Grafting modalities onto substructural implication systems

Studia Logica 59 (1):65-102 (1997)
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Abstract

We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper.

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Author Profiles

Marcello D'Agostino
Università degli Studi di Milano
Dov Gabbay
Hebrew University of Jerusalem

Citations of this work

Tracking reasons with extensions of relevant logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
What is categorical structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 151--161.
Non-normal modalities in variants of linear logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.

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References found in this work

Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Entailment: The Logic of Relevance and Necessity, Vol. 1.A. Anderson & N. Belnap (eds.) - 1975 - Princeton, NJ, USA: Princeton University Press.
The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
Sequent-systems and groupoid models. I.Kosta Došen - 1988 - Studia Logica 47 (4):353 - 385.

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