Inter-organizational business processes require extensive information sharing between organizations. To acquire a holistic overview of an inter-organizational process, insight in both its control flow and data model is required. Business artifacts are a well-positioned mechanism to model these two dimensions. However, when business artifacts and their associated lifecycle and information models are shared between organizations, a single source of truth is preferred. To maintain such a single source without centralized administration, blockchain-based smart contracts may be used. We claim that an artifact-centric approach to business processes is well-suited for smart contract implementations. However, the conceptual relationship between business process artifacts and smart contracts has not yet been extensively analyzed. In this paper, we present a novel ontological analysis of artifact-centric processes managed by smart contracts. We adopt the method of enterprise ontology and regard an inter-organizational process as a set of causally related transactions in which the state of the lifecycle and associated data objects of business artifacts is transformed by sending messages to smart contracts. Our conceptual models are visualized in OntoUML, a modeling language based on the Unified Foundational Ontology.