Logic for Modeling Product Structure

A fragment of type theory with OWL class constructions for types and binary properties is used to formalize SysML Structural Block Diagram models. A structural SysML block diagram model is a model that does not have behavior in the sense that values of properties do not change. A structural model may include properties, variables and operations. Individuals are a special case of operators with no arguments. Type theory is chosen as the target semantic formalism as SysML constructions correspond closely to type theory term constructions. The type theoretic semantics defined in terms of introduction and elimination fits well with the informal SysML semantics. An abstract version of a structural model, called an Abstract Block Diagramversion of a structural model, called an Abstract Block Diagram (ABD), is introduced. An ABD is a theory closed under specific type, property, and operator constructions with additional axioms. The ABD corresponding to the SysML model contains axioms in the form of equations for types, and properties, and operators. This formalism captures the syntactic constructons of the SysML models and the type theoretic semantics appears to be in accord with the informal semantics, as documented in the OMG specification. ABD theory gives an explicit mechanism for introducing instances for types defined by property restrictions. This construction is useful for parts decompositions. ABD theory constructions have a limited kind of property union used to construct parts decompositions. An ABD determines a Description Logic (DL) closed under union, intersection, and existential type constructions and property constructions restricted by typing relations. The ABD constructions are useful in identifying potential extensions for SysML and may be useful, as well, for adding operator terms to Description Logic.