Common knowledge and quantification |
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Authors: | Holger Sturm Frank Wolter Michael Zakharyaschev |
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Institution: | Institut für Informatik, Universit?t Leipzig, Augustus-Platz 10-11, 04109 Leipzig, GERMANY, DE Department of Computer Science, King's College, Strand, London WC2R 2LS, U.K., GB
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Abstract: | Summary. The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate)
logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable,
in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic
operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge
predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable
subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable.
Received: March 7, 2001; revised version: April 4, 2001 |
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Keywords: | and Phrases: Epistemic logic Common knowledge First-order epistemic logic Axiomatizability Monodic fragments |
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