Structural Models in Axiomatic SysML

An overall goal of the INCOSE MBSE initiative is to provide SysML with a formal semantics and to integrate reasoning services as part of system engineering. UML class diagrams have been encoded as Knowledge Bases (KB) within the Description Logic (DL), ALCQI. The encoding provides a formal semantics for class diagrams which accords with the informal semantics. The encoding applies to SysML which is a profile of UML. The SysML block definition and internal block diagrams are not covered by the class diagram encoding. These diagrams are essential for representing composite structure such as manufactured products and molecular structures. The class diagram encoding is extended to composite structure diagrams in the DL ALCQIbid. A composite structure diagram describes structures in terms of part decompositions and connections between objects. A SysML composite structure diagram can be encoded in the language of OWL2, but is not an OWL2 axiom set, as the diagrams contain property equations which violate the regularity ordering constraints for complex property inclusions. Conditions are given for an ALCQIbid KB which are sufficient to encode a SysML composite structure diagram. Further conditions are given for a KB, called a template, which ensure that within an interpretation all realizations of the composite structure have the same graph structure.