Related papers: Automating proof search when equality is a logical…
We present a framework for deriving inference relations between Dutch sentence pairs. The proposed framework relies on logic-based reasoning to produce inspectable proofs leading up to inference labels; its judgements are therefore…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
We propose an analysis of corrections which models some of the requirements corrections place on context. We then show that this analysis naturally extends to the interaction of corrections with pronominal anaphora on the one hand, and…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
The symbolic-heap fragment of separation logic has been actively developed and advocated for verifying the memory-safety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing…
Table-based fact verification task aims to verify whether the given statement is supported by the given semi-structured table. Symbolic reasoning with logical operations plays a crucial role in this task. Existing methods leverage programs…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
Prompting language models to provide step-by-step answers (e.g., "Chain-of-Thought") is the prominent approach for complex reasoning tasks, where more accurate reasoning chains typically improve downstream task performance. Recent…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…
Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving…
In this paper we present, by way of case studies, a proof of concept, based on a prototype working on a automotive data set, aimed at showing the potential usefulness of using formulas of {\L}ukasiewicz propositional logic to query…
ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…