Process calculi and graph transformation systems provide models of reactive
systems with labelled transition semantics. While the semantics for process
calculi is compositional, this is not the case for graph transformation
systems, in general. Hence, the goal of this article is to obtain a
compositional semantics for graph transformation system in analogy to the
structural operational semantics (SOS) for Milner's Calculus of Communicating
Systems (CCS).
The paper introduces an SOS style axiomatization of the standard labelled
transition semantics for graph transformation systems. The first result is its
equivalence with the so-called Borrowed Context technique. Unfortunately, the
axiomatization is not compositional in the expected manner as no rule captures
"internal" communication of sub-systems. The main result states that such a
rule is derivable if the given graph transformation system enjoys a certain
property, which we call "complementarity of actions". Archetypal examples of
such systems are interaction nets. We also discuss problems that arise if
"complementarity of actions" is violated.Comment: In Proceedings ICE 2011, arXiv:1108.014