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Intuitionistic phase semantics is almost classical

Published online by Cambridge University Press:  21 February 2006

MAX I. KANOVICH ,
MITSUHIRO OKADA  and
KAZUSHIGE TERUI
MAX I. KANOVICH
Affiliation:
Department of Computer Science, Queen Mary, University of London, Mile End Road, London E1 4NS and Department of Computer and Information Science, University of Pennsylvania Email: mik@dcs.qmul.ac.uk and maxkanov@cis.upenn.edu
MITSUHIRO OKADA
Affiliation:
Department of Philosophy, Faculty of Letters, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan Email: mitsu@abelard.flet.keio.ac.jp
KAZUSHIGE TERUI
Affiliation:
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan Email: terui@nii.ac.jp
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 16 , Issue 1 , February 2006 , pp. 67 - 86
Copyright
2006 Cambridge University Press

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