The domain of discourse is the set of natural numbers.

The domain of discourse forms the range for these quantifiers.

A term denotes a mathematical object from the domain of discourse.

In a more technical arena, the domain of discourse could be 'integers', say.

A domain of discourse D, usually required to be non-empty (see below).

Terms, informally, are expressions that represent objects from the domain of discourse.

A more natural way to restrict the domain of discourse uses guarded quantification.

A dot asserts the existence of some individual in the domain of discourse.

A common instance of a collection is the domain of discourse of a first order theory.

A formula is true according to M if there is some d in the domain of discourse such that holds.

Existential claims are more naturally expressed within the context of a specific domain of discourse.

In daily life, the domain of discourse could be 'apples', or 'persons', or even everything.

In some mathematical theories a single domain of discourse fixed in advance is assumed.

Ordinary first-order interpretations have a single domain of discourse over which all quantifiers range.

The definition above requires that the domain of discourse of any interpretation must be a nonempty set.

Logical conjunctions are used to restrict the domain of discourse to fulfill a given predicate.

It also determines a domain of discourse that specifies the range of the quantifiers.

The issue between realism and non-realism can arise in any domain of discourse which makes grammatical assertions.

In other words, given a domain of discourse "winged things", either we find p to be a member of this domain or not.

It expresses that a propositional function can be satisfied by at least one member of a domain of discourse.

These form the basis of model theory as the domain of discourse of predicate logic.

The domain of discourse D is a nonempty set of "objects" of some kind.

In particular, each constant symbol of the signature is assigned an individual in the domain of discourse.

A formula is assigned true if and evaluate to the same object of the domain of discourse (see the section on equality below).

Many common rules of inference are only valid when the domain of discourse is required to be nonempty.