Logica Universalis 3 (1):125-152 (2009)

Katalin Bimbo
University of Alberta
Jon Michael Dunn
Indiana University, Bloomington
Symmetric generalized Galois logics (i.e., symmetric gGl s) are distributive gGl s that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGl s by models on topological relational structures. On the other hand, topological relational structures are realized by structures of symmetric gGl s. We generalize the weak distributivity laws between fusion and fission to interactions of certain monotone operations within distributive super gGl s. We are able to prove appropriate generalizations of the previously obtained theorems—including a functorial duality result connecting classes of gGl s and classes of structures for them.
Keywords cut rule  gaggle theory  Routley–Meyer semantics  categorial grammars  functorial duality  topological representation
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DOI 10.1007/s11787-009-0004-3
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References found in this work BETA

An Introduction to Substructural Logics (Review).Kosta Dosen - 2001 - Bulletin of Symbolic Logic 7 (4):527-530.
Kripke Models for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.
Combinators and Structurally Free Logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.

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Citations of this work BETA

Symmetric Categorial Grammar.Michael Moortgat - 2009 - Journal of Philosophical Logic 38 (6):681-710.
Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.
Powerset Residuated Algebras.Mirosława Kołowska-Gawiejnowicz - 2014 - Logic and Logical Philosophy 23 (1):69-80.

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