The field of artificial intelligence and automated reasoning is witnessing significant developments, with a focus on enhancing the capabilities of symbolic provers and integrating them with large language models (LLMs). Recent research has explored the extraction of proof strategies from LLMs to improve the success rate of symbolic provers, as well as the development of novel frameworks for aligning code to mathematical statements and for conjecturing in formal mathematical reasoning. Furthermore, advancements in tensor logic and CoLF logic programming have opened up new directions for infinitary proof exploration and computation-as-proof-construction. Noteworthy papers include the Extended Triangular Method, which formalizes and extends the internal mechanisms of contradiction separation, and TopoAlign, which unlocks widely available code repositories as training resources for Math LLMs. Additionally, the Ax-Prover framework has demonstrated competitive performance in autonomous theorem proving, while the O-Forge framework has shown promise in asymptotic analysis. Overall, these developments are advancing the field of automated reasoning and theorem proving, with potential applications in various areas of mathematics and computer science. Notable papers: Extended Triangular Method enhances the capabilities of automated deduction, TopoAlign improves the performance of Math LLMs.
Advancements in Automated Reasoning and Theorem Proving
Sources
AI and Consciousness
Proof Strategy Extraction from LLMs for Enhancing Symbolic Provers
Nine lower bound conjectures on streaming approximation algorithms for CSPs
Extended Triangular Method: A Generalized Algorithm for Contradiction Separation Based Automated Deduction
DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theorems
GAR: Generative Adversarial Reinforcement Learning for Formal Theorem Proving
TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition
Conjecturing: An Overlooked Step in Formal Mathematical Reasoning
The Structure of In-Place Space-Bounded Computation
Tensor Logic: The Language of AI
CoLF Logic Programming as Infinitary Proof Exploration
O-Forge: An LLM + Computer Algebra Framework for Asymptotic Analysis
Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics
Mathematics with large language models as provers and verifiers
Recent Advances in Debordering Methods
From Minimal Existence to Human Definition: The CES-IMU-HSG Theoretical Framework