Summary: The Semantics of Rational Contractions
Jürgen Giesl Ingrid Neumann
Fachbereich Informatik Fakultät für Informatik
Technische Hochschule Darmstadt Universität Karlsruhe
Alexanderstr. 10 Kaiserstr. 12
64283 Darmstadt 76128 Karlsruhe
Tel.: ++49­6151­166658 Tel.: ++49­721­6084375
Fax: ++49­6151­165326
E­mail: giesl@inferenzsysteme.informatik.th­darmstadt.de E­mail: neumann@ira.uka.de
Abstract
This paper is concerned with the revision of beliefs in the face of new and possibly contradicting infor­
mation. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this non­
monotonic process consists of a contraction and an expansion of a set of formulas. To achieve minimal
change they formulated widely accepted postulates that rational contractions have to fulfill.
Contractions as defined by Alchourron, Gärdenfors and Makinson only operate on deductively closed
sets of formulas. Therefore they cannot be used in practical applications, eg. knowledge representation,
where only finitely representable sets can be handled.
We present a semantical characterization of rational finite contractions (the class of rational contrac­
tions maintaining finite representability) which provides an insight into the true nature of these opera­
tions. This characterization shows all possibilities to define concrete functions possessing these proper­

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

Collections: Computer Technologies and Information Sciences