Loose Semantics and Constraints for Graph Transformation Systems
Reiko Heckel, Hartmut Ehrig, Uwe Wolter, Andrea Corradini · 1997
. 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 defined 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 defined, which associates with each system a category of models (deterministic transition systems) defined as coalgebras over a suitable functor. Such category has a final object, which includes all finite and infinite transition sequences. Constraints are introduced in order to restrict the loose semantics of graph transformation systems. The coalgebraic framework makes it possible to define a general notion of logic of behavioural constrai...