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Structure itself, though important, is not the crucial determining or characteristic factor for models; semantic interpretation is. Structure is a side effect of the degree of semantic interpretation required. Knowledge (as encoded in ontologies, for example) is the relatively complex symbolic modeling (representation) of some aspect of a universe of discourse (i.e., what we are calling subject areas, domains, and that which spans domains).
Semantic interpretation is the mapping between some structured subset of data and a model of some set of objects in a domain with respect to the intended meaning of those objects and the relationships between those objects.
Tree Directed Acyclic Graph
0 Node ► Directed Edge
Figure 8.3 Trees and graphs.
Typically, the model lies in the mind of the human. We as humans "understand" the semantics, which means we symbolically represent in some fashion the world, the objects of the world, and the relationships among those objects. We have the semantics of (some part of) the world in our minds; it is very structured and interpreted. When we view a textual document, we see symbols on a page and interpret those with respect to what they mean in our mental model; that is, we supply the semantics (meaning). If we wish to assist in the dissemination of the knowledge embedded in a document, we make that document available to other human beings, expecting that they will provide their own semantic interpreter (their mental models) and will make sense out of the symbols on the document pages. So, there is no knowledge in that document without someone or something interpreting the semantics of that document. Semantic interpretation makes knowledge out of otherwise meaningless symbols on a page.4
If we wish, however, to have the computer assist in the dissemination of the knowledge embedded in a document—truly realize the Semantic Web—we
4For an extended discussion of these issues, including the kinds of interpretation required, see Obrst and Liu (2003).
need to at least partially automate the semantic interpretation process. We need to describe and represent in a computer-usable way a portion of our mental models about specific domains. Ontologies provide us with that capability. This is a large part of what the Semantic Web is all about. The software of the future (including intelligent agents, Web services, and so on) will be able to use the knowledge encoded in ontologies to at least partially understand, to semantically interpret, our Web documents and objects.
In formal language theory, one has a syntax and a semantics for the objects of that syntax (vocabulary), as we mentioned previously in our discussion of the syntax of programming languages and database structures. Ontologies try to limit the possible formal models of interpretation (semantics) of those vocabularies to the set of meanings you intend. None of the other model types with limited semantics—taxonomies, database schemas, thesauri, and so on—does that. These model types assume that humans will look at the "vocabularies" and magically supply the semantics via the built-in human semantic interpreter: your mind using your mental models.
Ontologists want to shift some of that "semantic interpretative burden" to machines and have them eventually mimic our semantics—that is, understand what we mean—and so bring the machine up to the human, not force the human to the machine level. That's why, for example, we are not still programming in assembler. Software engineering and computer science has evolved higher-level languages that are much more aligned with the human semantic/conceptual level. Ontologists want to push it even farther.
By machine semantic interpretation, we mean that by structuring (and constraining) in a logical, axiomatic language (i.e., a knowledge representation language, which we discuss shortly) the symbols humans supply, the machine will conclude via an inference process (again, built by the human according to logical principles) roughly what a human would in comparable circumstances.
For a fairly formal example of what's involved in trying to capture the semantics of a knowledge representation language such as the Semantic Web languages of RDF/S and DAML+OIL in an axiomatic way, see Fikes and McGuinness (2001). For an example that attempts to capture the semantics of a knowledge representation language with the semantic model theory approach, see Hayes (2002), who presents a model-theoretic semantics of RDF/S. In principle, both the axiomatic and the model-theoretic semantics of these two examples should be equivalent.
This means that given a formal vocabulary—alphabet, terms/symbols (logical and nonlogical), and statements/expressions (and, of course, rules by which to form expressions from terms)—one wants the formal set of interpretation models correlated with the symbols and expressions (i.e., the semantics) to