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Quantified logic of awareness and impossible possible worlds

By Giacomo Sillari


Abstract. Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have “epistemological” access; since such worlds need not behave consistently, the agents ’ knowledge is fallible relative to logical omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive. §1. Introduction. One of the contributions of this paper consists of the formal comparison between a first-order version of Fagin and Halpern’s logic of awareness 1,onthe one hand, and a version of Rantala’s quantified epistemic logic interpreted over impossible worlds structures, on the other. The semantics of both systems are here given by neighborhoo

Year: 2008
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