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

MPG-Autoren
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Sofronie-Stokkermans,  Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Zitation

Sofronie-Stokkermans, V. (2003). Representation Theorems and the Semantics of Non-classical Logics, and Applications to Automated Theorem Proving. In M. Fitting, & E. Orlowska (Eds.), Beyond Two: Theory and Applications of Multiple Valued Logic (pp. 59-100). Berlin, Germany: Springer.


Zitierlink: https://hdl.handle.net/11858/00-001M-0000-000F-2DF4-2
Zusammenfassung
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.