Intuitionistic ancestral logic

Liron Cohen, Robert L. Constable

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article we define pure intuitionistic Ancestral Logic (iAL), extending pure intuitionistic First-Order Logic (iFOL). This logic is a dependently typed abstract programming language with computational functionality beyond iFOL given by its realizer for the transitive closure, TC. We derive this operator from the natural type theoretic definition of TC using intersection. We show that provable formulas in iAL are uniformly realizable, thus iAL is sound with respect to constructive type theory. We further show that iAL subsumes Kleene Algebras with tests and thus serves as a natural programming logic for proving properties of program schemes. We also extract schemes from proofs that iAL specifications are solvable.

Original languageEnglish
Pages (from-to)469-486
Number of pages18
JournalJournal of Logic and Computation
Volume29
Issue number4
DOIs
StatePublished - 6 Jun 2019
Externally publishedYes

Keywords

  • Ancestral logic
  • intuitionistic logic
  • realizability semantics
  • transitive closure

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Arts and Humanities (miscellaneous)
  • Hardware and Architecture
  • Logic

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