The domain of discourse, sometimes called the universe of discourse, is an analytic tool used in deductive logic, especially predicate logic. It indicates the relevant set of entities that are being dealt with by quantifiers. Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. ... ...
The term "universe of discourse" generally refers to the entire set of terms used in a specific discourse, i.e. the family of linguistic or semantic terms that are specific to any one area of interest. In model-theoretical semantics, the term "universe of discourse" refers to the set of entities that a model is based on. Broadly conceived, linguistics is the study of human language, and a linguist is someone who engages in this study. ...
A database is a model of some aspect of the reality of an organisation. It is conventional to call this reality the "universe of discourse" or "domain of discourse".
This indicates the importance of the domain of discourse, which specifies which values n is allowed to take.
Further information on using domains of discourse with quantified statements can be found in the Quantification article.
But in particular, note that if you wish to restrict the domain of discourse to consist only of those objects that satisfy a certain predicate, then for universal quantification, you do this with a logical conditional.
In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain.
This demonstrates the importance of the domain of discourse, which specifies which values the variable n is allowed to take.
But in particular, note that if you wish to restrict the domain of discourse to consist only of those objects that satisfy a certain predicate, then for existential quantification, you do this with a logical conjunction.
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