Browsing by Author "Peppas, Pavlos"
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- Construction of system of spheres-based transitively relational partial meet multiple contractions: an impossibility resultPublication . Reis, Maurício D. L.; Fermé, Eduardo; Peppas, PavlosIn 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. Before proving the general result, we consider the class of system of spheres-based mul tiple contractions introduced in [17,5] and show that this class neither subsumes nor is subsumed by the class of transitively relational partial meet multiple contractions. Furthermore, we propose two system of spheres-based constructions of multiple con tractions which generate (only) transitively relational partial meet multiple contractions. Therefore we can conclude that, although it is impossible to obtain a system of spheres based definition of all the transitively relational partial meet multiple contractions, there are classes of system of spheres-based multiple contractions which are subsumed by the class of transitively relational partial meet multiple contractions.
- Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractionsPublication . Reis, Maurício D. L.; Peppas, Pavlos; Fermé, Eduardot In some recent works (Reis 2011, Ferme and Reis, J. Philos. Log. ´ 41, 29–52, 2012, Ferme 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 representa tion 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 contrac tion 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.