相关论文: Escape to Mizar for ATPs

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…

We study Monte Carlo Tree Search to guide proof search in tableau calculi. This includes proposing a number of proof-state evaluation heuristics, some of which are learnt from previous proofs. We present an implementation based on the…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…

We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…

The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…

As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40% of the theorems in the latest official version of the Mizar Mathematical Library (MML).…

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…

Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…

Many NLP applications require models to be interpretable. However, many successful neural architectures, including transformers, still lack effective interpretation methods. A possible solution could rely on building explanations from…

This paper proposes an iterative inference algorithm for multi-hop explanation regeneration, that retrieves relevant factual evidence in the form of text snippets, given a natural language question and its answer. Combining multiple sources…

There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation…

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…

There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.