13 February 2013, Algebra|Coalgebra Seminar, Sam van Gool

(joint work with Andrej Bauer, Karin Cvetko-Vah, Mai Gehrke and Ganna Kudryavtseva.)

Abstract:

In this talk on our recent paper*, I will describe a new Priestley-style duality for skew distributive lattices.

Since its introduction in Stone's seminal papers from 1936 and 1937, duality theory has been important in the study of propositional logics beyond the classical, such as intuitionistic, modal, and substructural logics. It provides the mathematical framework for studying the intimate link between the syntax and semantics of a logic.

The results that I describe in this talk form a generalization of duality theory beyond the commutative case. This opens the door to applications of duality theory to logical systems in which the basic operations of conjunction and disjunction are no longer assumed to be commutative. Such systems are of interest because of their possible relevance to both quantum logic and dynamic epistemic logic.

*preprint available on http://arxiv.org/pdf/1206.5848