Semiotics, entropy, and interoperability of simulation systems — Mathematical foundations of M&S standardization

Semiotics identifies which symbols are used (syntax), what the meaning of these symbols is (semantics), and what the intention of using symbols is (pragmatics). These ideas have already been mapped to integratability of networks, interoperability of simulations, and composability of models for modeling and simulation applications. New research on model theory and algorithmic information theory support this viewpoint. Applying the finding of mathematics allows to define three different entropies: syntactical entropy that measures the variety of data representation, semantic entropy that measures the variety of data interpretation, and pragmatic entropy that measures the variety of data utilization. The paper shows the interconnection between these ideas and their implication for interoperability challenges: standards are needed on all levels to ensure meaningful interoperation, but their application reduces the interoperability space of federated solutions to the intersection of models, not to the union of models as often assumed in naïve approaches.