A symbolic logical framework (L) consisting of first order logic augmented with a causal calculus has been provided to formalize, axiomatize and integrate theories of design. L is used to represent designs in the Function-Behavior-Structure (FBS) ontology in a single, widely applicable language that enables the following: seamless integration of representations of function, behavior and structure; and generality in the formalization of theories of design. FRs, constraints, structure and behavior are represented as sentences in L. FRs are represented (as abstractions of behavior) in the form of existentially quantified sentences, the instantiation of whose individual variables yields the representation of behavior. This enables the logical implication of FRs by behavior, without recourse to apriori criteria for satisfaction of FRs by behavior. Functional decomposition is represented to enable lower level FRs to logically imply the satisfaction of higher level FRs. The theory of whether and how structure and behavior satisfy FRs and constraints is represented as a formal proof in L. Important general attributes of designs such as solution-neutrality of FRs, probability of satisfaction of requirements and constraints (calculated in a Bayesian framework using Monte Carlo simulation), extent and nature of coupling, etc. have been defined in terms of the representation of a design in L. The entropy of a design is defined in terms of the above attributes of a design, based on which a general theory of what constitutes a good design has been formalized to include the desirability of solution-neutrality of (especially higher level) FRs, high probability of satisfaction of requirements and constraints, wide specifications, low variability and bias, use of fewer attributes to specify the design, less coupling (especially circular coupling at higher levels of FRs), parametrization, standardization, etc..
Arguing Satisfaction of Security Requirements