Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving

Abstract

We give a uniform presentation of representation and decidability results related to the Kripke-style semantics of several 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 semi-lattices) extends in a natural way to several classes of operators and allows to establish a relationship between algebraic and Kripke-style models. We illustrate the ideas on several examples. We conclude by showing how the Kripke-style models thus obtained can be used (if first-order axiomatizable) for automated theorem proving by resolution for some non-classical logics.KeywordsModal LogicDistributive LatticeRepresentation TheoremResiduated LatticeAlgebraic ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.