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• W1606793985 abstract "In this paper, we compare two modal frameworks for multi-agent belief revision: dynamic doxastic logics computing stepwise updates and temporal doxastic logics describing global system evolutions, both based on plausibility pre-orders. We prove representation theorems showing under which conditions a doxastic temporal model can be represented as the stepwise evolution of a doxastic model under successive ’priority updates’. We define these properties in a suitable doxastic-temporal language, discuss their meaning, and raise some related definability issues. Analyzing the behavior of agents in a dynamic environment requires describing the evolution of their knowledge as they receive new information. Moreover agents entertain beliefs that need to be revised after learning new facts. I might be confident that I will find the shop open, but once I found it closed, I should not crash but rather make a decision on the basis of new consistent beliefs. Such beliefs and information may concern ground-level facts, but also beliefs about other agents. I might be a priori confident that the price of my shares will rise, but if I learn that the market is rather pessimistic (say because the shares fell by 10%), this information should change my higher-order beliefs about what other agents believe. Tools from modal logic have been successfully applied to analyze knowledge dynamics in multi-agent contexts. Among these, Temporal Epistemic Logic [23], [19]’s Interpreted Systems, and Dynamic Epistemic Logic [2] have been particularly fruitful. A recent line of research [11, 10, 9] compares these alternative frameworks, and [10] presents a representation theorem that shows under which conditions a temporal model can be represented as a dynamic one. Thanks to this link, the two languages also become comparable, and one can merge ideas: for example, a new line The second author was supported by a GLoRiClass fellowship of the European Commission (Research Training Fellowship MEST-CT-2005020841). of research explores the introduction of protocols into the logic of public announcements PAL, as a way of modeling informational processes (see [9]). To the best of our knowledge, there are no similar results yet for multi-agent belief revision. One reason is that dynamic logics of belief revision have only been wellunderstood recently. But right now, there is work on both dynamic doxastic logics [5, 3] and on temporal frameworks for belief revision, with [14] as a recent example. The exact connection between these two frameworks is not quite like the case of epistemic update. In this paper we make things clear, by viewing belief revision as priority update over plausibility pre-orders. This correspondence allows for similar language links as in the knowledge case, with similar precise benefits. We start in the next section with background about earlier results and basic terminology. In section 2 we give the main new definitions needed in the paper. Section 3 presents the key temporal doxastic properties that we will work with. In section 4 we state and prove our main result linking the temporal and the dynamic frameworks, first for the special case of total pre-orders and then in general. We also discuss some variations and extensions. In section 5 we introduce formal languages, providing an axiomatization for our crucial properties, and discussing some related definability issues. We state our conclusions and mention some further applications and open problems in the last section." @default.
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• W1606793985 title "Multi-agent belief dynamics: bridges between dynamic doxastic and doxastic temporal logics" @default.
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