Validity of Models and Classes of Models in Semantic Composability

Composability is the capability to select and assemble simulation components in various combinations into simulation systems. The defining characteristic of composability is the ability to combine and recombine components. Composability exists in two forms, syntactic and semantic (also known as engineering and modeling). Syntactic composability is the implementation of components so that they can be combined. Semantic composability is the question of whether the models embodied by the composed components can be meaningfully composed. A theory of semantic composability has been developed that examines the semantic composability of models using formal definitions and reasoning. In this paper results of semantic composability theory concerned with validity are presented. After briefly restating formal definitions of model and simulation, labeled transition systems are defined and introduced as models of the computation of models and compositions. Bisimulation, which is a general relation between the states of labeled transition simulations, is specialized with the addition of a validity metric, and shown to serve as a formal definition of validity. The power of different validity metrics to represent application-specific validity is explained. Classes of models are defined and compared with the models used in simulation. Certain classes of models and validity metrics for which validity is (or is not) preserved under composition are defined and their validity (or lack thereof) under composition is proven.