Advanced Local Checking of Global Consistency in Heterogeneous Multimodeling

Software design requires deployment of interdependent models conforming to different metamodels. This set of models is called a multimodel, and it must satisfy a set of global constraints regulating interaction of the multimodel components. A straightforward approach to global consistency checking would require merging component metamodels modulo their overlap, adding, perhaps, new global constraints to this merge, merging component models modulo their overlap, and checking the latter merge against the constraints in the former one. Being a natural definition for global consistency, these steps can not be used algorithmically because of two major practical drawbacks: they involve costly (meta)model matching to specify overlaps, and require building big and unfeasible merged metamodels and models. The present paper makes two contributions. First, it presents a new algorithm to check each global constraint individually, and as local as possible, i.e., only using those (meta)model elements that affect the validity of the constraint. Second, it develops a mathematical foundation that allows us to formally prove that this individual local consistency checking is sound and complete w.r.t. the definition of global consistency.