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AGM Revision in Classical Modal Logics
CENTRIA seminar: AGM Revision in Classical Modal Logics
Main information
By:
Gregory Wheeler
(
CENTRIA
)
Date:
Wednesday, 10th of February 2010, 14h00
Location:
FCT/UNL, Seminar Room (Ed. II)
Abstract
Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. Several current KRR frameworks are based on classical modal logics, particularly monotone systems, including Parikh's Game Logic, Goldblatt's Concurrent Propositional Dynamic Logic, Kyburg and Teng's Risky Knowledge, Alur et. al.'s Alternating-time logic, and Pauly's Coalition Logic. Although revision has been studied for some particular logics in this class, the constructions are tailored and not readily generalizable to cover a wide range of classical systems.
This paper defines AGM revision operators on several first-order classical modal correspondents, where each first-order correspondence language is defined by Marc Pauly's version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into first-order logic, the revision is performed, and the new belief set is translated back to the original modal system. An example is provided for the logic of Risky Knowledge that uses modal AGM contraction to construct counter-factual evidence sets in order to investigate robustness of a probability assignment given an evidence set. A proof of correctness is given, along with pointers to some of the limitations to the approach, and a (very brief) discussion of complexity in the two steps that comprise the translation procedure between classical systems and their first-order correspondents.
Short-bio
Gregory Wheeler is a Senior Research Scientist and member of the board of directors of CENTRIA, The Center for Artificial Intelligence Research at the New University of Lisbon, and is Lecturer in Computational Logic in the Department of Computer Science. He holds a joint PhD in Philosophy and Computer Science from the University of Rochester and works primarily on uncertainty frameworks and the foundations of knowledge representation (a.k.a. formal epistemology). His new book, Probabilistic Logic and Probabilistic Networks (joint with R. Haenni, J-W Romeyn, and J. Williamson) will be published in Springer's Synthese Library Series in 2010.
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