Annals of Pure and Applied Logic 64 (3):273-291 (1993)

Valeria Correa Vaz De Paiva
University of Birmingham
In this paper we give a brief treatment of a theory of proofs for a system of Full Intuitionistic Linear Logic. This system is distinct from Classical Linear Logic, but unlike the standard Intuitionistic Linear Logic of Girard and Lafont includes the multiplicative disjunction par. This connective does have an entirely natural interpretation in a variety of categorical models of Intuitionistic Linear Logic. The main proof-theoretic problem arises from the observation of Schellinx that cut elimination fails outright for an intuitive formulation of Full Intuitionistic Linear Logic; the nub of the problem is the interaction between par and linear implication. We present here a term assignment system which gives an interpretation of proofs as some kind of non-deterministic function. In this way we find a system which does enjoy cut elimination. The system is a direct result of an analysis of the categorical semantics, though we make an effort to present the system as if it were purely a proof-theoretic construction.
Keywords full intuitionistic linear logic  multiconclusion sequents  constructive par
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DOI 10.1016/0168-0072(93)90146-5
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
A Game Semantics for Linear Logic.Andreas Blass - 1992 - Annals of Pure and Applied Logic 56 (1-3):183-220.
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Normalization as a Homomorphic Image of Cut-Elimination.Garrel Pottinger - 1977 - Annals of Mathematical Logic 12 (3):323.

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Citations of this work BETA

A Comparison Between Monoidal and Substructural Logics.Clayton Peterson - 2016 - Journal of Applied Non-Classical Logics 26 (2):126-159.
Investigations Into a Left-Structural Right-Substructural Sequent Calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
Proof Theory in the Abstract.J. M. E. Hyland - 2002 - Annals of Pure and Applied Logic 114 (1-3):43-78.
A Note on Full Intuitionistic Linear Logic.G. M. Bierman - 1996 - Annals of Pure and Applied Logic 79 (3):281-287.

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