In natural language, individual things are typically referenced by proper names or definite descriptions. Data modeling languages differ considerably in their support for such linguistic reference schemes. Understanding these differences is important both for modeling reference schemes within such languages and for transforming models from one language to another. This chapter provides a comparative review of reference scheme modeling within the Unified Modeling Language (version 2.5.1), the Barker dialect of entity relationship modeling, Object-Role Modeling (version 2), relational database modeling, the Web Ontology Language (version 2.0), and LogiQL (an extended form of datalog). The authors identify which kinds of reference schemes can be captured within these languages as well as those reference schemes that cannot be captured. The analysis covers simple reference schemes, compound reference schemes, disjunctive reference, and context-dependent reference schemes.
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In this article, the term “object” means any individual thing. If an object is currently in our view, we may refer to that object simply by ostension (pointing at the object). Whether or not an object is in view, we may refer to it by using a linguistic expression. This allows us to reference concrete objects from the past (e.g. Einstein), the present (e.g. this article), or the future (e.g. the next solar eclipse), as well as intangible objects (e.g. a specific course in logic).
An information system models a specific universe of discourse (UoD), also known as a business domain (a world about which users wish to discourse within the business). For example, one UoD might concern a company’s product sales, while another UoD might deal with flight bookings. In natural language, linguistic expressions used to reference objects within a given UoD are typically proper names (e.g. “Donald Trump”) or definite descriptions (e.g. “the president of the USA”) (Allen, 1995).
In philosophy, many proposals exist regarding the precise nature of proper names (e.g. see http://plato.stanford.edu/entries/rigid-designators/). The term “possible world” may be assigned different meanings. In this article, a possible world is treated as a state of the UoD being modeled by an information system, and proper names are treated as rigid identifiers within the UoD of interest. Definite descriptions are often characterized as non-rigid, since some of them may refer to different objects in different possible worlds. For example, if we take “the president of the USA” as shorthand for “the current president of the USA”, then uttering this expression in 2016 refers to Barack Obama, while uttering the same expression in 2018 refers to Donald Trump—a simple example of deixis where the denotation of a term depends on its context (in this case, the time of utterance). However, given our sense of possible world, some definite descriptions are rigid designators (within a given UoD). For example, if we restrict the UoD to our world history, the definite description “the 45th president of the USA” always refers to Donald Trump. Moreover, if we further restrict the UoD to the year 2018 then “the president of the USA” is a rigid designator within that UoD.