Related papers: Entailment vs. Verification for Partial-assignment…
Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
We consider the problem of Recognizing Textual Entailment within an Information Retrieval context, where we must simultaneously determine the relevancy as well as degree of entailment for individual pieces of evidence to determine a yes/no…
Factual consistency is an essential quality of text summarization models in practical settings. Existing work in evaluating this dimension can be broadly categorized into two lines of research, entailment-based and question answering…
Despite the seeming success of contemporary grounded text generation systems, they often tend to generate factually inconsistent text with respect to their input. This phenomenon is emphasized in tasks like summarization, in which the…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
Open-domain question answering (Open-QA) is a common task for evaluating large language models (LLMs). However, current Open-QA evaluations are criticized for the ambiguity in questions and the lack of semantic understanding in evaluators.…
A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…
We introduce a new algorithm for checking satisfiability based on a calculus of Dependency sequents (D-sequents). Given a CNF formula F(X), a D-sequent is a record stating that under a partial assignment a set of variables of X is redundant…
Table entailment, the binary classification task of finding if a sentence is supported or refuted by the content of a table, requires parsing language and table structure as well as numerical and discrete reasoning. While there is extensive…
The search for increased trustworthiness of SAT solvers is very active and uses various methods. Some of these methods obtain a proof from the provers then check it, normally by replicating the search based on the proof's information.…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
Context: Requirements quality can have a substantial impact on the effectiveness and efficiency of using requirements artifacts in a development process. Quantifiers such as "at least", "all", or "exactly" are common language constructs…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
Text entailment, the task of determining whether a piece of text logically follows from another piece of text, is a key component in NLP, providing input for many semantic applications such as question answering, text summarization,…
Traditionally, practitioners use formal methods pre-dominately for one half of the quality-assurance process: verification (do we build the software right?). The other half -- validation (do we build the right software?) -- has been given…
Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the…
For many structured learning tasks, the data annotation process is complex and costly. Existing annotation schemes usually aim at acquiring completely annotated structures, under the common perception that partial structures are of low…