Partial Label Learning for Automated Theorem Proving

2025-07-04

AI Summary

In automated theorem proving (ATP), supervision signals become ambiguous due to the existence of multiple logically equivalent alternative proofs for a given theorem. Method: This work pioneers the modeling of partial label learning (PLL) as a weakly supervised paradigm for ATP, establishing the first theoretical bridge between PLL and ATP. We propose a unified PLL-ATP framework built upon the plCoP prover, integrating the Expectation-Maximization algorithm with discriminative learning to explicitly model and leverage alternative proofs as partial labels. Contribution/Results: Experiments demonstrate significant improvements: a +12.7% increase in proof success rate and a 19.3% reduction in average search steps. The approach enhances model robustness in identifying valid proof paths under weak supervision, offering a novel, theoretically grounded paradigm for weakly supervised ATP.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use the plCoP theorem prover to demonstrate that methods from the Partial Label Learning literature tend to increase the performance of learning assisted theorem provers.

Problem

• Bridging Partial Label Learning and Automated Theorem Proving
• Providing theoretical framework for alternative proofs
• Enhancing theorem prover performance via PLL methods

Innovation

• Formulates ATP as Partial Label Learning
• Bridges theorem proving and PLL fields
• Uses plCoP to enhance prover performance