Integrating the Speci cation Techniques ofGraph Transformation and Temporal Logic ?

The aim of this paper is an integration of graph grammars with diierent kinds of behavioural constraints, in particular with temporal logic constraints. Since the usual algebraic semantics of graph transformation systems is not able to express constrained behaviour we introduce-in analogy to other approaches-a coalgebraic semantics which associates with each system a category of models (deterministic transition systems). Such category has a nal object, which includes all nite and innnite transition sequences. The coalgebraic framework makes it possible to introduce a general notion ofìogic of behavioural constraints'. Instances include, for example, graphical consistency constraints and temporal logic constraints. We show that the considered semantics can be restricted to a nal coalgebra semantics for systems with behavioural constraints. This result can be instantiated in order to obtain a nal coalgebra semantics for graph grammars with temporal logic constraints.