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QUANTIFIED LOGIC OF AWARENESS AND IMPOSSIBLE POSSIBLE WORLDS

Published online by Cambridge University Press:  01 December 2008

GIACOMO SILLARI
GIACOMO SILLARI*
Affiliation:
Philosophy, Politics, and Economics Program, University of Pennsylvania
*
*PHILOSOPHY, POLITICS, AND ECONOMICS PROGRAM UNIVERSITY OF PENNSYLVANIA 313 CLAUDIA COHEN HALL PHILADELPHIA, PA 19104 E-mail:[email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 4 , December 2008 , pp. 514 - 529
Copyright
Copyright © Association for Symbolic Logic 2008

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