COCOLOG macro languages and macro actions for logic control

The control of a discrete event system is handled in COCOLOG by use of an extra-logical representation of the control law. The conditional control rules (CCRs) constitute such a representation; they express condition-action rules where the conditions are formulas in the language (L_k) of the current control theory (Th_k) at the instant k which are tested for deducibility. Once one of them is found to be deducible, the control action associated with it is applied to the system. The simplicity of L_k leads to even the simplest concepts having a complex expression as well formed formulas in L_k. Furthermore, the triggering (via the CCRs) of elementary control actions often depends upon complex nested sets of conditional control formulas (CCFs) expressed in L_k. In response to this set of problems, this article presents the foundations for a theory of the expression of complex predicates and functions in terms of simple macro language symbols which can be defined in an extended language L ⁺_k, and for the construction of simple recursive systems of macro actions to express complex control actions