Related papers: Update report: LEO-II version 1.5

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…

We advance the state-of-the-art in automated symbolic analysis for e-voting protocols by introducing three conditions that together are sufficient to guarantee ballot secrecy. There are two main advantages to using our conditions, compared…

The two-watched literal scheme, a core component of efficient CDCL (Conflict-Driven Clause Learning) implementations for propositional logic, is extended to first-order logic. Given a set of first-order clauses and a set of ground literals,…

Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provably solve these problems in an iterative fashion. On one…

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…

The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…

We present PCL-Reasoner-V1.5, a 32-billion-parameter large language model (LLM) for mathematical reasoning. The model is built upon Qwen2.5-32B and refined via supervised fine-tuning (SFT) followed by reinforcement learning (RL). A central…

Arena-based evaluation is a fundamental yet significant evaluation paradigm for modern AI models, especially large language models (LLMs). Existing framework based on ELO rating system suffers from the inevitable instability problem due to…

The discovery of novel Ionic Liquids (ILs) is hindered by critical challenges in property prediction, including limited data, poor model accuracy, and fragmented workflows. Leveraging the power of Large Language Models (LLMs), we introduce…

The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…

Recent advancements in Large Language Models (LLMs) have shifted from explicit Chain-of-Thought (CoT) reasoning to more efficient latent reasoning, where intermediate thoughts are represented as vectors rather than text. However, latent…

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…

Recently, offline RL algorithms have been proposed that remain adaptive at runtime. For example, the LION algorithm \cite{lion} provides the user with an interface to set the trade-off between behavior cloning and optimality w.r.t. the…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

We report on improvements to ACL2 made since the 2013 ACL2 Workshop.

This paper reports our initial experiments with using external ATP on some corpora built with the ACL2 system. This is intended to provide the first estimate about the usefulness of such external reasoning and AI systems for solving ACL2…

We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…

In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…