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Synthesizing axiomatizations using logic learning

Authors:

Paul Krogmeier,

Adithya Murali,

P. MadhusudanAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 6, Issue OOPSLA2

Article No.: 185, Pages 1697 - 1725

https://doi.org/10.1145/3563348

Published: 31 October 2022 Publication History

Abstract

Axioms and inference rules form the foundation of deductive systems and are crucial in the study of reasoning with logics over structures. Historically, axiomatizations have been discovered manually with much expertise and effort. In this paper we show the feasibility of using synthesis techniques to discover axiomatizations for different classes of structures, and in some contexts, automatically prove their completeness. For evaluation, we apply our technique to find axioms for (1) classes of frames in modal logic characterized in first-order logic and (2) the class of language models with regular operations.

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Cited By

Mathur UMestel DViswanathan M(2025)The Decision Problem for Regular First Order TheoriesProceedings of the ACM on Programming Languages10.1145/37048709:POPL(986-1012)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704870
Pal ASaiki BTjoa RRichey CZhu AFlatt OWillsey MTatlock ZNandi C(2023)Equality Saturation Theory Exploration à la CarteProceedings of the ACM on Programming Languages10.1145/36228347:OOPSLA2(1034-1062)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622834
Zhang YTowey DPike M(2023)Automated Metamorphic-Relation Generation with ChatGPT: An Experience Report2023 IEEE 47th Annual Computers, Software, and Applications Conference (COMPSAC)10.1109/COMPSAC57700.2023.00275(1780-1785)Online publication date: Jun-2023
https://doi.org/10.1109/COMPSAC57700.2023.00275

Index Terms

Synthesizing axiomatizations using logic learning
1. Computing methodologies
  1. Machine learning
2. Theory of computation
  1. Logic
    1. Equational logic and rewriting
    2. Modal and temporal logics

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 6, Issue OOPSLA2

October 2022

1932 pages

EISSN:2475-1421

DOI:10.1145/3554307

Editor:
Philip Wadler
University of Edinburgh, UK

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Association for Computing Machinery

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Published: 31 October 2022

Published in PACMPL Volume 6, Issue OOPSLA2

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Cited By

Mathur UMestel DViswanathan M(2025)The Decision Problem for Regular First Order TheoriesProceedings of the ACM on Programming Languages10.1145/37048709:POPL(986-1012)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704870
Pal ASaiki BTjoa RRichey CZhu AFlatt OWillsey MTatlock ZNandi C(2023)Equality Saturation Theory Exploration à la CarteProceedings of the ACM on Programming Languages10.1145/36228347:OOPSLA2(1034-1062)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622834
Zhang YTowey DPike M(2023)Automated Metamorphic-Relation Generation with ChatGPT: An Experience Report2023 IEEE 47th Annual Computers, Software, and Applications Conference (COMPSAC)10.1109/COMPSAC57700.2023.00275(1780-1785)Online publication date: Jun-2023
https://doi.org/10.1109/COMPSAC57700.2023.00275

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