Related papers: Converting ALC Connection Proofs into ALC Sequents

The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…

With recent advances, neural models can achieve human-level performance on various natural language tasks. However, there are no guarantees that any explanations from these models are faithful, i.e. that they reflect the inner workings of…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

Argument structure learning~(ASL) entails predicting relations between arguments. Because it can structure a document to facilitate its understanding, it has been widely applied in many fields~(medical, commercial, and scientific domains).…

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…

The ease and speed of spreading misinformation and propaganda on the Web motivate the need to develop trustworthy technology for detecting fallacies in natural language arguments. However, state-of-the-art language modeling methods exhibit…

Relation linking is essential to enable question answering over knowledge bases. Although there are various efforts to improve relation linking performance, the current state-of-the-art methods do not achieve optimal results, therefore,…

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…

We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are…

For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition…

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…

This paper shows equivalence of several versions of applicative similarity and contextual approximation, and hence also of applicative bisimilarity and contextual equivalence, in LR, the deterministic call-by-need lambda calculus with…

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…

Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the…

The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…