Finite RDP-algebras: duality, coproducts and logic

Abstract

The variety of RDP-algebras forms the algebraic semantics of RDP-logic, the many-valued propositional logic of the revised drastic product left-continuous triangular norm and its residual. We prove a Priestley duality for finite RDP-algebras, and obtain an explicit description of coproducts of finite RDP-algebras. In this light, we give a combinatorial representation of free finitely generated RDP-algebras, which we exploit to construct normal forms, strongest deductive interpolants and most general unifiers.We prove that RDP-unification is unitary, and that the tautology problem for RDP-logic is coNP-complete.