The semantics of rational contractions

This paper is concerned with the revision of beliefs in the face
of new and possibly contradicting information. In the Logic of
Theory Change developed by Alchourron, Gärdenfors and Makinson
this nonmonotonic 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 contractions maintaining
finite representability) which provides an insight into the true
nature of these operations. This characterization shows all
possibilities to define concrete functions possessing these
properties.

When regarding concrete contractions known from literature in the
light of our characterization we have found that they are all
defined according to the same semantical strategy of minimal
... mehrsemantical change. As this strategy does not correspond to the
goal of keeping as many important fotmulas as possible in the
contracted set, we suggest a finite contraction defined according
to the new strategy of maximal maintenance.