ИСТИНА

As noticed some 50 years ago, Kripke frame semantics does not fit well for modal predicate logics. This contrasts to the propositional case, when we can expect the logics to be complete. The talk gives an overview of some well-known and some recent results in this field. We are mainly interested in minimal predicate extensions of propositional logics and their Kripke completions.In particular we consider a certain operation of `boxing’, show that it preserves strong Kripke completeness and find axiomatization for `boxed’ logics. We also axiomatize logics of some predicate Kripke frames based on finite trees.