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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.
- Epistemic entrenchment-based multiple contractionsPublication . Fermé, Eduardo; Reis, Maurício D. L.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 (Gardenfors, 1988; G ¨ ardenfors & 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 multi ple contractions coincides with the class of system of spheres-based multiple contractions introduced in Ferme & Reis (2012).
- Levi and Harper identities for non-prioritized belief base changePublication . Garapa, Marco; Fermé, Eduardo; Reis, Maurício D. L.In this paper, we investigate the relation between shielded base contraction postulates and credibility-limited (CL) base revision postulates. More precisely, we identify (i) the relation between the postulates satisfied by a shielded base contraction operator and the postulates satisfied by the CL base revision operator that is defined from it by means of the consistency-preserving Levi identity and (ii) the relation between the postulates satisfied by a CL base revision operator and the postulates satisfied by the shielded base contraction operator that is defined from it by means of the Harper identity. Furthermore, we show that the consistency-preserving Levi identity and the Harper identity establish a one-to one correspondence between the twenty classes of shielded base contractions presented in [21] and the twenty classes of credibility-limited base revisions presented in [22].
- 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.
- Shielded base contractionPublication . Garapa, Marco; Fermé, Eduardo; Reis, Maurício D. L.The one that is considered the standard model in the area of logic of belief change was proposed by Alchourrón, Gärdenfors and Makinson in 1985 and is, nowadays, known as the AGM model. Two of the main shortcomings pointed out to the AGM model of belief change are the (impractical) use of belief sets to represent belief states and the (unrealistic) acceptance of any new information. In this paper we study a kind of operators—known as shielded base contractions—which address both those issues. 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 informations are accepted. We propose twenty different classes of shielded base contractions 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 of those classes is or is not (strictly) contained in each of the remaining ones.
- Relevance, recovery and recuperation: a prelude to ring withdrawalPublication . Fermé, Eduardo; Garapa, Marco; Abhaya Nayak; Reis, Maurício D. L.; Reis, MaurícioIn this paper, we introduce recuperative withdrawals, belief change operators that satisfy recuperation, a postulate weaker than recovery, all the AGM postulates for contraction except recovery and another postulate which is a slightly stronger condition than conjunctive inclusion. Furthermore, we present a constructive definition for a class of operators —named ring withdrawals— which are such that the outcome of a ring withdrawal of a belief set 𝐊 by a sentence 𝛼 is obtained by adding to the set of most plausible models ‖𝐊‖ all the worlds which are as close to ‖𝐊‖ as its closest ¬𝛼-worlds. Ring withdrawals satisfy the Lindström and Rabinowicz’s interpolation thesis. We show that the classes of recuperative withdrawals and of ring withdrawals are identical. Additionally we show that the class of ring withdrawals is not contained in and does not contain the class of AGM contractions or the class of severe withdrawals. Finally we present methods for defining an operator of ring withdrawal by means of a severe withdrawal operator and by means of an AGM contraction operator, and vice-versa.