SOA has influenced business process modeling and management. Recent business process models have elevated data representation to the same level as control flows, for example, the artifact-centric business process models allow the life cycle properties of artifacts (data objects) to be specified and analyzed. In this paper, we develop a specification language ABSL based on computation tree logic for artifact life cycle behaviors (e.g., reachability). We show that given a business model and starting configuration, it can be decided if an ABSL sentence is satisfied when the domains are bounded, and if an ABSL-core (sublanguage of ABSL) sentence is satisfied when the domains are totally ordered but unbounded. We also show that if the starting configuration is not given, ABSL(-core) is still decidable if the number of artifacts is bounded with bounded (resp. unbounded but ordered) domains.