Single Axioms and Axiom-Pairs for the Implicational Fragments of $$\mathbf {R}$$ R , R-Mingle, and Some Related Systems

Ulrich, Dolph

doi:10.1007/978-3-319-29300-4_4

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…The discussed notions of regularity and lemma generation methods seem immediately suited for further investigations in the context of first-order theorem proving in general. For other aspects of the work we plan a stepwise generalization by considering further single axioms for the implicational fragment IF [23,21,38], single axioms and axiom pairs for further logics [38], the about 200 condensed detachment problems in the LCL domain of the TPTP, problems which involve multiple non-unit clauses, and adapting D-terms to a variation of binary resolution instead of detachment. In the longer run, our approach aims at providing a basis for approaches to theorem proving with machine learning (e.g.…”

Section: Discussionmentioning

confidence: 99%

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

Wernhard,

Bibel

2021

Preprint

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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 Łukasiewicz, 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.

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Section: Discussionmentioning

confidence: 99%

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

Wernhard,

Bibel

2021

Preprint

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“…5 On this technique, see [50,52,51]. 6 Recently, in [64] single axioms and axiom-pairs for further logics were developed. That paper also surveys the known single axioms for implicational logic and provides references to a uniqueness result about Łukasiewicz's shortest axiom, e.g., [61].…”

Section: Nicknamementioning

confidence: 99%

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures

Wernhard¹,

Bibel

2021

Automated Deduction – CADE 28

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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 Łukasiewicz, 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.

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Investigations into Proof Structures

Wernhard,

Bibel

2024

J Autom Reasoning

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We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is applied in an exemplary manner to a coherent and comprehensive formal reconstruction and analysis of historical proofs of a widely-studied problem due to Łukasiewicz. The underlying approach opens the door towards new systematic ways of generating lemmas in the course of proof search to the effects of reducing the search effort and finding shorter proofs. Among the numerous reported experiments along this line, a proof of Łukasiewicz ’s problem was automatically discovered that is much shorter than any proof found before by man or machine.

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Single Axioms and Axiom-Pairs for the Implicational Fragments of $$\mathbf {R}$$ R , R-Mingle, and Some Related Systems

Cited by 3 publications

References 22 publications

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures

Investigations into Proof Structures

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