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.

@article{paperbot1442,
  title = {Synthesizing axiomatizations using logic learning},
  author = {Paul Krogmeier and Zhengyao Lin and Adithya Murali and P. Madhusudan},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {6},
  number = {OOPSLA2},
  year = {2022},
  doi = {10.1145/3563348}
}