Time provides context for all our experiences, cognition, and coordinated collective action. Prior research in linguistics, artificial intelligence, and temporal databases suggests the need to differentiate between temporal facts with goal-related semantics (i.e., telic) from those are intrinsically devoid of culmination (i.e., atelic). To differentiate between telic and atelic data semantics in conceptual database design, we propose an annotation-based temporal conceptual model that generalizes the semantics of a conventional conceptual model. Our temporal conceptual design approach involves: 1) capturing 'what' semantics using a conventional conceptual model; 2) employing annotations to differentiate between telic and atelic data semantics that help capture 'when' semantics; 3) specifying temporal constraints, specifically nonsequenced semantics, in the temporal data dictionary as metadata. Our proposed approach provides a mechanism to represent telic/atelic temporal semantics using temporal annotations. We also show how these semantics can be formally defined using constructs of the conventional conceptual model and axioms in first-order logic. Via what we refer to as the 'semantics of composition,' i.e., semantics implied by the interaction of annotations, we illustrate the logical consequences of representing telic/atelic data semantics during temporal conceptual design.