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Representation theorems and the semantics of (semi)lattice-based logics

This paper gives a unified presentation of various non-classical logics. We show that a general representation theorem (which has as particular instances the representation theorems as algebras of sets for Boolean algebras, distributive lattices and semilattices) allows to establish a relationship between algebraic models and Kripke-style models, and illustrate the ideas on several examples. Based on this, we present a method for automated theorem proving by resolution for such logics. Other representation theorems, as algebras of sets or as algebras of relations, as well as relational models are also mentioned.