Common Knowledge and Quantiication

The paper consists of two parts. The rst one is a concise introduction to epistemic (both propositional and predicate) logic with common knowl-ege operator. As the full common knowledge predicate logics 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-nite Hilbert-style axiomatizations and single out a number of their decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable.