Related papers: Compositional pre-processing for automated reasoni…

Traditionally, the way one evaluates the performance of an Artificial Intelligence (AI) system is via a comparison to human performance in specific tasks, treating humans as a reference for high-level cognition. However, these comparisons…

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

A mimic computing oriented automaton can directly portray the behaviors of a mimic computing system. In this paper, we investigate the following theoretical problems on this type of automata: operational semantics and computational ability.…

We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…

Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…

Proving correctness of distributed or concurrent algorithms is a mind-challenging and complex process. Slight errors in the reasoning are difficult to find, calling for computer-checked proof systems. In order to build computer-checked…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within 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…

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…

Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading…

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 describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie…

In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…

Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator.…

Many real-world planning domains involve diverse information sources, external entities, and variable-reliability agents, all of which may impact the confidence, risk, and sensitivity of plans. Humans reviewing a plan may lack context about…

Many students in introductory programming courses fare poorly in the code writing tasks of the final summative assessment. Such tasks are designed to assess whether novices have developed the analytical skills to translate from the given…