You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
One challenge in fact checking is the ability to improve the transparency of the decision. We present a fact checking method that uses reference information in knowledge graphs (KGs) to assess claims and explain its decisions. KGs contain a formal representation of knowledge with semantic descriptions of entities and their relationships. We exploit such rich semantics to produce interpretable explanations for the fact checking output. As information in a KG is inevitably incomplete, we rely on logical rule discovery and on Web text mining to gather the evidence to assess a given claim. Uncertain rules and facts are turned into logical programs and the checking task is modeled as an inference problem in a probabilistic extension of answer set programs. Experiments show that the probabilistic inference enables the efficient labeling of claims with interpretable explanations, and the quality of the results is higher than state of the art baselines.

Cited Abstract(s):
[1]: The volume of information generated online makes it impossible to manually fact-check all claims. Computational approaches for fact checking may be the key to help mitigate the risks of massive misinformation spread. Such approaches can be designed to not only be scalable and effective at assessing veracity of dubious claims, but also to boost a human fact checker's productivity by surfacing relevant facts and patterns to aid their analysis. We present a novel, unsupervised network-flow based approach to determine the truthfulness of a statement of fact expressed in the form of a triple. We view a knowledge graph of background information about real-world entities as a flow network, and show that computational fact checking then amounts to finding a "knowledge stream" connecting the subject and object of the triple. Evaluation on a range of real-world and hand-crafted datasets of facts reveals that this network-flow model can be very effective in discerning true statements from false ones, outperforming existing algorithms on many test cases. Moreover, the model is expressive in its ability to automatically discover several useful patterns and surface relevant facts that may help a human fact checker.

[2]: Traditional fact checking by experts and analysts cannot keep pace with the volume of newly created information. It is important and necessary, therefore, to enhance our ability to computationally determine whether some statement of fact is true or false. We view this problem as a link-prediction task in a knowledge graph, and present a discriminative path-based method for fact checking in knowledge graphs that incorporates connectivity, type information, and predicate interactions. Given a statement S of the form (subject, predicate, object), for example, (Chicago, capitalOf, Illinois), our approach mines discriminative paths that alternatively define the generalized statement (U.S. city, predicate, U.S. state) and uses the mined rules to evaluate the veracity of statement S . We evaluate our approach by examining thousands of claims related to history, geography, biology, and politics using a public, million node knowledge graph extracted from Wikipedia and PubMedDB. Not only does our approach significantly outperform related models, we also find that the discriminative predicate path model is easily interpretable and provides sensible reasons for the final determination.

[3]: We consider the problem of embedding entities and relationships of multi-relational data in low-dimensional vector spaces. Our objective is to propose a canonical model which is easy to train, contains a reduced number of parameters and can scale up to very large databases. Hence, we propose TransE, a method which models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities. Despite its simplicity, this assumption proves to be powerful since extensive experiments show that TransE significantly outperforms state-of-the-art methods in link prediction on two knowledge bases. Besides, it can be successfully trained on a large scale data set with 1M entities, 25k relationships and more than 17M training samples.

[4]: The proliferation of falsehood and misinformation, in particular through the Web, has lead to increasing energy being invested into journalistic fact-checking. Fact-checking journalists typically check the accuracy of a claim against some trusted data source. Statistic databases such as those compiled by state agencies are often used as trusted data sources, as they contain valuable, high-quality information. However, their usability is limited when they are shared in a format such as HTML or spreadsheets: this makes it hard to find the most relevant dataset for checking a specific claim, or to quickly extract from a dataset the best answer to a given query. We present a novel algorithm enabling the exploitation of such statistic tables, by (i) identifying the statistic datasets most relevant for a given fact-checking query, and (ii) extracting from each dataset the best specific (precise) query answer it may contain. We have implemented our approach and experimented on the complete corpus of statistics obtained from INSEE, the French national statistic institute. Our experiments and comparisons demonstrate the effectiveness of our proposed method.

[5]: One of the main tasks when creating and maintaining knowledge bases is to validate facts and provide sources for them in order to ensure correctness and traceability of the provided knowledge. So far, this task is often addressed by human curators in a three-step process: issuing appropriate keyword queries for the statement to check using standard search engines, retrieving potentially relevant documents and screening those documents for relevant content. The drawbacks of this process are manifold. Most importantly, it is very time-consuming as the experts have to carry out several search processes and must often read several documents. In this article, we present DeFacto (Deep Fact Validation) --- an algorithm for validating facts by finding trustworthy sources for it on the Web. DeFacto aims to provide an effective way of validating facts by supplying the user with relevant excerpts of webpages as well as useful additional information including a score for the confidence DeFacto has in the correctness of the input fact.

[6]: 

[7]: Traditional fact checking by expert journalists cannot keep up with the enormous volume of information that is now generated online. Computational fact checking may significantly enhance our ability to evaluate the veracity of dubious information. Here we show that the complexities of human fact checking can be approximated quite well by finding the shortest path between concept nodes under properly defined semantic proximity metrics on knowledge graphs. Framed as a network problem this approach is feasible with efficient computational techniques. We evaluate this approach by examining tens of thousands of claims related to history, entertainment, geography, and biographical information using a public knowledge graph extracted from Wikipedia. Statements independently known to be true consistently receive higher support via our method than do false ones. These findings represent a significant step toward scalable computational fact-checking methods that may one day mitigate the spread of harmful misinformation.

[8]: 

[9]: Knowledge bases are an important resource for question answering and other tasks but often suffer from incompleteness and lack of ability to reason over their discrete entities and relationships. In this paper we introduce an expressive neural tensor network suitable for reasoning over relationships between two entities. Previous work represented entities as either discrete atomic units or with a single entity vector representation. We show that performance can be improved when entities are represented as an average of their constituting word vectors. This allows sharing of statistical strength between, for instance, facts involving the "Sumatran tiger" and "Bengal tiger." Lastly, we demonstrate that all models improve when these word vectors are initialized with vectors learned from unsupervised large corpora. We assess the model by considering the problem of predicting additional true relations between entities given a subset of the knowledge base. Our model outperforms previous models and can classify unseen relationships in WordNet and FreeBase with an accuracy of 86.2 and 90.0 , respectively.

[10]: 

[11]:
There are two main tasks in computational fact checking: (1) monitor and spot claims [11] [6] , (2) check claims and explain outcomes. We focus on the second task and on factual facts, specifically. Related approaches try to align the fact to trusted data resources, such as KGs [1] , Web documents [5] , and databases [4] [8] . These approaches create features for binary classifiers from the data in the KG. Features exploit the structure of the training examples, in the form of paths [2] [7] or geometric properties in a multi-dimensional space with embeddings [3] [9] . As providing interpretable descriptions of the outcome of a ML model, such as SVM, is an active topic of research [10] , we argue that semantically rich rules and their evidence facts are useful explanations for a fact checking outcome.