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Levi and Harper identities for non-prioritized belief base change

Publication . 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].

2023Journal article

Open access

Coherence of probabilistic constraints on Nash equilibria

Publication . Preto, Sandro; Fermé, Eduardo; Finger, Marcelo

In this work, we first deal with the modeling of game situations that reach one of possibly many Nash equilibria. Before an instance of such a game starts, an external observer does not know, a priori, what is the exact profile of actions – constituting an equilibrium – that will occur; thus, he assigns subjective probabilities to players’ actions. Such scenario is formalized as an observable game, which is a newly introduced structure for that purpose. Then, we study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, called the PCE-COHERENCE problem. We show several results concerning algorithms and complexity for PCE-COHERENCE when pure Nash equilibria and specific classes of games, called GNP-classes, are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed in GNP-classes of 2-player games.

2022Journal article

Open access

Belief revision and computational argumentation: a critical comparison

Publication . Baroni, Pietro; Fermé, Eduardo; Giacomin, Massimiliano; Simari, Guillermo Ricardo

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reason ing they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and on the other hand pointing out open issues and potential directions for future research.

2022Journal article

Open access

On the logic of theory change iteration of KM-update

Publication . Fermé, Eduardo; Gonçalves, Sara

We present a model for iterating the Katsuno and Mendelzon Update (KM-Update) process, which is inspired by models developed for iterated belief revision in the AGM framework. Our model adapts the postulates of belief revision proposed by Darwiche and Pearl, including the independence postulate. We characterize two classes of iterated update operators based on natural and lexicographic revision. The semantics of our models are characterized using the framework of possible worlds.

2023-11Journal article

Open access