his technical and artistic approach. He also developed a foundry sculpture course, which taught students all the various aspects of bronze reproduction. During 2007 Andre was commissioned to create nine large bronze relief panels for the Burj Khalifa Development in Dubai (tallest man-made structure in the world).
In 2008 Stead created a series of figurative studies of the female form. In 2009 Stead showcased the Female series (realistic bronze figures) in two solo exhibitions in Cape Town and Johannesburg. During 2010 works from the female series were exhibited in various group shows in South Africa.
In 2010 Stead started working on the Anamorphic series launching it with a solo exhibition in August 2011 in Franschhoek at IS ART gallery. His latest work focuses on pure form derived from the human figure and has already drawn significant attention from art dealers and collectors alike. In 2011 Stead was commissioned by Laurence Graff to create a sculptural installation, "Flight of the Swallows" for the Indochine restaurant at the Delaire Graff Wine Estate in Stellenbosch.
Other projects during 2011 include the installation of the "Large Reclining Figure", a large version (3 meter) of the anamorphic series figure. In early 2012 Stead produced the "Oxford Swallows", a smaller yet completely unique version of the stainless steel and plexiglass installation at Delaire. "Illumination", a solo exhibition, opened in July 2012 at the Christopher Møller Art Gallery in Cape Town. During 2013 Stead participated in the Woordfees exhibition "Heavenly" in Stellenbosch followed by his solo exhibition "Elemental man" at the Knysna Fine art gallery. 2014 had a view large projects as well as participation in the Cape Town Art Fair and the Woordfees in Stellenbosch.
During 2015 André completed a number of commissions including the life size bronze "Amare Abbraccio". The piece was commissioned by Anuoka Haese and depicts a father and son. There were also a number of group exhibitions during 2015. Exhibitions for 2016 include the Cape Town Art Fair, "A certain Kind Of Madness" at the Imibala Gallery and "Transmutation" at the Knysna Fine art Gallery ending the year with a solo exhibition at the Christopher Møller Art Gallery in Cape Town.


As of fall 2015, this tool is no longer available. Recent changes on University of Missouri servers have made this tool obsolete. We apologize for the inconvenience.
Maps can still be developed through NMTracker.
Want someone to run this report for you? Email John Lory and include your mailing address and either the legal description (section, township, range) or geographic coordinates (latitude and longitude) of the Missouri location you are interested in. A report for that location will be sent to you.


text:
\section{Introduction}

The principal task of this paper is to work towards integrating \emph{ceteris paribus} modalities into conditional logics so that some dissonant analyses of counterfactuals may be reconciled. We also suggest that ceteris paribus clauses may be understood dynamically, in the sense of dynamic epistemic logic \cite{van2007dynamic}, and we interpret our resulting ceteris paribus logic accordingly. Ceteris paribus clauses implicitly qualify many conditional statements that formulate laws of science and economics. A ceteris paribus clause adds to a statement a proviso requiring that other variables or states of affairs not explicitly mentioned in the statement are kept constant, thus ruling out benign defeaters. For instance, Avogadro's law says that if the volume of some ideal gas increases then, everything else held equal, the number of moles of that gas increases proportionally. Varying the temperature or pressure could provide situations that violate the plain statement of the law, but the ceteris paribus clause accounts for those. It specifically isolates the interaction between volume and number of moles by keeping everything else equal. In the same spirit, the Nash equilibrium in game theory is a solution concept that picks strategy profiles in which none of the agents could unilaterally (i.e., keeping the actions of others constant, or equal) deviate to their own advantage.

We may understand a ceteris paribus clause as a linguistic device
intended to shrink the scope of the sentence qualified by the clause. For instance, when I make the utterance ``I prefer fish to beef, \emph{ceteris paribus}" I may mean something different from if I simply uttered ``I prefer fish to beef." By enforcing the ceteris paribus condition I rule out some situations which affect my preference. For example if, whenever I eat fish I'm beaten with a mallet, while whenever I eat beef I'm left in peace, I might retract the second utterance and maintain the first. The ceteris paribus clause reduces the number of states of affairs under consideration. For modal logicians, `ruling out' states of affairs amounts to strengthening an accessibility relation, consequently changing the relational structure of a model. This bears similarity to the epistemological forcing of Vincent Hendricks \cite{hendricks2006mainstream}, which seeks to rule out `irrelevant alternatives' in a way which allows knowledge in spite of the possibility of error. Wesley Holliday \cite{holliday2014epistemic} develops several interpretations of the epistemic operator $K$ based on the relevant alternatives epistemology; namely, that in order for an agent to have knowledge of a proposition, that agent must eliminate each \emph{relevant alternative}. Holliday's semantics are based on the semantics for counterfactuals due to David Lewis \cite{RefWorks:170}. One could see relevant worlds as those which keep things equal. When reasoning using Avogadro's law, the relevant possible worlds are those where the temperature and pressure have not changed. Thus, in order for an agent to have knowledge, that agent must eliminate the alternatives among the worlds which `keep things equal.'

Previously, ceteris paribus formalisms have been given for logics of preference \cite{RefWorks:2} and logics of game forms \cite{grossi2013ceteris}. Here we extend the analysis to counterfactual reasoning. The importance of counterfactuals in game theory is well known (see, for instance, \cite{samet1996hypothetical}). For example, Bassel Tarbush \cite{tarbush2013agreeing} argues that the \emph{Sure-Thing Principle}\footnote{An outcome $o$ of an action $A$ is a \emph{sure-thing} if, were any other action $A'$ to be chosen, $o$ would remain an outcome. The Sure-Thing Principle \cite{savage1972foundations} states that sure-things should not affect an agent's preferences.} ought to be understood as an inherently counterfactual notion. We will motivate our discussion by thinking through  Kit Fine's well-known `minor-miracles' argument \cite{fine1975review}, a putative counterexample to Lewis' semantics. We will argue that ceteris paribus logic, suitably adapted to conditionals, provides a natural response to this kind of argument. Moreover, we will see that ceteris paribus logic reveals a useful feature missing from the standard formalisation of counterfactuals; namely, the explicit requirement that certain propositions must have their truth remain fixed during the evaluation of the counterfactual. This is implicitly thought to hold, to some degree, when one works with models which have similarity orders or systems of spheres. The conditional logic of Graham Priest \cite{priest2008introduction} makes just that assumption, but with no syntactic assurance. Ceteris paribus logic provides, in addition to the underlying similarity order over possible worlds, a syntactic apparatus to reason with such ceteris paribus clauses directly in the object language.

\section{Counterfactuals}

Here we shall formalise counterfactuals in the style of Lewis. Let $\mathname{Prop}$ be a set of propositional variables.
We are concerned with models of the form $\mathfrak{M} = (W, \preceq, V)$ such that the following obtain. \begin{enumerate}
\item $W$ is a non-empty set of \emph{possible worlds}.
\item $\preceq$ is a family $\{\preceq_w\}_{w\in W}$ of
  \emph{similarity orders}, i.e., relations on $W_w \times W_w$ (with $W_w \subseteq W$)  such that:
\begin{itemize}
 \item $w \in W_w$,
 \item $\preceq_w$ is reflexive,  transitive and total, and
 \item $w \prec_w v$ for all $v \in W_w\setminus \{w\}$.

\end{itemize}

\item $V$ is a \emph{valuation function} assigning a subset $V(p)
  \subseteq W$ to each propositional variable $p\in \mathname{Prop}$
\end{enumerate}
Intuitively, $W_w$ is the set of worlds which are entertainable from
$w$. Worlds which are not entertainable from $w$ are deemed simply too dissimilar from
$w$ to be considered.  Say that $u$ is at least as similar to $w$ as
$v$ is when $u \preceq_w v$, and that it is strictly more similar when
$u\prec_w v$.

If $\mathfrak{M}$ satisfies each of the three requirements we call $\mathfrak{M}$ a \emph{conditional model}. A relation $\le$ is said to be \emph{well-founded} if for every non-empty $S \subseteq W$ the set

\begin{align} \label{defmin}
\mathname{Min}^\mathfrak{M}_\le(S) = \{v \in S \cap W : \text{ there is no $u$ with } u < v\}
\end{align}

\noindent is non-empty.\footnote{As usual, $u < v$ is defined as $u \le v$ and
  not $v \le u$} We will suppress the superscript $\mathfrak{M}$ if it is clear
from the context which model we're discussing.  If a model $\mathfrak{M} = (W, \preceq, V)$ has only
well-founded similarity orders we say that $\mathfrak{M}$ satisfies the
\emph{limit assumption}. For ease of exposition, we will assume that our conditional models satisfy the limit assumption. Of course, we may generalise the semantics for counterfactuals in the usual way \cite{RefWorks:170}, so that our results work for models which do not satisfy the limit assumption as well.

\begin{definition}[Language $\mathcal{L}^\boxright$] The language $\mathcal{L}^\boxright$ of counterfactuals is given by the following grammar
\begin{align*} \phi \ ::= \ p \ | \ \lnot \phi \ | \ \phi \lor \psi \ | \ \phi \boxright \psi. \end{align*}
\end{definition}
We define $\phi \land \psi := \lnot(\lnot \phi \lor \lnot \psi)$, $\phi \rightarrow \psi := \lnot \phi \lor \psi$, $\phi \diamondright \psi := \lnot(\phi \boxright \lnot \psi)$.

\begin{definition}[Semantics] \label{defcfwf} Let $\mathfrak{M} = (W, \preceq, V)$ be a well-founded conditional model. Then

\begin{center}
\begin{tabular}{r c l}
$\lb p \rb^\mathfrak{M}$ & = & $V(p)$ \\
$\lb \lnot \phi \rb^\mathfrak{M}$ & = & $W \setminus \lb \phi \rb^\mathfrak{M}$ \\
$\lb \phi \lor \psi \rb^\mathfrak{M}$ & = & $\lb \phi \rb^\mathfrak{M} \cup \lb \psi \rb^\mathfrak{M}$ \\
$\lb \phi \boxright \psi \rb^\mathfrak{M}$ & = & $\{w \in W : \mathname{Min}_{\preceq_w}(\lb \phi \rb^\mathfrak{M}) \subseteq \lb \psi \rb^\mathfrak{M}\}$.
\end{tabular}
\end{center}
\end{definition}
Let $w \in W$. If $w \in \lb \phi \rb$ we write $\mathfrak{M}, w \models \phi$, and if $w \not \in \lb \phi \rb$ we write $\mathfrak{M}, w \not \models \phi$.

\section{The Nixon argument}

There is a problem dating back to the 1970s \cite{fine1975review,
  bennett1974review, bowie1979similarity} surrounding the semantics
for counterfactuals proposed by Lewis. We have found that our `ceteris
paribus counterfactuals' (defined below) provide a unique perspective
on the problem (a putative counterexample). The argument goes as
follows. Assume, during the Cold War, that President Richard Nixon had
access to a device which launches a nuclear missile at the
Soviets. All Nixon is required to do is press a button on the
device. Consider the counterfactual \emph{if Nixon had pushed the
  button, there would have been a nuclear holocaust}. Call it  the \emph{Nixon couterfactual}. It is not so
difficult to see that the Nixon counterfactual could be true, or could be
imagined to be true. Indeed, one could argue that the Nixon counterfactual ought to be true in any successful theory of counterfactuals. Fine and Lewis both agree (and so do we) that the counterfactual is true
(\cite[p.~452]{fine1975review},
\cite[p.~468]{lewis1979counterfactual}), but Fine used the Nixon counterfactual to argue that
the Lewis semantics yields the wrong verdict. This is because ``a world with a single miracle but no
holocaust is closer to reality than one with a holocaust but no
miracle.'' \cite[p.~452]{fine1975review} In response, Lewis argues that, provided the Nixon situation is modelled using a similarity relation which respects a plausible system of priorities (see below), the counterfactual will emerge true. We will provide a different response using ceteris paribus counterfactuals, but first let us see how Fine and Lewis model the situation.

Consider two classes of possible worlds. One class,
$\textbf{u}$, consists of those worlds in which Nixon pushes the
button, and the button successfully launches the missile. The second,
$\textbf{v}$, consists of those worlds in which Nixon pushes the
button, but some small occurrence -- such as a minor miracle --
prevents the button's correct operation. Certainly those worlds where
the button does \emph{not} launch the missile bear more similarity to
the present world than those where it does. This is Fine's
interpretation of Lewis' semantics. Any world in $\textbf{u}$ has
been devastated by nuclear warfare, countless lives have been lost,
there is nuclear winter, etc., whereas worlds in $\textbf{v}$
continue on as they would have done.

To illustrate Fine's interpretation, let $p, s, m, h$ be the propositions:

\medskip

\begin{center}
\begin{tabular}{l c l}
$p$ & = & ``Nixon \underline{p}ushes the button," \\
$s$ & = & ``the missile \underline{s}uccessfully launches," \\
$m$ & = & ``a \underline{m}iracle prevents the missile being launched," \\
$h$ & = & ``a nuclear \underline{h}olocaust occurs,"
\end{tabular}
\end{center}

\medskip

\noindent and consider the following model, the \emph{Fine model}:

\begin{center}
\begin{tabular}{c}
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};

\node (M) at (0,1.5) {$\mathcal{F}$};

\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};

\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};

\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\draw [->] (2) to (1);
\draw [->] (3) to (1);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick, fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};
\draw [->,decorate,decoration={snake,amplitude=.4mm,segment
  length=2mm, post length=1mm}] (u) to (v);
\end{configuration}
\end{tabular}
\end{center}

An arrow from $x$ to $y$ indicates relative similarity to $w$, so
$u_1$ is more similar to $w$ than $u_2$ is. Arrows are transitive, and
the `snake' arrow between $\textbf{v}$ indicates
that $v_i \preceq_w u_j$ for every $i,j$.  For each $u_i \in \textbf{u}$, $\mathcal{F}, u_i \models p \land s \land h$; and for each $v_i \in \textbf{v}$, $\mathcal{F}, v_i \models p \land m$. World $w$ is intended to represent the real world: Nixon did not push any catastrophic anti-Soviet buttons,\footnote{Although there is no way for us to know this, for the sake of the argument we assume that it is so.} no nuclear missile was successfully launched at the Soviets, no miracle prevented any such missile, and no nuclear holocaust occurred.   World $v_1$ is more similar to $w$ than any world in $\textbf{u}$ is, since in any $\textbf{u}$-world Nixon pushes the button and begins a nuclear holocaust. By (\ref{defmin}), $v_1$ is therefore the minimal $p$-world. At $v_1$ the proposition $h$ is false, and so $\mathcal{F}, w \not \models p \boxright h$. Therefore, Fine concludes, the Nixon counterfactual is false in Lewis' semantics.

In response, Lewis argues that the proper similarity relation to model the Nixon counterfactual should respect the following system of priorities:

\begin{enumerate}
\item It is of the first importance to avoid big, widespread, diverse violations of law.
\item It is of the second importance to maximize the spatio-temporal region throughout which perfect match of particular fact prevails.
\item It is of the third importance to avoid even small, localized, simple violations of law.
\item It is of little or no importance to secure approximate similarity of particular fact, even in matters that concern us greatly. (\cite[p.~472]{lewis1979counterfactual})
\end{enumerate}

Based on this system of priorities world $u_1$ is more similar to $w$ than $v_1$ is
because ``perfect match of particular fact counts for much more than
imperfect match, even if the imperfect match is good enough to give us
similarity in respects that matter very much to us.''
\cite[p.~470]{lewis1979counterfactual} That is, worlds in $\textbf{v}$
in which a small miracle prevents the missile being launched may look
quite similar to our world, but only approximately so. And in Lewis'
system of priorities, perfect match outweighs approximate
similarity. The \emph{Lewis model}, then, looks like this:

\begin{center}
\begin{tabular}{c}
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};

\node (M) at (0,1.5) {$\mathcal{L}$};

\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};

\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};

\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\draw [->] (2) to (1);
\draw [->] (3) to (1);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick,fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};
\draw [->,decorate,decoration={snake,amplitude=.4mm,segment
  length=2mm, post length=1mm}] (v) to (u);
\end{configuration}
\end{tabular}
\end{center}

In the Lewis model, $u_1$ is the world most similar to $w$, and in $u_1$ the missile successfully launches, there is a nuclear holocaust, and so the Nixon
counterfactual is true. Lewis thus responds to Fine by defending a
similarity order that favours $u_1$ over $v_1$. He is justified by
prioritising perfect over approximate match in a similarity
relation according to the aforementioned system.

The interpretation of the Nixon counterfactual we will offer is in line with Lewis', though we do not rely on his system of priorities. We will achieve a resolution similar to his without having to defend a model different from Fine's. After all, as Lewis says: ``I do not claim that this pre-eminence of perfect match is intuitively obvious. I do not claim that it is a feature of the similarity relations most likely to guide our explicit judgments. It is not; else the objection we are considering never would have been put forward.''\cite[p.~470]{lewis1979counterfactual} Instead, we will treat the Nixon counterfactual with an explicit ceteris paribus clause, dispatching with the unintuitive pre-eminence of perfect match in constructing the similarity relation.

Our interpretation of the Nixon counterfactual is much like in preference logic, where formal ceteris paribus reasoning was first applied \cite{RefWorks:373,
  doyle1994representing, RefWorks:2}. Consider the following diagram, which
shows a preference of a raincoat to an umbrella, provided wearing
boots is kept constant:
\begin{center}
\begin{tabular}{c}
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node (1a) [left] at (1.west) {\begin{tabular}{c}raincoat\\no boots\end{tabular}};
\node (2) at (3,0) {\textbullet};
\node (2a) [right] at (2.east) {\begin{tabular}{c}umbrella\\no boots\end{tabular}};
\node (3) at (0, -1.5) {\textbullet};
\node (3a) [left] at (3.west) {\begin{tabular}{c}raincoat\\boots\end{tabular}};
\node (4) at (3, -1.5) {\textbullet};
\node (4a) [right] at (4.east) {\begin{tabular}{c}umbrella\\boots\end{tabular}};
\draw [->] (2) to (1);
\draw [->] (4) to (3);
\draw [->, dotted] (1) to (4);
\end{configuration}
\end{tabular}
\end{center}
Arrows point to more preferred alternatives, and are transitive. Evidently, having an umbrella and boots is preferred to having a raincoat and no
boots. The variation of having boots \emph{skews} the preference. If a
ceteris paribus clause is enforced, guaranteeing that in either case
boots will be worn or boots will not be worn, then the correct
preference is recovered. A similar situation occurs in the logic of
counterfactuals. The variation of certain propositions can skew the
similarity order. In Fine's argument, this is done by the variation of
physical law, a miracle. If we were to restrict the worlds considered
during the evaluation of the counterfactual to those that agree with
$w$ on the proposition $m$, then in $\mathcal{F}$ the world $v_1$
would no longer assume the role of minimal $p$-world. Rather, $u_1$
would. In world $u_1$ a nuclear holocaust \emph{does} occur, whence
the counterfactual becomes true, as desired. This is our resolution of
the Nixon argument, which we next formalise.

\section{Ceteris paribus semantics}
We introduce into our language a new conditional operator which
  generalises the usual one. In particular, it accommodates explicit
  ceteris paribus clauses. The authors in \cite{RefWorks:2} were the first to
  define object languages in this way. They developed a modal logic of
  ceteris paribus preferences in the sense of von Wright
  \cite{RefWorks:373}. For now we will take the ordinary
  conditional operator and embed within it a finite set of formulas
  $\Gamma$ understood as containing the \emph{other things} to be kept
  equal.\footnote{The choice of $\Gamma$ finite is largely technical. We will mention some possibilities and difficulties regarding the case where the ceteris paribus set $\Gamma$ may be infinite in our concluding remarks.}

\begin{definition}[Language $\mathcal{L}_\mathname{CP}$] \label{cpcflanguage}
Let $\Gamma$ be a finite set of formulas. Then the language $\mathcal{L}_\mathname{CP}$ is given by the grammar\footnote{We redefine the language more precisely as Definition \ref{fulldefn} in the appendix. For simplicity we work with the one now stated.}
\begin{align*} \phi \ ::= \ p \ | \ \lnot \phi \ | \ \phi \lor \psi \ | \ [\phi, \Gamma]\psi.\end{align*}
\end{definition}
We understand the modality $[\phi, \Gamma]\psi$ as the counterfactual
$\phi \boxright \psi$ subject to the requirement that the truth of the
formulas in $\Gamma$ does not change. We define $\phi \land \psi :=
\lnot(\lnot \phi \lor \lnot \psi)$, $\phi \rightarrow \psi := \lnot
\phi \lor \psi$, $\langle \phi, \Gamma \rangle \psi := \lnot [\phi, \Gamma] \lnot \psi$. We call the conditional $[\phi, \Gamma]\psi$ a \emph{ceteris paribus conditional}, or, if the antecedent is false, a \emph{ceteris paribus counterfactual}. $\mathcal{L}_\mathname{CP}$ is interpreted over standard conditional models, and thus requires no additional semantic information.

Some additional notation is required, however. Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model and let $w, u, v \in W$. Let $\Gamma \subseteq\mathcal{L}_\mathname{CP}$ be finite.
\begin{itemize}
\item Define the relation $\equiv_\Gamma$ over $W$ by $u \equiv_\Gamma v$ if for all $\gamma \in \Gamma$, $\mathfrak{M}, u \models \gamma$ iff $\mathfrak{M}, v \models \gamma$. Then $\equiv_\Gamma$ is an equivalence relation.\footnote{Technically, the relation $\equiv_\Gamma$ should be defined together with the semantics in Definition \ref{defcpcf} by mutual recursion. Again, we favour the simpler presentation. }
\item Set $[w]_\Gamma = \{u \in W_w : w \equiv_\Gamma u\}$, the collection of $w$-entertainable worlds which agree with $w$ on $\Gamma$.
\item Define $\unlhd^\Gamma_w \, := \, \preceq_w \cap \ ([w]_\Gamma \times [w]_\Gamma)$, the restriction of $\preceq_w$ to the above worlds.
\end{itemize}
Thus if $u, v \in [w]_\Gamma$ then either $u \unlhd^\Gamma_w v$ or $v \unlhd^\Gamma_w u$.

\begin{definition}[Semantics] \label{defcpcf}
Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model. Then
\begin{center}
\item\begin{tabular}{r c l}
$\lb [\phi, \Gamma]\psi \rb^\mathfrak{M}$ & = & $\{w \in W : \mathname{Min}_{\unlhd^\Gamma_w}(\lb \phi \rb^\mathfrak{M}) \subseteq \lb \psi \rb^\mathfrak{M}\}$.
\end{tabular}
\end{center}
\end{definition}
The semantics for the regular connectives are the same as those in
Definition \ref{defcfwf}. Notice that we recover the ordinary counterfactual $\phi \boxright \psi$ with
 $[\phi, \emptyset]\psi$.

Consider again the Fine model $\mathcal{F}$. As before we have $\mathcal{F}, w \not \models p \boxright h$, but now \begin{align} \label{eq1} \mathcal{F}, w \models [p, \{m\}]h. \end{align}

We thus think about the Nixon counterfactual by way of ceteris paribus reasoning. Allowing the truth of arbitrary formulas to vary during the
evaluation of a counterfactual can distort the given similarity order,
thereby attributing falsity to a sentence which may be intuitively true. By forcing certain formulas to keep their truth status fixed one can rule out these cases, which has just been demonstrated with (\ref{eq1}). This ceteris paribus qualification is done in preference logic, and indeed in more general scientific and economic practice.\footnote{See Schurz \cite{RefWorks:401} on comparative ceteris paribus laws.} The Nixon counterfactual is simply a situation involving a defeater, or an irrelevant alternative, which ought to be forced out.

\section{Ceteris paribus as a dynamic action} \label{dynamicop}

The modality $[\phi, \Gamma]\psi$ behaves like a dynamic operator, in
the sense of dynamic epistemic logic. For modality-free formulas
$\phi$ and $\psi$, evaluating $[\phi, \Gamma]\psi$ at $w \in W$ amounts to transforming $$\mathfrak{M} = (W,\{\preceq_w\}_{w \in W}, V)$$ into $$[\Gamma]\mathfrak{M} = (W, \{\unlhd^\Gamma_w\}_{w \in W}, V)$$ and evaluating $\phi \boxright \psi$ at $[\Gamma]\mathfrak{M}, w$. This dynamic action is possible since we are altering the relational structure of $\mathfrak{M}$ with only a finite amount of information from $\Gamma$.

\begin{figure}[h]
\begin{center}
\begin{tabular}{|c|}
\hline \\
\textbf{Before} $\mathcal{F}$
\\
\
\\
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};
\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};
\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\draw [->] (2) to (1);
\draw [->] (3) to (1);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick,fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};
\draw [->,decorate,decoration={snake,amplitude=.4mm,segment
  length=2mm, post length=1mm}] (u) to (v);
\end{configuration}
\\
\hline \hline\\
\textbf{After} $[\{m\}]\mathcal{F}$
\\
\
\\
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};
\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};
\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\draw [->] (2) to (1);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick,fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};
\end{configuration}\\
\hline
\end{tabular}
\end{center}
\caption{The Fine model before and after $\preceq_{w}$ is upgraded to $\unlhd^{\{m\}}_{w}$.}
\label{fig2}
\end{figure}

Note that the set $W_w$ on which $\preceq_w$ is defined on may change after the update. By updating the model $\mathfrak{M}$ with a ceteris paribus clause $\Gamma$, worlds which disagree on $\Gamma$ are relegated to the class $W \setminus W_w$ of infinitely dissimilar (indeed, \emph{irrelevant}) worlds. Figure \ref{fig2} shows how the Fine model changes after being updated by a ceteris paribus clause forcing agreement on $m$. This forces out the $\textbf{v}$-worlds from consideration during the evaluation of the counterfactual; in some sense syntactically `correcting' the provided similarity order. Of course, if each world already agreed with $w$ on $\{m\}$ the ceteris paribus clause would have no effect.

The modality-free condition on $\phi$ and $\psi$ cannot be removed. In particular, one cannot iterate the dynamic ceteris paribus action and retain agreement with the static ceteris paribus counterfactual operator. To see this, consider the example in Figure \ref{noiteration}. Taking $\Gamma = \{s\}$ and $\Delta = \emptyset$, one has $\mathfrak{M}, w \models [p, \Gamma][q, \Delta]r$, but $[\Gamma]\mathfrak{M}, w \not \models p \boxright [q, \Delta] r$.

\begin{figure}
\begin{center}
\begin{tabular}{ | m{0.3cm} | m{3cm} | | m{3cm} |}
\cline{2-3}
\multicolumn{0}{r |}{} & \begin{center} $\mathfrak{M}$ \end{center} & \begin{center} $[\Delta][\Gamma]\mathfrak{M}$ \end{center} \\
\hline
$w$ &
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node [below] at (1.south) {$s$};
\node (2) at (1,0) {\textbullet};
\draw [->] (2) to (1);
\node [above] (2t1) at (2.north) {$u$};
\node [below] at (2.south) {$p,s$};
\node (3) at (2, 1) {\textbullet};
\draw [->] (3) to (2);
\draw [->, dotted, bend right] (3) to (1);
\node [above] (2t2a) at (3.north) {$v_1$};
\node [right] at (3.east) {$q,s$};
\node (4) at (2, -1) {\textbullet};
\draw [<-] (4) to (3);
\draw [->] (4) to (2);
\node [below] (2t2b) at (4.south) {$v_2$};
\draw [->, dotted, bend left] (4) to (1);
\node [right] at (4.east) {$q,r$};
\end{configuration}
&
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node [below] at (1.south) {$s$};
\node (2) at (1,0) {\textbullet};
\node [above] (2t1) at (2.north) {$u$};
\node [below] at (2.south) {$p, s$};
\node (3) at (2, 1) {\textbullet};
\draw [->] (2) to (1);
\draw [->] (3) to (2);
\node [above] (2t2a) at (3.north) {$v_1$};
\node [right] at (3.east) {$q, s$};
\node (4) at (2, -1) {\textbullet};
\node [below] (2t2b) at (4.south) {$v_2$};
\node [right] at (4.east) {$q, r$};
\draw [->, dotted, bend right] (3) to (1);
\end{configuration}
\\
\hline
$u$ &
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node (2) at (1,0) {\textbullet};
\node [below] at (1.south) {$s$};
\node [above] (2t1) at (2.north) {$u$};
\node (3) at (2, 1) {\textbullet};
\node [below] at (2.south) {$p,s$};
\draw [->] (1) to (2);
\draw [->] (3) to (2);
\node [above] (2t2a) at (3.north) {$v_1$};
\node (4) at (2, -1) {\textbullet};
\draw [->] (3) to (4);
\node [right] at (3.east) {$q,s$};
\node [below] (2t2b) at (4.south) {$v_2$};
\draw [->] (4) to (2);
\draw [->, dotted, bend right] (1) to (4);
\draw [->, dotted, bend left] (1) to (3);
\node [right] at (4.east) {$q,r$};
\end{configuration}
&
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node [below] at (1.south) {$s$};
\node (2) at (1,0) {\textbullet};
\node [above] (2t1) at (2.north) {$u$};
\node [below] at (2.south) {$p,s$};
\node (3) at (2, 1) {\textbullet};
\draw [->] (1) to (2);
\draw [->] (3) to (2);
\node [above] (2t2a) at (3.north) {$v_1$};
\node [right] at (3.east) {$q, s$};
\node (4) at (2, -1) {\textbullet};
\node [below] (2t2b) at (4.south) {$v_2$};
\node [right] at (4.east) {$q, r$};
\draw [->, dotted, bend left] (1) to (3);
\end{configuration}
\\
\hline
\end{tabular}
\end{center}
\caption{The horizontal panels labelled $w$ and $u$ define the similarity orders $\preceq_w$ and $\preceq_u$ respectively.}
\label{noiteration}
\end{figure}

\section{Uniformly selecting ceteris paribus clauses}

Having created a formalism which accommodates explicit ceteris paribus clauses, one
might desire a method for uniformly selecting the ceteris paribus set
$\Gamma$. For von Wright \cite{RefWorks:373}, ceteris paribus means
fixing every propositional variable which does not occur in the universe of discourse of the ceteris paribus expression under consideration. More precisely, let $\mathname{UD}(\phi)$ be the set of all propositional variables occurring in the formula $\phi$, defined inductively as follows.

\begin{center}
\begin{tabular}{l c l}
$\mathname{UD}(p)$ & = & $\{p\}$ \\
$\mathname{UD}(\lnot \phi)$ & = & $\mathname{UD}(\phi)$ \\
$\mathname{UD}(\phi \lor \psi)$ & = & $\mathname{UD}(\phi) \cup \mathname{UD}(\psi)$ \\
$\mathname{UD}([\phi, \Gamma]\psi)$ & = & $\mathname{UD}(\phi) \cup \mathname{UD}(\Gamma) \cup \mathname{UD}(\psi)$ \\
$\mathname{UD}(\{\gamma_1, \dots, \gamma_n\})$ & = & $\mathname{UD}(\gamma_1) \cup \dots \cup \mathname{UD}(\gamma_n)$.
\end{tabular}
\end{center}
\
\\

Then the ceteris paribus counterfactual \emph{if $\phi$ were the case
  then, ceteris paribus, $\psi$ would be the case} amounts to the
expression \begin{align}\label{vwcp}[\phi, \mathname{Prop} \setminus (\mathname{UD}(\phi)
             \cup \mathname{UD}(\psi))]\psi.\end{align} Now all propositional
           variables not occurring in the universe of discourse of the counterfactual antecedent or consequent are fixed.

Updating the Fine model with respect to von Wright's ceteris paribus
set yields the following model:

\begin{center}
\begin{tabular}{c}
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};
\node (M) at (0,1.5) {$[\{s, m\}]\mathcal{F}$};
\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};
\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};
\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick,fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};
\end{configuration}
\end{tabular}
\end{center}

We have $\mathcal{F}, w \models [p, \{m,s\}]h$, but vacuously! It appears that the relation $\unlhd^\Gamma$ is too strong to interact with von Wright's definition. We are requiring that \emph{everything else} is kept equal. This is questionable metaphysics, to say the least. Lewis made a similar observation in \cite{RefWorks:170}, about the counterfactual  \emph{`if kangaroos had no tails, they would topple over'}:

\begin{quote} We might think it best to confine our attention to
  worlds where kangaroos have no tails and \emph{everything} else is
  as it actually is; but there are no such worlds. Are we to suppose
  that kangaroos have no tails but that their tracks in the sand are
  as they actually are? Then we shall have to suppose that these
  tracks are produced in a way quite different from the actual
  way. [...] Are we to suppose that kangaroos have no tails but that their genetic makeup is as it actually is? Then we shall have to suppose that genes control growth in a way quite different from the actual way (or else that there is something, unlike anything there actually is, that removes the tails). And so it goes; respects of similarity and difference trade off. If we try too hard for exact similarity to the actual world in one respect, we will get excessive differences in some other respect. (\cite[p.~9]{RefWorks:170})
\end{quote}

In fact, for the logic of \emph{ceteris paribus} counterfactuals to function in
a meaningful fashion, every formula occurring in $\Gamma$
must be independent from the counterfactual antecedent. In the Fine model, we insist that the truth values of $s$ and $m$ are
kept fixed. These propositions, however, are nomologically related to $p$, so we
can't change the truth value of $p$ without affecting the truth values of $s$ and $m$. This is
why the counterfactual $[p, \{m,s\}]h$ is vacuously true, but
then so is the counterfactual $[p, \{m,s\}]\lnot h$.  To accommodate a uniform method for selecting ceteris paribus clauses, more flexibility is required.  What \emph{ought} to be kept equal when we can't
keep \emph{everything else} equal? In the next section we will consider two strategies for relaxing the interpretation of \emph{ceteris paribus} to address this question.

\section{Relaxing the ceteris paribus clause}

\subsection{Na\"{i}ve counting}

We will now introduce another interpretation for the modality $[\phi, \Gamma]\psi$. Let us write $\lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_{\mathname{CP}}$ for the set $\lb [\phi, \Gamma]\psi \rb^\mathfrak{M}$ from Definition \ref{defcpcf}, and let $\models_{\mathname{CP}}$ act as the ordinary satisfaction relation for Boolean formulas, but with \begin{center}$\mathfrak{M}, w \models_{\mathname{CP}} [\phi, \Gamma]\psi$ iff $w \in \lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_{\mathname{CP}}$. \end{center}

Whereas in Definition \ref{defcpcf} we required strict agreement on the set $\Gamma$, in order to develop a logic for ceteris paribus counterfactuals with a weaker semantics we will instead relax the requirement to \emph{maximal agreement}. The best we can do is preserve the set $\Gamma$ as much as possible for any given model.

Let $\Gamma \subseteq \mathcal{L}_\mathname{CP}$ be finite, and let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model. Define $A_\Gamma^\mathfrak{M}: W \times W \to 2^\Gamma$ by \begin{align}A_\Gamma^\mathfrak{M}(u, v) = \{\gamma \in \Gamma: \mathfrak{M}, u \models \gamma \text{ iff } \mathfrak{M}, v \models \gamma\}. \end{align}
Define the relation $\preceq_w^\Gamma$ on $W_w$ by $u \preceq_w^\Gamma v$ iff
\begin{center} $\text{either } |A_\Gamma^\mathfrak{M}(u, w)| > |A_\Gamma^\mathfrak{M}(v, w)|, \text{ or } |A_\Gamma^\mathfrak{M}(u, w)| = |A_\Gamma^\mathfrak{M}(v, w)| \text{ and }u \preceq_w v. $
\end{center}

The relation $\preceq_w^\Gamma$ can be seen as a transformed $\preceq_w$, reordering the similarity order so that worlds closer to $w$ preserve at least as much of $\Gamma$ as worlds further away, and if any two worlds agree on $\Gamma$ to the same quantity, then the nearer world is more similar to $w$ with respect to $\preceq$.

\begin{definition}[Semantics] Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model satisfying the limit assumption. Let $\Gamma \subseteq \mathcal{L}_\mathname{CP}$ be finite. Then \\
\begin{center}
\begin{tabular}{r c l}
$\lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_\mathname{NC}$ & = & $\{w \in W : \mathname{Min}_{\preceq^\Gamma_w}(\lb \phi \rb^\mathfrak{M}) \subseteq \lb \psi \rb^\mathfrak{M}\}$.
\end{tabular}
\end{center}
\end{definition}

We write $\mathfrak{M}, w \models_{\mathname{NC}} [\phi, \Gamma]\psi$ iff $w \in \lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_{\mathname{NC}}$.

\begin{fact} Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model. Let $w \in W$, and let $\mathbf{X} \in \{\mathname{CP}, \mathname{NC}\}$. Then the following are true, where $\pm \alpha$ is shorthand which uniformly stands for either $\alpha$ or $\lnot \alpha$:  \label{cf} \
\begin{enumerate}
\item $\mathfrak{M}, w \models \phi \boxright \psi$ iff $\mathfrak{M}, w \models_{\mathbf{X}}[\phi, \emptyset]\psi$
\item $\mathfrak{M}, w \models_\mathbf{X} (\pm \alpha \land \langle \varphi, \Gamma \rangle (\pm \alpha \land \psi)) \rightarrow \langle \varphi, \Gamma \cup \{\alpha\} \rangle \psi$
\item $\mathfrak{M}, w \models_{\mathname{CP}} \langle \phi, \Gamma \rangle \psi  \Rightarrow \mathfrak{M}, w \models_{\mathname{NC}} \langle \phi, \Gamma \rangle \psi$
\item $\mathfrak{M}, w \models_{\mathname{NC}} [\phi, \Gamma]\psi  \Rightarrow \mathfrak{M}, w \models_{\mathname{CP}}[\phi, \Gamma]\psi$
\end{enumerate}

\end{fact}

The original ceteris paribus preference logic \cite{RefWorks:2} could be axiomatised using standard axioms together with Fact 1.2 and its converse. A crucial difference with \mathname{NC} \ semantics is that the converse of Fact 1.2 does not hold. The existence of a $\phi \land\psi$-world which maximally agrees on $\Gamma \cup \{\alpha\}$ does not ensure that $\alpha$ actually holds at that world. In fact, it is not guaranteed that \emph{any} formula from $\Gamma \cup \{\alpha\}$ is obtained.

\subsection{Maximal supersets}

An approach to counterfactuals familiar to the AI community
\cite{katsuno1991propositional, dalal1988investigations,
  del1994interference, del1996belief} makes use of a selection
function which chooses the `closest' world according to maximal sets
of propositional variables. More specifically, each world $w$ satisfies some set $\textbf{P}_w \subseteq \mathname{Prop}$ of propositional variables, and a world $u$ is a world closest to $w$ if there is no $v$ with $\textbf{P}_u \subset \textbf{P}_v \subseteq \textbf{P}_w$. Taking this as a kind of ceteris paribus formalism we obtain the following variant of our ceteris paribus counterfactuals. First let us define the relation $\sqsubseteq_w^\Gamma$ on $W_w$ by $u \sqsubseteq_w^\Gamma v$ iff
\begin{center} $\text{either } A_\Gamma^\mathfrak{M}(v, w) \subset A_\Gamma^\mathfrak{M}(u, w), \text{ or }  A_\Gamma^\mathfrak{M}(v, w) = A_\Gamma^\mathfrak{M}(u, w) \text{ and }u \preceq_w v. $
\end{center}

\begin{definition}[Semantics] Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model satisfying the limit assumption. Let $\Gamma \subset \mathcal{L}_\mathname{CP}$ be finite. Then
\
\\
\begin{center}
\begin{tabular}{r c l}
$\lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_\mathname{MS}$ & = & $\{w \in W : \mathname{Min}_{\sqsubseteq^\Gamma_w}(\lb \phi \rb^\mathfrak{M}) \subseteq \lb \psi \rb^\mathfrak{M}\}$.
\end{tabular}
\end{center}
\end{definition}
We write $\mathfrak{M}, w \models_\mathname{MS} [\phi, \Gamma]\psi$ iff $w \in \lb [\phi, \Gamma]\psi \rb^\mathfrak{M}_\mathname{MS}$. Now $\Gamma$ is maximally preserved in the sense that worlds which preserve the same propositions as another, and furthermore preserve additional propositions from $\Gamma$, are deemed to approximate $\Gamma$ more closely; while worlds $u, v$ with neither $A^\mathfrak{M}_\Gamma(u, w) \subseteq A^\mathfrak{M}_\Gamma(v, w)$ nor $A^\mathfrak{M}_\Gamma(v, w) \subseteq A^\mathfrak{M}_\Gamma(u, w)$ are considered incomparable.

\begin{fact} [Extends Fact \ref{cf}] Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model. Let $w \in W$. Then the following are true.
\begin{enumerate}
\item $\mathfrak{M}, w \models \phi \boxright \psi$ iff $\mathfrak{M}, w \models_{\mathname{MS}}[\phi, \emptyset]\psi$
\item $\mathfrak{M}, w \models_\mathname{MS} (\pm \alpha \land \langle \varphi, \Gamma \rangle (\pm \alpha \land \psi)) \rightarrow \langle \varphi, \Gamma \cup \{\alpha\} \rangle \psi$
\item $\mathfrak{M}, w \models_{\mathname{CP}} \langle \phi, \Gamma \rangle \psi  \Rightarrow \mathfrak{M}, w \models_{\mathname{MS}} \langle \phi, \Gamma \rangle \psi$
\item $\mathfrak{M}, w \models_{\mathname{MS}} [\phi, \Gamma]\psi  \Rightarrow \mathfrak{M}, w \models_{\mathname{CP}}[\phi, \Gamma]\psi$
\end{enumerate}
\end{fact}

\section{Dynamics and the Nixon counterfactual}

Given a ceteris paribus interpretation $\mathbf{X} \in \{\mathname{CP}, \mathname{NC},
\mathname{MS}\}$, let us write $[\Gamma]_\mathbf{X}\mathfrak{M}$ for the model
$\mathfrak{M}$ updated with a ceteris paribus clause $\Gamma$
according to interpretation $\mathbf{X}$. Specifically, we have the following definition.

\begin{definition}
Let $\mathfrak{M} = (W, \preceq, V)$ be a conditional model, and let $\Gamma \subseteq \mathcal{L}_\mathname{CP}$ be a finite set of formulas. We define the \emph{updated models} $[\Gamma]_\mathbf{X}\mathfrak{M}$, for $\mathbf{X} \in \{\mathname{CP}, \mathname{NC}, \mathname{MS}\}$, by \\
\begin{center}
\begin{tabular} {l c l}
$[\Gamma]_\mathname{CP}\mathfrak{M}$ & $:=$  & $(W, \unlhd^\Gamma, V);$ \\
$[\Gamma]_\mathname{NC}\mathfrak{M}$ & $:=$ & $(W, \preceq^\Gamma, V);$ \\
$[\Gamma]_\mathname{MS}\mathfrak{M}$ & $:=$ & $(W, \sqsubseteq^\Gamma, V).$
\end{tabular}
\end{center}
\end{definition}

This provides us with three dynamic \emph{ceteris paribus} updates. Let us see how they treat the Nixon counterfactual. We have already witnessed the $\mathname{CP}$ update with ceteris paribus sets $\{m\}$ and $\{m,s\}$, and concluded that both make the counterfactual true (vacuous truth with $\{m, s\}$). $\mathname{NC}$ and $\mathname{MS}$ updates agree on the truth of the Nixon counterfactual with the $\mathname{CP}$ update on $\{m\}$, but disagree on $\{m,s\}$. Updating the Fine model with von Wright's ceteris paribus clause $\{m, s\}$ according to the $\mathname{NC}$ interpretation yields $\mathcal{F}$ again. Thus $\mathcal{F}, w \not\models_\mathname{NC} [p, \{m,s\}]h$. Updating Fine's model with $\{m, s\}$ according to the $\mathname{MS}$ interpretation gives the following model:

\begin{center}
\begin{tabular}{c}
\begin{configuration}
\node (1) at (0,0) {\textbullet};
\node [above] at (1.north) {$w$};

\node (M) at (0,1.5) {$[\{m,s\}]_\mathname{MS}\mathcal{F}$};

\node (2) at (2,1) {\textbullet};
\node [above] (2t1) at (2.north) {$u_1$};
\node (2a) at (3.5, 1) {\textbullet};
\draw [->] (2a) to (2);
\node [above] (2t2a) at (2a.north) {$u_2$};
\node (2b) at (5, 1) {\textbullet};
\draw [->, dotted] (2b) to (2a);
\node [above] (2t2b) at (2b.north) {$u_n$};
\node (2c) at (6, 1) {$\textbf{u}$};
\node [below] (2p1) at (2c.south) {$p, s, h$};

\node (3) at (2, -1) {\textbullet};
\node [above] (3t1) at (3.north) {$v_1$};
\node (3a) at (3.5, -1) {\textbullet};
\draw [->] (3a) to (3);
\node [above] (3t3a) at (3a.north) {$v_2$};
\node (3b) at (5, -1) {\textbullet};
\draw [->, dotted] (3b) to (3a);
\node [above] (3t3b) at (3b.north) {$v_k$};
\node (3c) at (6, -1) {$\textbf{v}$};
\node [below] (3p1) at (3c.south) {$p, m$};

\draw [->] (2a) to (2);
\draw [->] (2a) to (2);
\draw [->] (2) to (1);
\draw [->] (3) to (1);
\node [draw, dotted, thick, fit=(2) (2a) (2b) (2t1) (2t2a) (2t2b) ] (u) {};
\node [draw ,dotted, thick, fit=(3) (3a) (3b) (3t1) (3t3a) (3t3b)] (v) {};

\end{configuration}
\end{tabular}
\end{center}

In $[\{m,s\}]_\mathname{MS}\mathcal{F}$ the Nixon counterfactual is not true, and neither is $p \boxright \lnot h$.

We summarise the truth of the Nixon counterfactuals $p \boxright h$ and $p \boxright \lnot h$ in the various updated Fine models in the following table.

\begin{center}
\begin{tabular}{cc|c|c|c|}
\cline{3-5}
                                                                   &        & \multicolumn{3}{c|}{\emph{Interpretation}} \\ \hline
\multicolumn{1}{|c|}{\emph{Counterfactual}}                               & \emph{Clause} & $ \quad \mathname{CP} \quad$       & $\quad\mathname{NC}\quad$       & $\quad\mathname{MS}\quad$       \\ \hline
\multicolumn{1}{|c|}{\multirow{2}{*}{$p \boxright h$}}     & $\{m\}$      & $\mathsf{true}$       & $\mathsf{true}$     & $\mathsf{true}$     \\ \cline{2-5}
\multicolumn{1}{|c|}{}                                             & $\{m,s\}$     & $\mathsf{true}$       & $\mathsf{false}$     & $\mathsf{false}$     \\ \hline
\multicolumn{1}{|c|}{\multirow{2}{*}{$p \boxright \lnot h$}} & $\{m\}$      & $\mathsf{false}$      & $\mathsf{false}$      & $\mathsf{false}$      \\ \cline{2-5}
\multicolumn{1}{|c|}{}                                             & $\{m,s\}$     & $\mathsf{true}$       & $\mathsf{true}$      & $\mathsf{false}$     \\ \hline
\end{tabular}
\end{center}

The rows labelled with $p \boxright h$ and $p \boxright \lnot h$ indicate the truth value of those counterfactuals in the updated models $[\Gamma]_\mathbf{X}\mathcal{F}$, where $\Gamma$ is given by the cell in the \emph{Clause} column and $\mathbf{X}$ is given by the \emph{Interpretation} column.

Formally, the table illustrates how different truth values for the Nixon counterfactual may be obtained by combining the various interpretations of ceteris paribus ($\mathname{CP}, \mathname{NC}, \mathname{MS}$) with the different ceteris paribus sets (the selected set $\{m\}$ or von Wright's set $\{m, s\}$). But this doesn't mean that all combinations are legitimate formalisations of Fine's argument. Fine's story is about small miracles that can interfere with Nixon's ploy, not about whether the missile would successfully launch should Nixon press the button. That the proposition $s$ must be able to vary is crucial to the story, so one shouldn't attempt to keep it equal, on a par with $m$.
  We adhere to our favoured formalisation of the Nixon argument in which the proposition $m$ is the only one that needs to be kept equal. We have given principled reasons for this choice, and our selection makes the counterfactual true -- all interpretations agree on that. The point of the table is a formal one, namely that the truth-values of counterfactuals vary with different ceteris paribus updates according to their interpretation.

\section{Theorems}

In the appendix (Corollary \ref{col1}) we prove that the logic $\Lambda^{\mathcal{L}_\mathname{CP}}_{\mathfrak{C}}$ of ceteris paribus counterfactuals over the class of conditional frames $\mathfrak{C}$ is complete for $\mathname{CP}/\mathname{NC}/\mathname{MS}$ semantics. The proof works by translating formulas of $\mathcal{L}_\mathname{CP}$ into formulas of a \emph{comparative possibility} language, in the style of Lewis, and axiomatising the equivalent logic. This permits a clearer reduction of ceteris paribus modalities to basic comparative possibility operators, albeit with a translation exponential in the size of $\Gamma$.

\section{Concluding remarks}

This paper has introduced a ceteris paribus logic for counterfactual
reasoning by adapting the formalism in \cite{RefWorks:2}. We have
introduced some variants on ceteris paribus logic in light of
philosophical difficulties arising in the application of
conditionals. We apply our framework to the \emph{Nixon counterfactual}, and with this bring a new perspective to the problem.  We have suggested and explored the dynamic
perspective of our various syntactic interpretations of \emph{ceteris paribus}, which has resulted in a richer understanding of
so-called \emph{comparative} ceteris paribus reasoning in formal settings. We
have provided completeness theorems which demonstrate that the ceteris
paribus logics so obtained ultimately reduce to the underlying
counterfactual logic; in our case Lewis' VC. With our framework we
defend Lewisian semantics by appealing to examples from preference
logic, where ceteris paribus reasoning is more widely discussed.

Finally, we outline some limitations of our framework and directions for future research.

\noindent\emph{Iterated ceteris paribus actions.} We saw in Section \ref{dynamicop} that iterated ceteris paribus counterfactuals deviate in truth-value from the corresponding update-then-counterfactual sequence.  Such difficulties with iterated counterfactuals are not so uncommon. We leave the task of understanding the full interaction between the two for further investigation.

\noindent\emph{Cardinality restrictions on $\Gamma$.} In general, ceteris paribus
reasoning requires keeping equal as much information as possible, and
sometimes unknown information (for example, unanticipated defeaters of
laws). Keeping everything else equal may indeed mean keeping equal an
indefinite, and possibly infinite, set of things. Exploring ceteris
paribus logic without cardinality restrictions to $\Gamma$ is thus
more than a mere technical exercise. But it is not so straightforward
to extend the present framework to accommodate the presence of
infinite $\Gamma$. The translations presented in the appendix
  only carry over to the infinite case for infinitary languages,
  which is not much of a solution. For the strict
  ceteris paribus semantics, we instead suggest following the $\delta$-flexibility
  approach of \cite{RefWorks:390}. For the relaxed ceteris paribus semantics, there
  are conceptual difficulties which arise with the comparison of infinite
  sets: when should we say of two infinite sets that one keeps more
  things equal than the other? Clearly na\"{i}ve counting will not suffice. Minimising distance with respect to $\sqsubseteq^\Gamma$ is more promising, but has its own problems. We leave this challenging technical enterprise for future research.

\section{Acknowledgments}

We  wish to thank the participants at the Australasian Association of Logic and the Analysis, Randomness and Applications meetings held in New Zealand in 2014. We also wish to thank Sam Baron, Andrew Withy, and the anonymous referees for valuable comments.

redpajama_set_name: RedPajamaArXiv


text:
PluginLibrary::PluginLibrary(LibraryHandle library, IPluginActivator* activator)
: mLibrary(library), mPluginActivator(activator), mPlugin(nullptr)
{
	assert(library != nullptr);
	assert(mPluginActivator != nullptr);
}

PluginLibrary::~PluginLibrary()
{
	if (mPlugin) {
		delete mPlugin;
		mPlugin = nullptr;
	}

	if (mLibrary != nullptr) {
		ModuleLoader::UnloadLibrary(mLibrary);
		mLibrary = nullptr;
	}
}

bool PluginLibrary::Start(PluginContext* pluginContext)
{
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	GPM_RES res = mPluginActivator->Start(mPlugin);
	return res == GPM_OK;
}

void PluginLibrary::Stop()
{
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	mPlugin->UnloadObjects();
}

IPluginObject* PluginLibrary::FindObjectByType(GPM_TYPE type) const
{
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}

void PluginLibrary::NotifyObjectListeners(GPM_TYPE type, IPluginObject* object, ObjectListenerStatus::Enum status)
{
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redpajama_set_name: RedPajamaGithub


text:
Q: Alternative approach to virtual template method i am trying to solve this for some time and i hope to find some help here. I have a base class and inside the base class i need a template method. But this method can not be virtual (which i know) so i can not override it in the child class, but is there any alternative or workaround? Some kind of design pattern? Thanks
#include <iostream>
#include <vector>
#include <map>

class ABase {
public:
    ABase() :
        id(s_id++)
    {}

    size_t static   s_id;
    size_t          id;
};

size_t ABase::s_id(0);

class A1 : public ABase {
public:
};

class A2 : public ABase {
public:
};

class BBase {
public:
};

class B1 : public BBase {
public:
};

class B2 : public BBase {
public:
};

class ComboBase {
public:
    //  this cannot be virtual :(
    //  so i cannot store b in bs in the child class
    /* virtual */ template<typename T>
    void addB(T b) {
    }
};

template<class T, class T2>
class Combo : public ComboBase {
public:
    //  override of template method is not possible
    /*
    template<typename T>
    void addB(T b) override {
        bs.push_back(b);
    }
    */

    size_t                              id;
    std::shared_ptr<T>                  a;
    std::vector<std::shared_ptr<T2>>    bs;
};

int main() {
    std::map<size_t, std::shared_ptr<ComboBase>> combos;
    auto combo1 = std::make_shared<Combo<A1, B1>>();
    auto combo2 = std::make_shared<Combo<A2, B2>>();
    combos[combo1->id] = combo1;
    combos[combo2->id] = combo2;

    //  here is the problem... later i the code
    //  i would like to add Bs to the existing combo but i cannot use
    //  virtual templates
    auto b1 = std::make_shared<B1>();
    auto b2 = std::make_shared<B2>();

    auto it1 = combos.find(0);
    if (it1 != combos.end()) {
        it1->second->addB(b1);
        it1->second->addB(b2);
    }

    auto it2 = combos.find(0);
    if (it2 != combos.end()) {
        it2->second->addB(b1);
        it2->second->addB(b2);
    }
}