On constructive connectives and systems

Research output: Contribution to journalArticlepeer-review

Abstract

Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a general non-deterministic Kripke-style semantics is provided. This general semantics is then used to provide a constructive (and very natural), sufficient and necessary coherence criterion for the validity of the strong cut-elimination theorem in such a system. These results suggest new syntactic and semantic characterizations of basic constructive connectives.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalLogical Methods in Computer Science
Volume6
Issue number4
DOIs
StatePublished - 2010

Keywords

  • Cut-elimination
  • Kripke semantics
  • Non-deterministic semantics
  • Nonclassical logics
  • Sequent calculus

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