Modal specifications are a syntactic fragment of the Mu-calculus

In this report we introduce modal specifications, a new object dedicated to specify some branching-time properties for systems. Modal specifications are a useful tool for studying Petri net synthesis although this aspect is not presented here. The main purpose of this report is to establish the equivalence between a syntactic fragment of the Mu-calculus, namely the conjunctive Nu-calculus and modal specifications. We give the algorithm for constructing a conjunctive Nu-calculus sentence equivalent to a modal specification and the converse. We also study the structure of the set of models of a modal specification