Characterization of systems properties by F-Morphism as a new morphism for similarity

This paper introduces a new concept of a morphism, called F-morphism, which makes it possible to discuss the similarity between models of different types. As one of the applications of F-morphisms this paper will characterize systems properties by an equivalence relation defined on them. In this paper a first order language is employed as a language to describe system models, and systems properties are represented as a set of sentences of those languages. As an example, some systems properties of a state-transition system are characterized using F-morphisms. The result of the framework developed in this paper will show that the concept of reachability essentially depends on how the time scale of a dynamical system is recognized.