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- Possible worlds semantics for partial meet multiple contractionPublication . Reis, Maurício D. L.; Fermé, EduardoIn the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this paper we present the possible worlds semantics for partial meet multiple contractions.
- 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.
- System of spheres-based multiple contractionsPublication . Fermé, Eduardo; Reis, Maurício D. L.We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the 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.
- On theory multiple contractionPublication . Reis, Maurício Duarte LuísThe one which is considered the standard model of theory change was presented in [AGM85] and is known as the AGM model. In particular, that paper introduced the class of partial meet contractions. In subsequent works several alternative constructive models for that same class of functions were presented, e.g.: safe/kernel contractions ([AM85, Han94]), system of spheres-based contractions ([Gro88]) and epistemic entrenchment-based contractions ([G ar88, GM88]). Besides, several generalizations of such model were investigated. In that regard we emphasise the presentation of models which accounted for contractions by sets of sentences rather than only by a single sentence, i.e. multiple contractions. However, until now, only two of the above mentioned models have been generalized in the sense of addressing the case of contractions by sets of sentences: The partial meet multiple contractions were presented in [Han89, FH94], while the kernel multiple contractions were introduced in [FSS03]. In this thesis we propose two new constructive models of multiple contraction functions, namely the system of spheres-based and the epistemic entrenchment-based multiple contractions which generalize the models of system of spheres-based and of epistemic entrenchment-based contractions, respectively, to the case of contractions (of theories) by sets of sentences. Furthermore, analogously to what is the case in what concerns the corresponding classes of contraction functions by one single sentence, those two classes are identical and constitute a subclass of the class of partial meet multiple contractions. Additionally, and as the rst step of the procedure that is here followed to obtain an adequate de nition for the system of spheres-based multiple contractions, we present a possible worlds semantics for the partial meet multiple contractions analogous to the one proposed in [Gro88] for the partial meet contractions (by one single sentence). Finally, we present yet an axiomatic characterization for the new class(es) of multiple contraction functions that are here introduced.