Functorial duality for ortholattices and de Morgan lattices

Logica Universalis 1 (2):311-333 (2007)
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.  Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.



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Katalin Bimbo
University of Alberta

Citations of this work

The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - forthcoming - Journal of Philosophical Logic:1-77.
Stone duality for lattice expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
Dual Gaggle Semantics for Entailment.Katalin Bimbó - 2009 - Notre Dame Journal of Formal Logic 50 (1):23-41.
Topological duality for orthomodular lattices.Joseph McDonald & Katalin Bimbó - 2023 - Mathematical Logic Quarterly 69 (2):174-191.

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References found in this work

Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
Algebraic Methods in Philosophical Logic.J. Michael Dunn - 2001 - Oxford, England: Oxford University Press.
The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
The Algebra of Intensional Logics.Jon Michael Dunn - 1966 - Dissertation, University of Pittsburgh

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