Phase semantics for light linear logic

Authors:
Max I. Kanovich;Mitsuhiro Okada;Andre Scedrov
Affiliations:
Department of Theoretical and Applied Linguistics, Russian State University for the Humanities, Miusskaya 6, 125267 Moscow, Russia;Department of Philosophy, Faculty of Letters, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan;Department of Mathematics, University of Pennsylvania, Philadelphia, PA
Venue:
Theoretical Computer Science - Linear logic
Year:
2003

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Abstract

Light linear logic (Girard, Inform. Comput. 14 (1998) 175-204) is a refinement of the propositions-as-types paradigm to polynomial-time computation. A semantic setting for the underlying logical system is introduced here in terms of fibred phase spaces. Strong completeness is established, with a purely semantic proof of cut elimination as a consequence. A number of mathematical examples of fibred phase spaces are presented that illustrate subtleties of light linear logic.