The logic-algebraic equations method in system dynamics

Abstract

Abstract. An algorithm is proposed for constructing conditions that ensure the preservation of properties of many-sorted algebraic systems. The functions and relations of such systems are defined on arbitrary steps in the sense of Bourbaki. Preservation conditions are generated as solutions of logic-algebraic equations. The coupling mappings between systems have a nature of morphisms and their canonical expansions to steps. The method is illustrated by the example of analysis of a dynamical property of a discrete-event system.

Derivation of preservation conditions for properties of mathematical models

“…The reduction method [6] is free of a number of limitations of the comparison method and consists in determining non trivial solutions D of logical equations, such as equa tions of the form D & A → (P' → P), where, as previ ously, the known terms A, P', and P of the equation must satisfy certain consistency conditions. In [7], for polybasic algebraic systems and their properties expressible in a language with appropriate signature, a method for obtaining solutions D without the a priori conditions A was proposed. Other known methods for solving logical equations of general and special form are not applicable, because they do not take into account the specifics of the preservation problem under consideration.…”