Denoting

Denoting is the relation between a linguistic expression and the object, class of objects, or property that it stands for in a given context. In philosophy of language and formal semantics, a term denotes its denotation, which can be an individual object (as with proper names), a set of objects (as with general terms), or a property or relation described by a model.

Denotation is often distinguished from sense (the way an expression presents its denotation). Expressions can share a denotation while differing in sense, and some theories treat sense as essential to determining reference or denotation in particular contexts.

In linguistic and logical analysis, denotations are modeled through semantics that map expressions to interpretations within a model. For example, "London" denotes the city of London; "dog" denotes the set of all dogs; "the current president" denotes whichever individual holds that office at the evaluation time. Some phrases may fail to denote anything in a given model, yielding a non-denoting term under certain conditions, such as empty definite descriptions or non-referring names.

Denotation interacts with truth conditions: a sentence is true if its denotation under a given interpretation satisfies the predicate expressed by the sentence. Non-denoting terms often raise technical questions, leading to theories that assign them special semantic status (such as presuppositions or partial truth conditions) rather than straightforward reference.

In computer science, denotation also appears in denotational semantics, where the meaning of a program or language construct is defined as a mathematical object corresponding to its behavior, separate from syntax. This use mirrors the broader aim of linking linguistic or symbolic forms to their intended objects or effects.