Definite description

Definite description is a definite noun phrase which is used to refer to exactly one individual.

Example
the king of France in (i) is a definite description that can only be properly used if France has one and only one king:

(i) The king of France is bald

According to Russell, the grammatical form of these sentences misleadingly suggests that the king of France is a referring phrase, while in the underlying logical form this sentence is analyzed as a conjunction of three sentences:

(ii) a	There is at least one king of France, and b	He is the only king of France, and c	He is bald

This analysis implies that sentence (i) is false when there is no king of France or when there is more than one. Russell's analysis was criticized by Strawson, who argued that the sentences (iia,b) should not be analyzed as parts of the assertion, but as presuppositions for the proper use of the definite description. When one of these presuppositions is not satisfied, the truth value of (i) cannot be determined. (iia) is sometimes called the existence presupposition and (iib) the uniqueness presupposition.

Link
Utrecht Lexicon of Linguistics