## Tagged Questions

2answers
129 views

### Validity in Kripke frames whose points are finite or infinite sequences

Suppose $D$ is a non-empty set and $\{ R_i : i \in \mathbb{N} \}$ is a family of binary relations on sequences over $D$ so that $R_i \subseteq D^i \times D^i$. Let \$R_\omega \subse …
0answers
51 views

### On the Combinatorial Classification of Modal Kripke Frames

We have that S5 modal logic is characterized by the modal axioms $K$, $M$ (reflexive), $4$ (transitive), and $B$ (symmetric). That is, an equivalence relation on a set of possible …
4answers
674 views

### How are Modal Logic and Graph Theory related?

I am currently taking a graduate logic course on Modal Logic and I can't help notice that there are a certain class of graphs characterized by the modal axioms such as (4) \$\Box p …
3answers
234 views

### Why the preimage rather than image in Stone-type dualities.

I am seeking a deeper understanding of the representation of set-based objects in terms of Boolean algebras. Let $\wp(A)$ be the set of subsets of a set $A$. A relation \$R \subset …
3answers
228 views

### Why are possibility and necessity dual?

Hello, Recently, I'm studying modal logic for my master's thesis, and my research background is category theory. So, I naturally have a question that why it is said that necessity …
1answer
283 views

### Non-trivial consequences of Lob’s theorem

Informally, Löb's theorem (Wikipedia, PlanetMath) shows that: a mathematical system cannot assert its own soundness without becoming inconsistent [Yudkowsky] In symbols: …
2answers
396 views

### A necessary condition for S4-completeness?

It is well-known that the modal logic S4 is complete with respect to the class of all finite quasi-trees (where we interpret the $\Box$ modality as topological interior, and topolo …
1answer
316 views

### Looking for papers and articles on the Tarskian Möglichkeit

Some background: Łukasiewicz many-valued logics were intended as modal logics, and Łukasiewicz gave an extensional definition of the modal operator: \$\Diamond A =_{def} \neg A \to …
3answers
780 views

### Modal logic - box rules

Hi guys, In modal logic i.e. propositional logic with box and diamond, are then any laws to get a box or a diamond from outside a bracket to inside? I.e. \$\Box (x \rightarrow \Bo …
0answers
179 views

### Local consecuence in modal logic [closed]

which means the local consecuence? in a modal logic
1answer
296 views

### Is it possible to define a closure operator in terms of partial ordering?

For boolean algebra, let's take Roman Sikorski's Boolean Algebras as our reference. After giving a set of axioms, he proves (p.9) that the join of A and B is the least element of t …
2answers
409 views

### How many models are there, for a particular propositional modal logic?

Background/motivation: A model for the classical propositional calculus is a boolean function b(S) which assigns 1 or 0 to each (modal-free) sentence S according to the usual rules …
2answers
442 views

### Modal logic - satisfiability

Hi there, Assuming X and Y are modal formulae and diamond X is satisfiable and diamond Y is satisfiable, how would one show that they X AND Y is satisfiable? I don't think it req …
1answer
102 views

### how to determine the condition on frame if some axiom schema is given together with K axiom?

In semantics for modal logic, if a new axiom schema is given together with K in question then how can one find out that what conditions the frame for the new system need to satisfy …
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