Dynamic Epistemic Logic makes it possible to model and reason about information change in multi-agent systems. Information change is mathematically modeled through epistemic action Kripke models introduced by Also, van Ditmarsch interprets the information change as a relation between epistemic states and sets of epistemic states and to describe it formally, he considers a special constructor LB called learning operator. Inspired by this, it seems natural to us that the basic source of information change in a multi-agent system should be learning an announcement by some agents together, privately, concurrently or even wrongly. Hence moving along this path, we introduce the notion of a learning program and prove that all finite K45 action models can be described by our learning programs
By introducing @math models and actions, we may think of a theory of multi-agent belief revision. A related work is @cite_11 , which generalize AGM @cite_12 , to a multi-agent belief revision theory.
@cite_12 @cite_11
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We generalize AGM belief revision theory to the multi-agent case. To do so, we first generalize the semantics of the single-agent case, based on the notion of interpretation, to the multi-agent case. Then we show that, thanks to the shape of our new semantics, all the results of the AGM framework transfer. Afterwards we investigate some postulates that are specific to our multi-agent setting. In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called ''dynamic'' belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a ''cheating version'' of the Muddy Children Puzzle. In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourron, Gardenfors and Makinson (AGM revision, (1985)). The approach is illustrated by considering the modal logic K , Belnap's four-valued logic, and Łukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we analyse in what circumstances the properties of the AGM revision are preserved and discuss the advantages of the approach from both theoretical and practical viewpoints. This paper describes a change theory based on abductive reasoning. We take the AGM postulates for revisions, expansions and contractions, and Katsuno and Mendelzon postulates for updates and incorporate abduction into them. A key feature of the theory is that presents a unified view of standard change operators and abductive change operators rather than a new and independent change theory for abductive changes. Abductive operators reduce to standard change operators in the limiting cases.