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...

Let z = (z1, z2, · · · , zn) be noncommutative free variables and t a formal parameter which commutes with z. Let k be a unital commutative ring of any characteristic and Ft(z) = z−Ht(z) with Ht(z) ∈ k[[t]]〈〈z〉〉 ×n and o(Ht(z)) ≥ 2. Note that Ft(z) can be viewed as a deformation of the formal map F (z) := z−Ht=1(z) when it makes sense. The inverse map Gt(z) of Ft(z) can always be written as Gt(...