International audience

Belief change is an important topic of knowledge representation and reasoning in artificial intelligence. Within the logical framework, the AGM approach has become a standard and various belief change operations have been considered. While revision, contraction and updating have given rise to a great deal of work, erasure has so far attracted less interest. Erasure is to contraction what update is to revision.This article deals with the study of erasure within the framework of propositional logic. It extends Katsuno and Mendelzon’s approach with additional postulates capturing the minimality of change and proposes two representation theorems for erasure operators, one in terms of total preorders on interpretations, the other in terms of partial preorders on interpretations. Finally, it completes the work of Caridroit, Konieczny and Marquis for contraction by proposing a new representation theorem for contraction operators in terms of partial preorders on interpretations.

Abstract Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments and that the result of revision remains in the fragment under consideration. Later, this notion of refinement was generalized to belief change operators. Whereas refinement allowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction and erasure. We propose a specific notion of refinement for contraction and erasure operators, called reasonable refinement. This allows us to provide refined contraction and erasure operators that satisfy the basic postulates. We study the logical properties of reasonable refinement of two model-based contraction operators and two model-based erasure operators. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Krom and affine fragments.

The present paper describes briefly a project idea in progress about the evolvement of individuals' opinions, beliefs and perceptions on social networks (such as Facebook, Twitter, Instagram, youtube...) which is a thorny subject that has whetted nowadays the curiosity of a hulk of researchers from various disciplines. For this purpose, differently from a lot of works in the literature, we rely on logical knowledge representation tools in order to investigate the belief merging operation of Artificial Intelligence (AI). The major objective of this project is to provide efficient operator for merging heterogeneous, inconsistent and uncertain multiple sources information in the context of social networks taking into account the fact that opinion can be formed and developed through the concept of social influence with its two forms (informational social influence and normative social influence) and the concept of social trust. We intend thus through this research work presenting an adaptative version to our context of an approach [7] expressed thanks to Answer Set Programming (ASP) paradigm with stable model semantics. It is worth to say that our approach profits from the impressive volume data produced by users in social networks about a particular topic by learning from opinions, beliefs and perceptions that their freinds/neighbors share and therefore allows to use this kind of data to extract initial opinions, and to validate the proposed opinions merging process allowing even the prediction of users' behaviors.

Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. In this paper we generalize this notion of refinement to belief change operators. Whereas the notion of refinement allowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction. We propose a specific notion of refinement for contraction operators, called reasonable refinement. This allows us to provide refined contraction operators that satisfy the basic postulates for contraction. We study the logical properties of reasonable refinements of two well-known model-based contraction operators. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Horn, Krom and affine fragments.