An Indexed System for Multiplicative Additive Polarized Linear Logic

Authors:
Masahiro Hamano;Ryo Takemura
Affiliations:
National Institute of Informatics, Tokyo 101-8430, Japan, and SFC Research Institute, Fujisawa 252-8520, Japan;Department of Philosophy, Keio University, Tokyo, Japan 108-8345
Venue:
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Year:
2008

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Abstract

We present an indexed logical system MALLP(I)for Laurent's multiplicative additive polarized linear logic (MALLP) [14]. The system is a polarized variant of Bucciarelli-Ehrhard's indexed system for multiplicative additive linear logic [4]. Our system is derived from a web-based instance of Hamano-Scott's denotational semantics [12] for MALLP. The instance is given by an adjoint pair of right and left multi-pointed relations. In the polarized indexed system, subsets of indexes for Iwork as syntactical counterparts of families of points in webs. The rules of $\sf MALLP({\it I})$ describe (in a proof-theoretical manner) the denotational construction of the corresponding rules of MALLP. We show that $\sf MALLP({\it I})$ faithfully describes a denotational model of MALLPby establishing a correspondence between the provability of indexed formulas and relations that can be extended to (non-indexed) proof-denotations.