On the Equivalence of Incremental and Fixpoint Semantics for Business Entities with Guard-Stage-Milestone Lifecycles

Business entities with lifecycles (BEL’s) (a.k.a. business artifacts) are used to model conceptual entities that are central to guiding the operations of a business, and whose content changes as they move through those operations. The recently introduced Guard-StageMilestone (GSM) meta-model for BEL lifecycles is declarative in nature, and allows concurrent execution of long-running (possibly humanexecuted) activities. Modularity is incorporated through the use of hierarchical clustering of activities. The GSM operational semantics is based on a variant of Event-Condition-Action (ECA) rules, which are used to control the start and termination of individual and composite activities. This paper introduces, in an abstract setting, three different and provably equivalent formulations of the GSM operational semantics. The semantics is specified in terms of how a single external event is incorporated into the current “snapshot” (i.e. full description) of a running execution of a BEL model. The “incremental” formulation corresponds to the sequential application of the ECA-like rules in response to the event; the “fixpoint” formulation characterizes the mathematical properties of pairs of snapshots corresponding to the full impact of incorporating the event; and the “closed-form” formulation captures the fixpoint one in terms of first-order logic. The paper introduces a formally specified wellformedness condition on GSM models that guarantees the equivalence of the three formulations while permitting all of the commonly arising patterns for using GSM constructs to model business operations.