An Adequate Logic for Heterogeneous Systems

Abstract

Abstract-We coalgebraically define a unified semantics for systems with an emphasis on the notion of time. Such a semantics intends to formalize system that underly system engineering (i.e. the discipline focusing on the integration mastery of large industrial systems). Moreover, we give a formal meaning to another important aspect of systems engineering : system requirements, constraining the expected properties of a system. To express such requirements, we define a logic that extends µ-calculus to our coalgebraic definition of systems. We establish an important property of this logic: adequacy.

A Logic for Complex Computing Systems: Properties Preservation Along Integration and Abstraction

“…where components can be defined over discrete or continuous time scales). To do so, first we propose to introduce the notion of monad to components in [2] to take into account different computation situations, and then to study the results of properties preservation for the logic defined in [3]. Thus, the defined formalism would be allowed to be used as a formal semantics for the system modelling language SysML.…”

“…Of course, as already said in the introduction, the logic will be allowed to be restricted to the propositional case. Within the formalism in [2,3], particular attention should be given to time scale mainly when dealing with continuous times. Indeed, although continuous time scales in [2,3] are discretely defined and then (non-standard) induction works, their cardinality is not denumerable which is not to allow their computability.…”

“…Within the formalism in [2,3], particular attention should be given to time scale mainly when dealing with continuous times. Indeed, although continuous time scales in [2,3] are discretely defined and then (non-standard) induction works, their cardinality is not denumerable which is not to allow their computability. In a series of papers, Y. Sergueyev has recently defined a positional numeral system that may allow us to carry out effective computation with infinitesimal and infinitely large numbers [39,40].…”

“…In a series of papers, Y. Sergueyev has recently defined a positional numeral system that may allow us to carry out effective computation with infinitesimal and infinitely large numbers [39,40]. We then propose to study how to introduce the ideas developed in [39,40] within the formalism developed in [2,3], with defining algorithms issues in mind both for the synthesis and properties satisfaction in the presence of complex heterogeneous (discrete and continuous) systems.…”

“…More precisely, following our work in [3], we propose a variant of first-order fixed point modal logic [26,44]. This extension to the first-order will allow us to export expected properties from components to systems, and thus allowing to study their preservation along integration operators.…”