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the semantic web a gide to the future of XML, Web Services and Knowledge Management - Daconta M,C.

Daconta M,C. the semantic web a gide to the future of XML, Web Services and Knowledge Management - Wiley publishing , 2003. - 304 p.
ISBN 0-471-43257-1
Download (direct link): thesemanticwebguideto2003.pdf
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Even in the context of the party, Harry Jones could have other properties (we also sometimes call these properties predicates, meaning they are predications or statements/descriptions that hold or synonymously are true of a particular individual). He could be "the drummer for the CyberHogs" or "the husband of that woman who works in the Accounting Department who is always complaining at our staff meetings about the lack of microwaves available to employees." The same individual can have multiple properties at the same or different times. Conversely, the same properties can apply to different individuals at the same or different times.
Developing an Ontology (Theory) of Interesting Things
In this section, we describe the difference between an intension and an extension by giving an extended example. A simple example of the distinction between intension and extension in a pseudo-formal/natural language is the following.
Class Father:
Subclass_of: Person Subclass_of: Male
Father_of: <default: none>, <range: Person>, constraints: <non-reflexive, anti-symmetric>
This roughly means that no Father is his own Father (nonreflexive). If X is the Father_of Y, Y is not the Father_of X (antisymmetric), though of course if X is a Father and the Father_of Y, Y can be a Father.
There will probably be additional properties inherited from the Person and Male classes, such as:
Works_at: <company>, etc.
Chapter 8
This is a formal description/specification of what a Father is and what properties a Father has. Following is a formal description/specification of what a specific instance of the class Father is (John Q. Public) and what specific property values that instance of a Father has:
Instance John Q. Public Instance_of: Father
Father_of: <person instances: <Ralph R. Public>, <Sally S. Public» Lives_at: <location instance: <123 Main St.>>
Work_at: <company instance: <Very Big Company, Inc.>>, etc.
A simplified way to state this is as follows:
Intension. Father(X), where X is a variable for the domain (Male Person)
Extension. {John Q. Public, ...}, that is, the actual set of instances/individuals who are X for whom it is true that Father(X)
The important point here is that an intension is a description I, and an extension E is the set of things that actually have those properties of I (in a given database, object model, universe of discourse, world)—that is,
Some description I holds of (is true of) some set of individuals E. For example:
I: The current President of the United States E: {George W. Bush}
The same I a few years ago would have had a different E: {Bill Clinton}:
I: The man in the hat over there E: {Harry Jones}
The same I yesterday would have had a different E: {Joe}.
Now, the various technical communities will call I the following: a taxonomy, a schema, a conceptual/object model, an intensional semantics, an ontology. They will call E the following, respectively: leaves of the taxonomy (meaning: the bottommost objects in a taxonomy), tuples, instances, the extension, instances/individuals.
So what does all of this mean to you? It means that in an ontology (or its correlate), you describe a set of structured, generic properties that have a particular semantics (meaning). This is called a model, meaning that it defines and represents information about some aspects of the world that you (as the modeler) care to model.
For example, in an ontology, you could represent information describing the semantics of many domains: person, location, event, and so on, and the relationships among them (a person is at a location when an event occurs, a person causes an event to occur at a location, a person is in some relation to an event that occurs at a location, and so on).
Understanding Ontologies
Let's say you're a marketing analyst and you'd like to develop an ontology that would represent the things you are currently interested in. This ontology (if it's a high-end ontology, we would call it a logical theory) would use the usual domain ontologies (or correlates), in other words, the usual generic knowledge/semantics about persons, locations, events—assuming you had such, which unfortunately we don't have much of today. It would be a model of My Theory of Interesting Things; at the top that might consist of the following description/specification. Let's give an example of this kind of intension I:
I_1: Person P at Location L while Event E occurs is Interesting: where P is any Person, Location L ranges over {US_Cities, Canada_Cities, Mexico_Cities} and Event Ev ranges over the conjunction of the following event types: {Credit_Card_Purchases_of_Sporting_Events AND Credit_Card_Purchases_of_Book_Merchandise AND Credit_Card_Purchases_of_Clothing_Merchandise}
This means that we are interested only in those persons who purchased sporting events, book merchandise, and clothing merchandise using credit cards. Now, let's assume that this I is defined at a specific Time T, December 19, 2002. At that time, I had an extension consisting of the following:
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