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

Authors
Yde Venema
University of Amsterdam
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 a limited possibility to use structural rules. Following the literature, 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 the meet of the marked formula with a special type Q. 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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DOI 10.1007/bf01058530
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Citations of this work BETA

Multimodal Linguistic Inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
Type Logical Grammar: Categorial Logic of Signs.G. V. Morrill - 1994 - Dordrecht, Netherland: Springer.
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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