Formal requirement management for the Responsive and Formal Design process

In this paper, we present the formal requirement management of the Responsive and Formal Design (RFD) process that extracts a formal theory from requirements written in a natural language. The RFD process was developed as a procedure used in designing Cyber-Physical Systems (CPS) and represents an integration of Model-Based Systems Engineering (MBSE) with formal methods to ensure a 'correct-by-construction' design. The extraction of a formal theory is based on Channel Theory as developed by Barwise and Seligman, which is established as a framework for the 'flow of information' in terms of category theory. A system consists of components connected via channels. Each component is viewed as an information-flow network and mathematically modeled using a notion of a classification. A classification is a table representation of an information-flow network. Regularities (that represent global behavior of the system) of a classification are captured using a theory (a set of formulas or constraints). One goal of the RFD process is to insure that the requirements are formally consistent. In this paper, we develop a set of algorithms that extracts a theory from a classification, though the theory is not necessarily unique. This work is inclusive of an algorithm which checks whether a regular closure (based on structural rules) of a theory is a theory of a given classification. An example of this work is demonstrated through a satellite communication Store and Forward operation.