Representation theorems and the semantics of non-classical logics, and applications to automated theorem proving

Authors:
Viorica Sofronie-Stokkermans
Affiliations:
Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, Saarbrücken, Germany
Venue:
Beyond two
Year:
2003

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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 semilattices) 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.