Abstract
In some recent works (Reis 2011, Fermé and Reis, J. Philos. Log. 41, 29–52, 2012, Fermé and Reis, Rev. Symb. Log. 6, 460–487, 2013) two new kinds of multiple contraction functions have been proposed, namely the system of spheres-based multiple contractions and the epistemic entrenchment-based multiple contractions, as generalizations (to the case of multiple contraction) of the well-known classes of systems of spheres-based and of epistemic entrenchment-based (singleton) contractions. Additionally, a representation theorem for the class of epistemic entrenchment-based multiple contraction has been proposed, and it has been shown that the two newly proposed constructions are equivalent, in the sense that a multiple contraction function is a system of spheres-based multiple contraction if and only if it is an epistemic entrenchment-based multiple contraction. In this paper we present two axiomatic characterizations for those multiple contraction functions which differ from the one mentioned above and, in particular, make use of some more intuitive postulates.
Highlights
One of the central goals of the area known as logic of theory change is to model how information is removed from the epistemic state of an agent
On the other hand, having in mind the informal meaning of each of the postulates (M1)−(M3) that we have presented right after introducing them, we notice that those are properties that we might naturally expect to be satisfied by a reasonable multiple contraction function
The other axiomatic characterization for those two classes of multiple contraction functions was introduced in Corollary 3.9 and only differs from the above described one in the following: it uses the postulates of package inclusion, package success, package uniformity, package relevance instead of the postulates (K÷1)−(K÷6)
Summary
One of the central goals of the area known as logic of theory change is to model how information is removed from the epistemic state of an agent. Several proposals have been presented in the literature for modelling operations of that kind — commonly known as contraction functions — which, roughly speaking (and assuming that the beliefs of an agent are represented by sentences), receive a set of beliefs and a sentence that is intended to be removed from it and return a new set of beliefs that no longer contains the given sentence. As a result of the awareness of the need to develop models of theory multiple contractions, several generalizations of the most well-known models of (AGM) singleton contractions were presented in the literature. In [3, 14] it was show that those two classes of multiple contraction functions are identical and an axiomatic characterization for the epistemic entrenchment-based multiple contractions was provided.
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