Universe of Discourse

"The Linking Open Data cloud"

What is the universe of discourse? Pat and Brian say, “The semantics treats all RDF names as expressions which denote. The things denoted are called ‘resources’, following [RFC 2396], … ; ‘resource’ is treated here as synonymous with ‘entity’, i.e. as a generic term for anything in the universe of discourse.” The universe of discourse represents all of things as resource in RDF, and it is expressed by symbol RI.

The notion of universe of discourse was emerged from the development of logic theory, which is started by Gottlob Frege, along with establishing classical set theory, which is started by Georg Cantor. Today, it has become the most important notion as one of basic foundations of formal theory for computer languages, or denotational semantics.

In mathematics, there is no doubt on what a number means, and consequently what number operations mean. For example, nobody doubts the truth of “1 + 2 = 3”. However, when someone says that the wine of which color is red is red wine ‘(Wine and (Wine’s_color is Red)) = RedWine’, is it true or not? If it is true, how can you prove it? How can you let machines calculate it? We had here faced the problem to establish the meanings of terms in logical expressions in order to clarify meanings of logical expressions for human beings and let machines compute the validity of expressions.

The foundation of formal language or denotational semantics is laid by Alfred Tarski. In 1941, Tarski explained the concept of universe of discourse in his book [1] for a particular mathematical theory. If we may, today, rephrase it by substituting the mathematical theory with RDF theory, it is turned to “Instead of using the general logical concept of individual within RDF theory, it is sometimes more convenient to specify exactly what is considered an individual thing within the framework of this theory; the class of all those things will then be denoted again by RI and will be called the universe of discourse of the theory.”

The framework of one theory for logical computation is called a model. In the integer model, we agree the meanings of number and operations in the framework of integer theory. However, we must set up a framework of theory, if we want to treat semantically Webs, or to let machines compute the meanings of the Webs. That is RDF theory, in which the world is captured as directed labeled graph as a model, and then the discourse of universe is a set of all of nodes and edges in the graph or resources and relations in the Webs.

Do you think the number of entities in the universe of discourse is infinite or finite? Do you think the universe of discourse is open or close? Do you think THE universe of discourse or UNIVERSES of discourse? I would like to discuss about these questions in the following talk.

[1] Tarski, Alfred: Introduction to Logic and to the Methodology of Deductive Sciences, Oxford (1941), Dover (1995)

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About seijikoide

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