Adaptive human–machine theorem proving system

M. Joudakizadeh ; A. P. Bel'tyukov

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 64 (2024), pp. 17-33

Résumé

This paper presents a novel approach to constructing human–machine theorem proving systems. These systems integrate machine learning capabilities, human expert knowledge, and rigorous logical control for the effective construction and verification of proofs. The innovation of this approach lies in its openness: the user is given a tool for building such systems. Users can create theorem proving systems by selecting existing logical inference strategies or adding new ones in accordance with the provided interfaces or relationship agreements. The systems being built have a significant human–machine adaptive nature. During their operation, a meta-strategy is developed and trained based on the foundational elements of the existing strategies. The system is designed as a universal framework for managing various strategies, with the provision of a basic architecture and a library of strategies with the possibility of adding new ones. During the learning process, a system of structural characteristics is also accumulated and trained, on the basis of which a decision is made on the use of specific strategy elements at the next step. The presentation is conducted for the sequential calculus of minimal positive predicate logic as the most suitable for the deductive synthesis of programs and algorithms, for which it is proposed to use this approach.

Détail

Keywords: automated theorem proving, minimal predicate logic, machine learning, human–machine interaction, artificial intelligence, sequential calculus, deep learning, proof verification