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The Entity-Relational (ER) model or language (and the Enhanced or Extended ER or EER model)7 that is used to define a conceptual schema for a database is also considered a conceptual modeling language. When one designs a database, one first creates a conceptual schema (which is where the initial conception of the domain of the eventual database is modeled), reduces that to a logical schema, and finally reduces that in turn to a physical schema. These schemas represent levels of abstraction: from the human conceptual level to the database table/column level to the actual implemented tables, columns, and keys.
The upper-right endpoint designates a logical theory. Ontologies represented as logical theories are directly semantically interpretable by our software. This is the high-end notion of an ontology: a logical theory. Much of current ontological engineering and knowledge representation (we will talk about these disciplines in more detail later) aspires to building ontologies as logical theories. We investigate ontologies and Semantic Web languages used to express ontologies more in Chapter 8. For now, all we need to say about logical theories is that they are built on axioms (a range of primitive to complex statements asserted to be true) and inference rules (rules that, given premises/ assumptions, provide valid conclusions), which together are used to prove theorems about the domain represented by the ontology-as-logical-theory. The whole set of axioms, inference rules, and theorems together constitute the logical theory.
In a logical theory, we can express the semantics of a model to the highest degree possible. The subclass of relation can become a richer relation, perhaps defined as the disjoint subclass of relation with the property of transitivity. A class's superclass relation to its subclasses can also be defined as exhaustive— that is, the subclasses exhaustively partition the superclass. Similar fine semantic distinctions can be made of relations and attributes, and other modeling constructs such as facets, which represent meta data associated with relations (or assertions on assertions).
Now that we have looked at the Ontology Spectrum, ranging from taxonomies to logical theories, can we define what an ontology is? Let's look at a preliminary definition and save the elaboration until next chapter. An ontology defines the common words and concepts (meanings) used to describe and represent an area of knowledge, and so standardizes the meanings. Ontologies are used by
7 For the distinction between ER and EER and the kinds of schemas built for databases, refer to nearly any standard database text. We like Halpin (1995) and Ullman (1989).
people, databases, and applications that need to share domain information (a domain is just a specific subject area or area of knowledge, like medicine, counterterrorism, imagery, automobile repair, etc.). Ontologies include computer-usable definitions of basic concepts in the domain and the relationships among them. They encode knowledge in a domain and also knowledge that spans domains. So, they make that knowledge reusable.
An ontology includes the following:
■ Classes (general things) in the many domains of interest
■ Instances (particular things)
■ Relationships among those things
■ Properties (and property values) of those things
■ Functions of and processes involving those things
■ Constraints on and rules involving those things
Having completed our discussion of the Ontology Spectrum, let's now turn to describing a language (actually a language and an entire modeling paradigm) that is often used to model Web objects and the things that can be said of Web objects, and that can structure that model into a taxonomy or a set of taxonomies.
This section briefly describes Topic Maps (sometimes abbreviated TM). Topic Maps is a technology that has arisen in recent years to address the issue of semantically characterizing and categorizing documents and sections of documents on the Web with respect to their content—in other words, what topics or subject areas those documents actually address. As such, they are closely related to other efforts in general characterized as the Semantic Web. Topic Maps provides a content-oriented index into a set of documents, much like the index of a book but with this qualification: an index of a book does not typically characterize the contents of that book as a set of linked topics, but rather as a set of mostly isolated subject references with occasional cross-references to other subjects.
A Topic Map, however, does act as a set of linked topics that index a document collection. In addition, in the Topic Maps paradigm, one can have multiple topic maps indexing the same Web document collections (much as a book may have multiple indexes, such as a subject index, a name index, and so forth; the important point here is that one can have multiple topic maps indexing the subjects in different ways). Topic maps can be viewed as information overlays on documents or arbitrary information resources. They enable content-based