Integrating Induction and Coinduction via Closure Operators and Proof Cycles

Liron Cohen, Reuben N.S. Rowe

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

4 Scopus citations

Abstract

Coinductive reasoning about infinitary data structures has many applications in computer science. Nonetheless developing natural proof systems (especially ones amenable to automation) for reasoning about coinductive data remains a challenge. This paper presents a minimal, generic formal framework that uniformly captures applicable (i.e. finitary) forms of inductive and coinductive reasoning in an intuitive manner. The logic extends transitive closure logic, a general purpose logic for inductive reasoning based on the transitive closure operator, with a dual ‘co-closure’ operator that similarly captures applicable coinductive reasoning in a natural, effective manner. We develop a sound and complete non-well-founded proof system for the extended logic, whose cyclic subsystem provides the basis for an effective system for automated inductive and coinductive reasoning. To demonstrate the adequacy of the framework we show that it captures the canonical coinductive data type: streams.

Original languageEnglish
Title of host publicationAutomated Reasoning - 10th International Joint Conference, IJCAR 2020, Proceedings
EditorsNicolas Peltier, Viorica Sofronie-Stokkermans
PublisherSpringer
Pages375-394
Number of pages20
ISBN (Print)9783030510732
DOIs
StatePublished - 1 Jan 2020
Event10th International Joint Conference on Automated Reasoning, IJCAR 2020 - Virtual, Online
Duration: 1 Jul 20204 Jul 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12166 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Joint Conference on Automated Reasoning, IJCAR 2020
CityVirtual, Online
Period1/07/204/07/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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