相关论文: Escape to Mizar for ATPs

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…

We describe several datasets and first experiments with creating conjectures by neural methods. The datasets are based on the Mizar Mathematical Library processed in several forms and the problems extracted from it by the MPTP system and…

We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…

We present the results from Meno, a simple autoformalizer that proves theorems in Lean by systematically exploring the space of both formal and informal proofs, and tactic ablation, a new method for exploring mathematical creativity under…

In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…

In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…

In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.

In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

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…

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…

A lot of mathematical knowledge has been formalized and stored in repositories by now: different mathematical theorems and theories have been taken into consideration and included in mathematical repositories. Applications more distant from…

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…

When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the…

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching…

Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…