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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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Chapter 8
approximate those models that a human would identify as those he or she intended (i.e., close to the human conceptualization of that domain space). The syntax is addressed by proof theory, and the semantics is addressed by model theory. One way of looking at these relationships is depicted in Figure 8.4. In this figure, the relationship between an alphabet and its construction rules for forming words in that alphabet is mapped to formal objects in the semantic model for which those symbols and the combinatoric syntactic rules for composing those symbols having a specific or composed meaning. On the syntactic side, you have symbols; on the semantic side, you have rules. In addition, you have rules mapping the constructs on the syntactic side to constructs on the semantic side.
The important issue is that you have defined a specification language that maps to those semantic objects that you want that language and its constructs to refer to (i.e., to mean). If those syntactic constructs (such as Do or While or For or Goto or Jump or Shift or End or Catch or Throw) do not correspond (or map) to a semantic object that corresponds to what you want that syntactic object to mean. "Do" in a programming language such as C means that you enter a finite state automaton that enforces particular transitions between states that:
■ Declare what input values enable the state transition; what values are used, consumed, and transformed; and what values are output (think of a procedure or function call that passes arguments of specific types and values and returns results of specific types and values).
■ Performs other tasks called side effects, or arbitrary other things that are not directly functions of the input.
Figures 8.4 to 8.6 illustrate a specific example of the mapping between the syntax and semantics of a programming language. Syntactic objects are associated with their semantic interpretations, each of which specifies a formal set-theoretic domain and a mapping function (that maps atomic and complex syntactic objects to semantic elements of the formal domain). Figures 8.4 to 8.6 display, respectively, the mapping between syntactic objects and a simple semantics for those objects, then a mapping between a simple semantics and a complex semantics for those objects, and finally between a complex semantics and an even more complex semantics for those objects. The mappings between semantics levels can also be viewed as simply the expansion of the semantics from more simple to more complex elaborations
In Figure 8.4, the syntactic objects are mapped to a descriptive shorthand for the semantics. "zDLKFL" is a string constant, "4+3" is an addition operation, and so on.
Understanding Ontologies
199
Syntax
Simple Semantics String Constant IntegerConstant IntegerType Variable Variable
Addition(Integer Type
■►Negation Boolean Type (Boolean Type Variable InclusiveOr Boolean Type Variable)
Type Constant)
Constant, Integer
Figure 8.4 Mapping between syntax and semantics.
Figure 8.5 expands that simple shorthand for the semantics to a more complex semantics based on set theory from mathematics. "zDLKFL," which is a string constant, is elaborated to be a specific string that is an element from the set of all possible strings (an infinite set) composed of ordinary English letters (we loosen our formal notation here some, but you should understand *S* to be the infinite expansion of all possible strings from the English alphabet). In both Figures 8.5 and 8.6, we have attached the note "* Where [[X]] signifies the semantic or truth value of the expression X." The next section on logic discusses truth values (a value that is either true or false). The semantic value is a little more complicated than that, and we will not get into it in much detail in this book.5 Suffice it to say that the semantic value of a term is formalized as a function from the set of terms into the set of formal objects in the domain of discourse (the knowledge area we are interested in).
Figure 8.6 elaborates the semantics even more. The syntactic object X that is a variable in Figure 8.4 is shown to be an element of the entire Universe of Discourse (the domain or portion of the world we are modeling) of Figure 8.5. This means that X really ranges over all the classes defined in the model in Figure 8.6; it ranges over the disjunction of the set Thing, the set Person, and so on, all of which are subsets of the entire Universe of Discourse. Again, the formal notation in these figures is simplified a bit and presented mainly to give you an appreciation of the increasingly elaborated semantics for simple syntactic objects.
5A formal introduction to semantic value can be found at http://meta2.stanford.edu/kif/Hypertext/ node11.html.
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Chapter 8
Simple Semantics Complex Semantics
String Constant-—{"zDLKFL" e {"a", "b", "c",.
Integer Constant s infinite"*S*"}
Integer Type Variable^->-{12323} e {1, 2, ..., n}
Variable-------------I X e {1, 2, •••, n}
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