describedandP

DescribedandP is a term used in formal semantics and logic to denote a construct that combines a descriptive content with a predicate. It is employed to model phrases in which a description and an additional property must be satisfied by the same object, such as in complex noun phrases or definite descriptions modified by adjectives or relative clauses.

Formally, describedandP can be viewed as a function that takes a description D and a unary predicate P and returns a new predicate describing the intersection of the objects that meet the description and that satisfy P. If D(x) expresses that x fits the description D, and P(x) expresses that x has property P, then describedandP(D, P)(x) is defined as D(x) ∧ P(x). In some treatments, D is treated as a context-dependent modifier, so describedandP may also be indexed by the description content in a given discourse.

Example: in the phrase “the author of War and Peace who is a mathematician,” D corresponds to “is the author of War and Peace,” and P corresponds to “is a mathematician.” The describedandP construction identifies those individuals who both satisfy the descriptive content and possess the additional predicate.

Applications and relevance: describedandP is used to analyze the semantics of definite descriptions with modifiers, intersection semantics, and reference resolution in natural language. It highlights how description-based reference interacts with predication, while also drawing attention to issues of uniqueness, presupposition, and potential referential failure when a description is non-unique or undefined.