Nick Galatos (University of Denver), Amalgamation for certain conic idempotent residuated lattices

Tue, 6 April 2021, 1 pm MDT

Residuated lattices were introduced by Ward and Dilworth as tools in the study of ideal lattices of rings. Residuated lattices have a monoid and a lattice reduct, as well as division-like operations; examples include Boolean algebras, lattice-ordered groups and relation algebras. Also, they form algebraic semantics for substructural logics and are connected to mathematical linguistics and computer science (for example pointer management and memory allocation). We focus on a class of residuated lattices that have an idempotent multiplication and all elements are comparable to the monoid identity; these are related to algebraic models of relevance logic. After establishing a decomposition result for this class, we show that it has the strong amalgamation property, and extend the result to the variety generated by this class; this implies that the corresponding logic has the interpolation property and Beth definability.

[slides] [video]