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The Semantics of Rational Contractions J urgen Giesl 1 and Ingrid Neumann 2

Summary: The Semantics of Rational Contractions
J¨ urgen Giesl 1 and Ingrid Neumann 2
1 Dept. of Computer Science, Technical University Darmstadt, Alexanderstr. 10,
64283 Darmstadt, Germany, Email: giesl@inferenzsysteme.informatik.th­darmstadt.de
2 Dept. of Computer Science, University of Karlsruhe, Kaiserstr. 12,
76128 Karlsruhe, Germany, Email: neumann@ira.uka.de
The Logic of Theory Change developed by Alchourr'on, G¨ ardenfors and Makinson is
concerned with the revision of beliefs in the face of new and possibly contradicting
information. This nonmonotonic process consists of a contraction and an expansion
transforming one belief into another. Beliefs are represented by consistent deduc­
tively closed sets of formulas. To achieve minimal change Alchourr'on, G¨ ardenfors
and Makinson suggested widely accepted postulates that rational contractions have
to fulfill.
In practical applications, e.g. knowledge representation, deductively closed sets
of formulas have to be representable in a finite way. Therefore our main interest is in
rational finite contractions, i.e. rational contractions that transform sets of formulas
possessing a finite base into finitely representable sets again.
We have formulated a semantical characterization of rational finite contractions
which provides an insight into the true nature of these operations and shows all


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences