Belief Update without Compactness in Non-finitary Languages[zur Übersicht]
How a rational agent should change its beliefs when acquiring a new piece of information is the main subject of Belief Change. The field is underpinned by the idea that an agent should change its beliefs minimally: only beliefs that contradict the new information could be discarded. Rationality postulates, that determine minimal change principles of belief change, and constructions that satisfy such postulates are central in Belief Change. The main paradigms of Belief Change make strong assumptions about the underlying logics used to represent an agent corpus of beliefs, as for instance being Tarskian, Compact and Finitary. Except for propositional logics, and some of its fragments, such as Horn Logic, a number of expressive logics used in AI are non-finitary, as for instance temporal logics such as LTL and CTL. We consider the KM paradigm of belief update, when the underlying logic is not necessarily finitary or compact. We show that, in these logics, the representation theorem between rationality postulates and its standard constructions breaks down. As a remedial measure, we introduce a novel class of belief update constructions that reconnect with all the KM rationality postulates of belief update.
18.06.20 - 10:15
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