Domain of discourse

In logic and philosophy of language, a universe of discourse is understood to be the totality of objects to which statements like "all objects are ... " (all-statement) or "there are no objects that are ... " (negative existential statement). Such statements are meaningful only if the meaning of "object" is restricted to a particular domain, the universe of discourse. The extent and nature of the restriction depend on the content and context of the statements. Therefore, there is not only one universe of discourse, but different universes of discourse.

The English term Universe of Discourse is also used in the German-language logic and computer science literature. It goes back to Augustus De Morgan (1847) and refers to the range of objects (in the broadest sense) that are to be talked about at all.

Misunderstandings and disputes often arise in logic, as in everyday life, because people talk "past each other" about different things. Someone claims, for example, that there are no winged horses. His counterpart rejects this by referring to the Pegasus. Both move mentally in different worlds. Their dispute can be settled if they agree on a common universe of discourse, i.e. negotiate what the discourse should be about, whether only about physically existing horses or also about mythical creatures.

The universe of discourse also plays a role in the use of negative (complementary) terms. Expressions such as "non-swimmer", "non-expert", "non-voter" can meaningfully be applied only to persons. Non-voters, together with voters, form the universe of discourse restricted to persons who are eligible to vote. The restriction happens automatically when such terms are used. If the automaticity is put out of action, for example by calling a disused chimney a non-smoker, a pun is created. In general, for any term: if it is unified with the corresponding negative term (more precisely, if their extensions are unified), the two together form the universe of discourse or the domain of use cases of the positively determined complementary term:

In set theory the universe of discourse corresponds to the basic set, the sets correspond to the concepts, the complements of sets correspond to the negation of concepts. In predicate logic, the universe of discourse corresponds to the range of the definition set through which the subject variable of a quantified statement can pass.

The Universe of Discourse is mostly abbreviated with U in logic, in computer science also with UoD.

The U is usually a subset of all existing objects and, especially in predicate logic, the range of objects specified or presupposed when quantifiers are used.