Related papers: Prolog Technology Reinforcement Learning Prover

Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of…

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for…

We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…

Large language models (LLMs) have demonstrated strong capabilities in language understanding and reasoning, yet they remain limited when tackling real-world tasks that require up-to-date knowledge, precise operations, or specialized tool…

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further…

The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…

While Chain-of-Thought (CoT) prompting advances LLM reasoning, challenges persist in consistency, accuracy, and self-correction, especially for complex or ethically sensitive tasks. Existing single-dimensional reflection methods offer…

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…

Reinforcement learning with verifiable reward (RLVR) has become a promising paradigm for post-training large language models (LLMs) to improve their reasoning capability. However, when the rollout accuracy is low on hard problems, the…

Large Language Models (LLMs), when enhanced through reasoning-oriented post-training, evolve into powerful Large Reasoning Models (LRMs). Tool-Integrated Reasoning (TIR) further extends their capabilities by incorporating external tools,…

Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…

Existing approaches to learning to prove theorems focus on particular logics and datasets. In this work, we propose Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human…

Recent progress in (multimodal) large language models ((M)LLMs) has shifted focus from pre-training to inference-time computation and post-training optimization, largely due to concerns over the availability of high-quality human data.…

Large language models (LLMs) are increasingly employed for complex multi-step planning tasks, where the tool retrieval (TR) step is crucial for achieving successful outcomes. Two prevalent approaches for TR are single-step retrieval, which…

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we…

Large Language Models (LLMs) excel at reasoning and generation but are inherently limited by static pretraining data, resulting in factual inaccuracies and weak adaptability to new information. Retrieval-Augmented Generation (RAG) addresses…

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…

This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…