Authors
Katalin Bimbo
University of Alberta
Abstract
A sequent calculus for the positive fragment of entailment together with the Church constants is introduced here. The single cut rule is admissible in this consecution calculus. A topological dual gaggle semantics is developed for the logic. The category of the topological structures for the logic with frame morphisms is proven to be the dual category of the variety, that is defined by the equations of the algebra of the logic, with homomorphisms. The duality results are extended to the logic of entailment that includes a De Morgan negation
Keywords entailment   relevance logics   gaggle theory   topological duality theory   sequent calculus   cut-free proofs
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DOI 10.1215/00294527-2008-025
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Combinators and Structurally Free Logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.
A Decision Procedure For the SystemEĪ of Entailment with Negation.Nuel D. Belnap & John R. Wallace - 1965 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (4):277-289.
Duality for Algebras of Relevant Logics.Alasdair Urquhart - 1996 - Studia Logica 56 (1-2):263 - 276.

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Citations of this work BETA

Trees for E.Shawn Standefer - 2018 - Logic Journal of the IGPL 26 (3):300-315.
Symmetric Generalized Galois Logics.Katalin Bimbó & J. Michael Dunn - 2009 - Logica Universalis 3 (1):125-152.
Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.

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