On Natural Deduction in First-Ortder Fixpoint Logics

In the current paper we present a powerful technique of obtaining natural deduction proof systems for rst-order xpoint logics. The term xpoint logics refers collectively to a class of logics consisting of modal logics with modalities deenable at meta-level by xpoint equations on formulas. The class was found very interesting as it contains most logics of programs with e.g. dynamic logic, temporal logic and the-calculus among them. In this paper we present a technique that allows us to derive automatically natural deduction systems for modal logics from xpoint equations deening the modalities.