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New techniques and completeness results for preferential structures

Published online by Cambridge University Press:  12 March 2014

Karl Schlechta
Karl Schlechta*
Affiliation:
Laboratoire d'informatique de Marseille, CNRS ESA 6077, CMI, Technopôle de Château-Gombert, F-13453 Marseille Cedex 13, France, E-mail: [email protected]
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Abstract

Preferential structures are probably the best examined semantics for nonmonotonic and deontic logics: in a wider sense, they also provide semantical approaches to theory revision and update, and other fields where a preference relation between models is a natural approach. They have been widely used to differentiate the various systems of such logics, and their construction is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for completeness proofs. Since our main interest is to provide general techniques, which can be applied in various situations and for various base logics (propositional and other), we take a purely algebraic approach, which can be translated into logics by easy lemmata, in particular, we give a clean construction via indexing by trees for transitive structures, this allows us to simplify the proofs of earlier work by the author, and to extend the results given there.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 719 - 746
Copyright
Copyright © Association for Symbolic Logic 2000

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