Formalizing Both Refraction-Based and Sequential Executions of Production Rule Programs

Abstract Production systems are declarative, in that they do not ex-plicitly specify the control flow. Yet, the concept of a production system does not include the definition of a given control strategy. The control be-tween rules in a production rule program is, in practice, defined by each implementation of a production rule engine. Engines have traditionally been implemented using the Rete algorithm. Since the turn of the cen-tury, however, production systems have evolved into industrial products known as Business Rules Management Systems (BRMS). BRMS have in-troduced new compilation and execution schemes, which are often called sequential in contrast with the incremental behavior of Rete. This change in execution scheme came with a change in semantics for rule programs. In this paper, we propose a formal description of the execution of pro-duction rule programs. Existing descriptions either ignore the control strategy, or assume a Rete semantics. Ours isolates the handling of rule eligibility in the control strategy, which allows us to describe the sequen-tial execution semantics of rule programs, as well as the Rete semantics, and others.