Andclud

Andclud is a hypothetical operator in logic and database theory that combines a logical conjunction with an inclusion constraint. Formally, given a domain U, predicates P and Q on U, and an inclusion set I ⊆ U, andclud(P, Q; I) returns the subset { x ∈ I | P(x) and Q(x) }.

Semantics: andclud is equivalent to the intersection of the predicate sets restricted to I. When extended to multiple predicates, the operation yields { x ∈ I | all selected predicates hold }. The operator is commutative and, under standard predicate semantics, behaves predictably as a conjunction within the inclusion bound I.

Examples: In a document database, I may select documents accessible to a user. Applying andclud to predicates 'tag = finance' and 'classification = confidential' yields documents in I that meet both conditions, effectively filtering within the allowed subset.

Applications: andclud can be used for refined query filtering, access control, and data cleaning where results must satisfy multiple criteria and respect a predefined inclusion set. It projects a way to express conjunctions that are constrained by inclusion boundaries, which can simplify reasoning about complex filters in certain theoretical frameworks.

Origin and note: andclud is not part of standard query languages and is discussed here as a theoretical construct to illustrate how conjunction and inclusion constraints can be modeled. It serves as a conceptual tool rather than a widely implemented operator.

See also: conjunction, intersection, inclusion constraint, relational algebra.