Uniform inductive reasoning in transitive closure logic via infinite descent

Liron Cohen, Reuben N.S. Rowe

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive definitions, the addition of the transitive closure operator uniformly captures all finitary inductive definitions. In this paper we present an infinitary proof system for transitive closure logic which is an infinite descent-style counterpart to the existing (explicit induction) proof system for the logic. We show that, as for similar systems for first-order logic with inductive definitions, our infinitary system is complete for the standard semantics and subsumes the explicit system. Moreover, the uniformity of the transitive closure operator allows semantically meaningful complete restrictions to be defined using simple syntactic criteria. Consequently, the restriction to regular infinitary (i.e. Cyclic) proofs provides the basis for an effective system for automating inductive reasoning.

Original languageEnglish
Title of host publicationComputer Science Logic 2018, CSL 2018
EditorsDan R. Ghica, Achim Jung
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770880
StatePublished - 1 Aug 2018
Externally publishedYes
Event27th Annual EACSL Conference Computer Science Logic, CSL 2018 - Birmingham, United Kingdom
Duration: 4 Sep 20187 Sep 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference27th Annual EACSL Conference Computer Science Logic, CSL 2018
Country/TerritoryUnited Kingdom


  • Completeness
  • Cyclic proof systems
  • Henkin semantics
  • Induction
  • Infinitary proof systems
  • Soundness
  • Standard semantics
  • Transitive closure

ASJC Scopus subject areas

  • Software


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