Substructural logics as logics of residuated lattices

Substructural logics have received a lot of attention in recent years from communities of both logic and algebra. In this talk, we discuss the algebraization of substructural logics, their close connection to residuated lattices, and local deduction theorem for them. As an application, we give algebraic characterization of some of logical properties, including interpolation property. This is a joint work with Nick Galatos.