Meeting strength in substructural logics

Studia Logica 54 (1):3 - 32 (1995)
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Abstract

This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzen-style proof theory in which there is only alimited possibility to use structural rules. Following the literture, we use an operator to mark formulas to which the extra structural rules may be applied. New in our approach is that we do not see this as a modality, but rather as themeet of the marked formula with a special typeQ. In this way we can make the specific structural behaviour of marked formulas more explicit.The main motivation for our approach is that we can provide a nice, intuitive semantics for hybrid substructural logics. Soundness and completeness for this semantics are proved; besides this we consider some proof-theoretical aspects like cut-elimination and embeddings of the strong system in the hybrid one.

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Yde Venema
University of Amsterdam

Citations of this work

Multimodal linguistic inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
Normal modal substructural logics with strong negation.Norihiro Kamide - 2003 - Journal of Philosophical Logic 32 (6):589-612.

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References found in this work

Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–102.
Quantales and (noncommutative) linear logic.David N. Yetter - 1990 - Journal of Symbolic Logic 55 (1):41-64.
Completeness Results for Lambek Syntactic Calculus.Wojciech Buszkowski - 1986 - Mathematical Logic Quarterly 32 (1‐5):13-28.
Completeness Results for Lambek Syntactic Calculus.Wojciech Buszkowski - 1986 - Mathematical Logic Quarterly 32 (1-5):13-28.

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