相关论文: Formalization of PAL$\cdot$S5 in Proof Assistant

The paper presents an approach to verification of a multi-agent data analysis algorithm. We base correct simulation of the multi-agent system by a finite integer model. For verification we use model checking tool SPIN. Protocols of agents…

Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…

We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability modality and the interpretability modality can come with a label. This label indicates that in the arithmetical interpretation the axiom set of…

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…

We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…

Arbitrary Public Announcement Logic with Common Knowledge (APALC) is an extension of Public Announcement Logic with common knowledge modality and quantifiers over announcements. We show that the satisfiability problem of APALC on S5-models,…

We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort…

Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…

Large language models (LLMs) remain unreliable for high-stakes claim verification due to hallucinations and shallow reasoning. While retrieval-augmented generation (RAG) and multi-agent debate (MAD) address this, they are limited by…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask…

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…

We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending…

Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…

This paper demonstrates the undecidability of a number of logics with quantification over public announcements: arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). In APAL we…

Epistemic logics model how agents reason about their beliefs and the beliefs of other agents. Existing logics typically assume the ability of agents to reason perfectly about propositions of unbounded modal depth. We present DBEL, an…

The paper presents a comprehensive analysis of the European AI Act in terms of its logical modalities, with the aim of preparing its formal representation, for example, within the logic-pluralistic Knowledge Engineering Framework and…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…