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- Selective base revisionsPublication . Garapa, MarcoBelief Revision addresses the problem of rationally incorporating pieces of new information into an agent’s belief state. In the AGM paradigm, the most used frame work in Belief Revision, primacy is given to the new information, which is fully incorporated into the agent’s belief state. However, in real situations, one may want to reject the new information or only accept a part of it. A constructive model called Selective Revision was proposed to meet this need but, as in the AGM framework, focused on belief sets (sets closed under logical consequence). In this paper we adapt the selective revision operators, that were proposed for belief sets, to the belief base context, obtaining a model in which an agent’s epistemic state is represented by a belief base and that allows the acceptance of only part of the new information. We present several representation theorems for selective base revision operators based on different base revision operators.
- Advances on belief base dynamicsPublication . Garapa, Marco Paulo Ferreirinha; Fermé, Eduardo Leopoldo; Reis, Maurício Duarte LuísThe main goal underlying the research area of belief change consists in finding appropriate ways of modelling the belief state of a rational agent and, additionally, the changes which occur in such a state when the agent receives new information. The most important model of belief change is the so-called AGM model, proposed in [AGM85]. In this model, the belief state of an agent is represented by a belief set—a deductively closed set of sentences. A change consists in adding or removing a specific sentence from a belief set to obtain a new belief set. Two of the main shortcomings pointed out to the AGM model of belief change are the use of belief sets to represent belief states and the (unrealistic) acceptance of any new piece of information. In this thesis we address both those issues. We present axiomatic characterizations for ensconcement-based contractions and for brutal contractions, two kinds of belief bases contraction operators introduced in [Wil94b] that are based on the concept of ensconcement, which is a generalization to the case of belief bases of the concept of epistemic entrenchment introduced in [Ga¨r88, GM88]. We compare the axiomatic characterizations of these operators with those of other well-known base contraction operators and study the interrelations among the former and the contraction operators based on epistemic entrenchments. We study non-prioritized base change operators, namely shielded base contractions and credibility-limited base revisions. We propose several different classes of shielded base contractions and obtain axiomatic characterizations for each one of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. Afterwards we perform a similar study for credibility-limited base revisions. Finally, we study the interrelation between the different proposed classes of operators of credibility-limited base revision and of shielded contraction by means of the consistency-preserving Levi identity and the Harper identity.
- 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.
- 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.
- Two level credibility-limited revisionsPublication . Garapa, MarcoIn this paper, we propose a new kind of nonprioritized operator which we call two level credibility-limited revision. When revising through a two level credibility-limited revision there are two levels of credibility and one of incredibility. When revising by a sentence at the highest level of credibility, the operator behaves as a standard revision, if the sentence is at the second level of credibility, then the outcome of the revision process coincides with a standard contraction by the negation of that sentence. If the sentence is not credible, then the original belief set remains unchanged. In this article, we axiomatically characterize several classes of two level credibility-limited revision operators.
- 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.
- 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.