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- Residual contractionPublication . Garapa, Marco; Reis, Maurício D. L.In this paper, we propose and axiomatically characterize residual contractions, a new kind of contraction operators for belief bases. We establish that the class of partial meet contractions is a strict subclass of the class of residual contractions. We identify an extra condition that may be added to the definition of residual contractions, which is such that the class of residual contractions that satisfy it coincides with the class of partial meet contrac tions. We investigate the interrelations in the sense of (strict) inclusion among the class of residual contractions and other classes of well known contraction operators for belief bases.
- 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.
- Credibility-limited base revision: new classes and their characterizationsPublication . Garapa, Marco; Fermé, Eduardo; Reis, MaurícioIn this paper we study a kind of operator —known as credibility-limited base revisions— which addresses two of the main issues that have been pointed out to the AGM model of belief change. Indeed, on the one hand, these operators are defined on belief bases (rather than belief sets) and, on the other hand, they are constructed with the underlying idea that not all new information is accepted. We propose twenty different classes of credibility limited base revision operators and obtain axiomatic characterizations for each of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. More precisely, we analyse whether each one of those classes is or is not (strictly) contained in each of the remaining ones.
- On ensconcement and contractionPublication . Fermé, Eduardo; Garapa, Marco; Reis, MaurícioIn this article we present an axiomatic characterization for the ensconcement-based contractions. We study the interrelation among ensconcement-based contractions and brutal contractions, and we present two ways of defining an ensconcement relation by means of a base contraction operation. Finally, we study the interrelations among ensconcement-based contraction and epistemic entrenchment-based contractions and among brutal contractions and severe withdrawals.
- Studies on brutal contraction and severe withdrawalPublication . Garapa, M.; Fermé, E.; Reis, M. D. L.In this paper we present an axiomatic characterization for brutal contractions. Then we consider the particular case of the brutal contractions that are based on a bounded ensconcement and also the class of severe withdrawals which are based on bounded epis temic entrenchment relations that are defined by means of bounded ensconcements (using the procedure proposed by Mary-Anne Williams). We present axiomatic characterizations for each one of those classes of functions and investigate the interrelation among them.
- 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.
- Studies in credibility: limited base revisionPublication . Garapa, Marco; Fermé, Eduardo; Reis, Maurício D. L.In this paper we present axiomatic characterizations for several classes of credibility-limited base revision functions and establish the interrelation among those classes. We also propose and axiomatically characterize two new base revision functions.
- 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.