A Logical Characterization of a Reactive System Language

Typical reactive system languages are programmed by means of rules of the form if antecedent then consequent. However, despite their seemingly logical character, hardly any reactive system languages give such rules a logical interpretation. In this paper, we investigate a simplified reactive system language KELPS, in which rules are universally quantified material implications, and computation attempts to generate a model that makes the rules true. The operational semantics of KELPS is similar to that of other reactive system languages, and is similarly incomplete. It cannot make a rule true by making its antecedent false, or by making its consequent true whether or not its antecedent becomes true. In this paper, we characterize the reactive models computed by the operational semantics. Informally speaking, a model is reactive if every action in the model is an instance of an action in the consequent of a rule whose earlier conditions are true.