Some observations on the logical foundations of inductive theorem proving

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspec...

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Veröffentlicht in:Logical methods in computer science Jg. 13, Issue 4; H. Automated deduction
Hauptverfasser: Hetzl, Stefan, Wong, Tin Lok
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Logical Methods in Computer Science e.V 01.01.2017
Schlagworte:
computer science - logic in computer science
mathematics - logic
ISSN:1860-5974, 1860-5974
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Zusammenfassung:In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017.
ISSN:1860-5974
1860-5974
DOI:10.23638/LMCS-13(4:10)2017