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Common knowledge and quantification 总被引:5,自引:0,他引:5
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 相似文献
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