Temporal Conceptual Modelling with DL-Lite

Conceptual modelling formalisms such as the Entity-Relationship model (ER) and Unified Modelling Language (UML) have become a de facto standard in database design by providing visual means to describe application domains in a declarative and reusable way. On the other hand, both ER and UML turned out to be closely connected with description logics that are underpinned by formal semantics and thus capable of providing services for effective reasoning over conceptual models; see, e.g., [11, 4]. Temporal conceptual data models (TCMs) [18, 25] have been introduced in the context of temporal databases [20, 15, 13]. In this case, apart from the classical constructs—such as inheritance between classes and relationships, cardinality constraints restricting participation in relationships, and disjointness and covering constraints—temporal constructs are used to capture the temporal behaviour of various components of conceptual schemas. Such constructs can be grouped into 3 categories. Timestamping constraints discriminate between those classes, relationships and attributes that change over time and those that are timeinvariant [28, 18, 16, 6, 25]. Evolution constraints control how domain elements evolve over time by ‘migrating’ from one class to another [19, 23, 26, 25, 3]. We distinguish between qualitative evolution constraints describing generic temporal behaviour, and quantitative ones specifying the exact moment of migration. Temporal cardinality constraints restrict the number of times an instance of a class participates in a relationship. Snapshot cardinality constraints do it at each moment of time, while lifespan cardinality constraints impose restrictions over the entire existence of the instance as a member of the class [27, 22]. Temporal conceptual data models can be encoded in various temporal description logics (TDLs), which have been designed and investigated since the seminal paper [24] with the aim of understanding the computational price of introducing a temporal dimension in DLs; see [21] for a recent survey. A general conclusion one can draw from the obtained results is that—as far as there is nontrivial interaction between the temporal and DL components—TDLs based on full-fledged DLs like ALC turn out to be too complex for effective reasoning (see the end of the introduction for details). The aim of this paper is to tailor ‘minimal’ TDLs that are capable of representing various aspects of TCMs and investigate their computational behaviour. First of all, as the DL component we choose the ‘light-weight’ DL-Lite logic Proc. 23rd Int. Workshop on Description Logics (DL2010), CEUR-WS 573, Waterloo, Canada, 2010.