Title: Nonclassical relation algebras as expansions of residuated lattices
Speaker: Peter Jipsen (Chapman University).
Time: 8 September 9AM AEST (this is the evening of 7 September in American time zones).
Abstract: This talk is about some old and new research on generalizations of algebras of binary relations, spanning joint work with Roger Maddux and Nick Galatos. Tarski defined the variety RA of relation algebras as a finitely based approximation of the variety RRA of representable relation algebras. The logical part of such algebras has the structure of a Boolean algebra, i.e., classical propositional logic, while the “relative” or “dynamic” part has the structure of a distributive involutive residuated lattice. The common structure is an underlying (distributive) lattice, and relaxing the axioms for either part gives rise to a collection of more general varieties. I will discuss how sequential algebras, FL’-algebras, quasi relation algebras, skew relation algebras, weakening relation algebras, Heyting relation algebras (= bounded GBI-algebras) and FL^2-algebras fit into this framework. Results about these generalizations, some applications and a few open problems will also be mentioned.