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

  • Viorica Sofronie-Stokkermans
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 114)

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.

Keywords

Modal Logic Distributive Lattice Representation Theorem Residuated Lattice Algebraic Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Viorica Sofronie-Stokkermans
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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