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A proposition for the correct by design of abstraction with respect to the simulation objectives based on the concepts of approximate bisimulation, Galois connections and ontology is presented. It addresses the fundamental problem of fidelity in simulation, namely, given a class of models and a class of properties that must be preserved, how to extract modeling abstractions that preserves the properties of interest which allows to conclude about the system being simulated. Fidelity and validity are explained in the framework of the experimental frame and discussed in the context of modeling abstractions. A formal method for the fidelity quantification is explained by abstraction inclusion relations for syntactic and semantic compatibility. Abstraction inclusion in dynamic systems for semantic compatibility by approximate bisimulation and the problem of finding surjection maps compatible with simulation objectives are discussed. Syntactic compatibility is explained by ontologies followed by a brief discussion on the Galois connections and building Galois surjections compatible with the simulation objectives at the end.

ions of experimental frame components with respect to simulation objectives are discussed with a hybrid system simulation application. Validity assessment through behavioural compatibility criteria described by the trace inclusion framework is given. The simulation objectives are associated with modelling abstractions by such a framework and described in established modeling & simulation framework. Consistent abstractions from hierarchically ordered posets for stimulant and observer models in experimental frame are discussed. A landing gear example is taken and testability through primary experimental frame component abstractions was observed for the given simulation requirements. The formal framework under development is briefly discussed at the end in the context of applicability and derivability of experimental frame and fidelity of simulation.

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A general notion of the simulation fidelity in system verification and validation is explained in the modeling & simulation framework of the experimental frame and discussed in the context of modeling abstractions. A formal method for fidelity measurement is presented for semantic compatibility through abstraction inclusion relations. Behavioral modeling abstractions of dynamical systems consistent with simulation objectives are explained in the experimental frame formalism using bisimulation relations and their approximations. Property-preserving bisimulation relations consistent with the simulation objectives are explained in the context of hierarchical abstractions and composition of experimental frame components. The behavioral fidelity problem is presented by finding bisimilarity preserving surjection maps of desired abstraction precision. In abstraction of linear time invariant systems, the paper discusses the problem of extending the classical results to finding surjections whose null space is a controlled invariant subspace with respect to fidelity requirements. Applicability and derivability of experimental frames are discussed through such consistent abstractions. In conclusion, challenges in research and implementation of a semi-formal unified fidelity framework encompassing both syntactic and semantic aspects are discussed.