partialand

Partialand is a term used to describe a partially defined conjunction operator. It has no universally accepted definition and is mostly encountered in informal or speculative writings.

One common interpretation treats partialand as a binary operator that agrees with ordinary conjunction on defined inputs, but yields an undefined result if either input is undefined. This mirrors three-valued logics such as Kleene's, with values true, false, and unknown.

In programming contexts, partialand may refer to a function that combines two partial results only when both are present, otherwise indicating an undefined or incomplete result.

Example: if a = true and b = unknown, partialand(a,b) = unknown; if a = false and b = unknown, partialand(a,b) = false. Semantics vary by model: some definitions preserve a-decision tendencies (false dominates), while others keep the result undefined when any input is undefined.

Status and history: The term appears sporadically and lacks standard citations or formal endorsement. It is mainly used to illustrate the handling of partial information in logical or computational frameworks. Because it is not a widely adopted term, it is often conflated with related concepts such as partial functions, three-valued logics, or short-circuit evaluation, though these are distinct ideas.

See also: conjunction; partial function; three-valued logic; Kleene logic; short-circuit evaluation.