Loose Semantics and Constraints for GraphTransformation Systems ?

The main aim of this paper is an extension of the theory of algebraic graph transformation systems by a loose semantics. For this purpose, graph transitions are introduced as a loose interpretation of graph productions. They are deened using a double pullback construction in contrast to classical graph derivations based on double-pushouts. Two characterisation results relate graph transitions to the classical double-pushout derivations and to amalgamated derivations, respectively. Moreover, a loose semantics for graph transformation systems is deened, which associates with each system a category of models (deterministic transition systems) deened as coalgebras over a suitable functor. Such category has a nal object, which includes all nite and innnite transition sequences. Constraints are introduced in order to restrict the loose semantics of graph transformation systems. The coalgebraic framework makes it possible to deene a general notion of logic of behavioural constraints. Instances include, for example , start graphs, application and consistency conditions, and temporal logic constraints. We show that the considered semantics can be restricted to a nal coalgebra semantics for systems with behavioural constraints. Parts of the paper are submitted for publication as HEWC97a,HEWC97b].