Construction of System of Spheres-based Transitively Relational Partial Meet Multiple Contractions: An Impossibility Result (Extended Abstract)

In this paper we show that, contrary to what is the case in what concerns contractions by a single sentence, there is not a system of spheres-based construction of multiple contractions which generates each and every transitively relational partial meet multiple contraction. Furthermore, we propose two system of spheres-based constructions of multiple contractions which generate (only) transitively relational partial meet multiple contractions.

EPISTEMIC ENTRENCHMENT-BASED MULTIPLE CONTRACTIONS

In this article we present a new class of multiple contraction functions—the epistemic entrenchment-based multiple contractions—which are a generalization of the epistemic entrenchment-based contractions (Gärdenfors, 1988; Gärdenfors & Makinson, 1988) to the case of contractions by (possibly nonsingleton) sets of sentences and provide an axiomatic characterization for that class of functions. Moreover, we show that the class of epistemic entrenchment-based multiple contractions coincides with the class of system of spheres-based multiple contractions introduced in Fermé & Reis (2012).