Logical vs. Behavioural Specifications

There are two fundamentally different approaches to specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations. In this paper we provide translations between the logical formalism of nu-calculus and the behavioural formalism of disjunctive modal transition systems. The translations preserve structural properties of the specification and allow us to perform logical operations on the behavioural specifications as well as behavioural compositions on logical formulae. The unification of both approaches provides additional methods for component-based stepwise design