论文信息 - Functorial Duality for Ortholattices and De Morgan Lattices

Functorial Duality for Ortholattices and De Morgan Lattices

Abstract.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.

Katalin Bimbó | K. Bimbó

[1] Steven Givant,et al. Logic As Algebra , 1998 .

[2] Robert Goldblatt,et al. Semantic analysis of orthologic , 1974, J. Philos. Log..

[3] J. Michael Dunn,et al. Relevance Logic and Entailment , 1986 .

[4] R. Goldblatt. Topoi, the Categorial Analysis of Logic , 1979 .

[5] M. Stone. Topological representations of distributive lattices and Brouwerian logics , 1938 .

[6] M. Stone. The theory of representations for Boolean algebras , 1936 .

[7] Vito F. Sinisi,et al. Entailment: The Logic of Relevance and Necessity , 1996 .

[8] Gary M. Hardegree,et al. Algebraic Methods in Philosophical Logic , 2001 .

[9] Robert Goldblatt,et al. The Stone Space of an Ortholattice , 1975 .

[10] David M. Clark,et al. Natural Dualities for the Working Algebraist , 1998 .

[11] Hilary A. Priestley,et al. Representation of Distributive Lattices by means of ordered Stone Spaces , 1970 .

[12] Alasdair Urquhart,et al. Duality for algebras of relevant logics , 1996, Stud Logica.

[13] B. Davey,et al. Introduction to Lattices and Order: Appendix B: further reading , 2002 .

[14] Nuel D. Belnap,et al. Entailment : the logic of relevance and necessity , 1975 .

[15] Katalin Bimbó,et al. Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi , 2008 .