Related papers: TableauxRocq: A Deep Embedding of Free-Variable Ta…

In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

Proof certificates can be used to validate the correctness of algebraic derivations. However, in practice, we frequently observed that the exact same proof steps are repeated for different sets of variables, which leads to unnecessarily…

In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…

We introduce V-tableR1, a process-supervised reinforcement learning framework that elicits rigorous, verifiable reasoning from multimodal large language models (MLLMs). Current MLLMs trained solely on final outcomes often treat visual…

This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…

Large Language Models (LLMs) struggle with multi-step reasoning over structured tables. The primary reason is the lack of explicit supervision for intermediate reasoning states. Existing learned reward models or executor-based verifiers are…

Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…

To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…

To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method.…

The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in…

This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…

This paper investigates the logical reasoning capabilities of large language models (LLMs). For a precisely defined yet tractable formulation, we choose the conceptually simple but technically complex task of constructing proofs in Boolean…

Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…

Formal verification using proof assistants, such as Coq, enables the creation of high-quality software. However, the verification process requires significant expertise and manual effort to write proofs. Recent work has explored automating…

Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…