Satisfiability of High-Level Conditions

In this paper, we consider high-level structures like graphs, Petri nets, and algebraic specifications and investigate two kinds of satisfiability of conditions and two kinds of rule matching over these structures. We show that, for weak adhesive HLR categories with class A of all morphisms and a class M of monomorphisms, strictly closed under decompositions, Aand M-satisfiability and Aand M-matching are expressively equivalent. The results are applied to the category of graphs, where M is the class of all injective graph morphisms.