Intuitionistic phase semantics is almost classical

Max I. Kanovich, Mitsuhiro Okada, Kazushige Terui

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the relationship between classical phase semantics for classical linear logic (LL) and intuitionistic phase semantics for intuitionistic linear logic (ILL). We prove that (i) every intuitionistic phase space is a subspace of a classical phase space, and (ii) every intuitionistic phase space is phase isomorphic to an 'almost classical' phase space. Here, by an 'almost classical' phase space we mean an intuitionistic phase space having a double-negation-like closure operator. Based on these semantic considerations, we give a syntactic embedding of propositional ILL into LL.

Original languageEnglish
Pages (from-to)67-86
Number of pages20
JournalMathematical Structures in Computer Science
Volume16
Issue number1
DOIs
Publication statusPublished - 2006 Feb

Fingerprint

Phase Space
Linear Logic
Semantics
Intuitionistic Logic
Syntactics
Closure Operator
Classical Logic
Isomorphic
Subspace

ASJC Scopus subject areas

  • Computer Science Applications
  • Mathematics (miscellaneous)

Cite this

Intuitionistic phase semantics is almost classical. / Kanovich, Max I.; Okada, Mitsuhiro; Terui, Kazushige.

In: Mathematical Structures in Computer Science, Vol. 16, No. 1, 02.2006, p. 67-86.

Research output: Contribution to journalArticle

Kanovich, Max I. ; Okada, Mitsuhiro ; Terui, Kazushige. / Intuitionistic phase semantics is almost classical. In: Mathematical Structures in Computer Science. 2006 ; Vol. 16, No. 1. pp. 67-86.
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