By Jerng H.H.
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Extra resources for Final Fantasy X. Manual
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But for the updated plausibility relation we need to take into account a third possibility: the case when either the initial states or the actions are distinguishable, belonging to different information cells. 6 (A Third Sample Case). , non-comparable): ¬P • P • This means that, if given the supplementary information that the real state is either s or s′ , the agent immediately knows which of the two is the real states, and thus she knows whether P holds or not. It is obvious 44 A. Baltag, S. Smets that, after any of the actions considered in the previous two examples, a perfect-recall agent will continue to know whether P held or not, and so the output-states after σ and σ ′ will still be distinguishable (non-comparable).
11–24. [10] A. Baltag & S. Smets. The logic of conditional doxastic actions: a theory of dynamic multi-agent belief revision. In S. Artemov & R. , Proceedings of ESSLLI Workshop on Rationality and Knowledge, pp. 13–30. ESSLLI, 2006. [11] A. Baltag & S. Smets. From conditional probability to the logic of doxastic actions. In D. , Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), pp. 52– 61. UCL Presses Universitaires de Louvain, 2007. [12] A. Baltag & S.
This notion is called “strong belief” by Battigalli and Siniscalchi [13], while Stalnaker [51] calls it “robust belief”. Another characterization of strong belief is the following s |= Sba Q iff: s |= Ba Q and s |= BaP Q for every P such that s |= ¬Ka (P → ¬Q). In other words: something is strong belief if it is believed and if this belief can only be defeated by evidence (truthful or not) that is known to contradict it. An example is the “presumption of innocence” in a trial: requiring the members of the jury to hold the accused as “innocent until proven guilty” means asking them to start the trial with a “strong belief” in innocence.
