Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse (or simply universe), is the set of entities over which certain variables of interest in some formal treatment may range. The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables.

For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals that the quantifiers range over. In one interpretation, the domain of discourse could be the set of real numbers; in another interpretation, it could be the set of natural numbers. If no domain of discourse has been identified, a proposition such as $∀x (x^{2} ≠ 2)$ is ambiguous. If the domain of discourse is the set of real numbers, the proposition is false, with $x = √2$ as counterexample; if the domain is the set of naturals, the proposition is true, since 2 is not the square of any natural number.

The term universe of discourse generally refers to the collection of objects being discussed in a specific discourse. In model-theoretical semantics, a universe of discourse is the set of entities that a model is based on. The term universe of discourse is generally attributed to Augustus De Morgan (1846) and was also used by George Boole (1854) in his Laws of Thought.

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".