English

Learning from {\L}ukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

Artificial Intelligence 2021-07-14 v1 Logic in Computer Science

Abstract

The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the potential of guiding proof search in a more direct way. The studied problems are of the wide-spread form of "axiom(s) and rule(s) imply goal(s)". The features include the well-known concept of lemmas. For their elaboration both human and automated proofs of selected theorems are taken into a close comparative consideration. The study at the same time accounts for a coherent and comprehensive formal reconstruction of historical work by {\L}ukasiewicz, Meredith and others. First experiments resulting from the study indicate novel ways of lemma generation to supplement automated first-order provers of various families, strengthening in particular their ability to find short proofs.

Keywords

Cite

@article{arxiv.2104.13645,
  title  = {Learning from {\L}ukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)},
  author = {Christoph Wernhard and Wolfgang Bibel},
  journal= {arXiv preprint arXiv:2104.13645},
  year   = {2021}
}
R2 v1 2026-06-24T01:35:33.206Z