Formal semantics of the unified modeling language [formula omitted

Abstract

A formal semantics is an essential element of language design because it supports comparison of language designs, provides implementation guidelines, and enables properties about a language to be proved. However, in the field of model management, there has been a lack of attention to the formal semantics of modeling languages. In this paper, the philosophy and formal semantics of the Unified Modeling Language ( L U ) are presented. The L U supports integrated modeling environments with a large number of models from diverse domains and management science paradigms. We discuss the philosophy of the L U in which logical deduction about empirical worlds is combined with efficient computations about mathematical worlds. We argue that measurement theory stressing homomorphic mappings from empirical to mathematical worlds is an ideal foundation for integrated modeling environments. A denotational semantics is given for the L U including the semantic domain, meta functions, and semantic equations. The L U is unique because measurement theory plays a salient role in its underlying denotational semantics. In particular, the semantic domain of the L U includes explicit homomorphic mappings from empirical to mathematical worlds and semantic equations define conditions, based on homomorphisms, that must be satisfied by valid models.