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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.
- Funções teste e funções generalizadas em dimensão 1. Descrição e caracterizaçãoPublication . Ferreira, Jorge; Gouveia, Délia; Reis, Maurício; Silva, José LuísNeste trabalho introduzimos uma família de espaços de funções teste definidas em R associadas à medida Gaussiana µ. Por dualidade obtemos a correspondente família de espaços de distribuições (ou funções generaliza das). A caracterização destas famílias à custa de funções inteiras com um certo tipo de crescimento é feita usando a transformada S. Como exemplo de aplicação apresentamos o produto de Wick entre funções generalizadas.
- 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.
- 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).
- 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.
- How to construct remainder sets for paraconsistent revisions: preliminary reportPublication . Testa, Rafael; Fermé, Eduardo; Garapa, Marco; Reis, MaurícioRevision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision op eration should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those dis tinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors.
- 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].
- 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.