boolean-valued functionBooleanValuedFunction2009-05-20 14:06:032009-05-20 14:06:03Definitionboolean function% This is the default PlanetPhysics preamble.
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A \textbf{Boolean-valued function} is a function of type $f : X \to \mathbb{B}$, where $X$ is an arbitrary set and where $\mathbb{B}$ is a Boolean domain.
A \textbf{Boolean function} (of finite arity $k$) is a Boolean-valued function of type $f : \mathbb{B}^k \to \mathbb{B}$.
In some contexts a Boolean-valued function may be referred to as a \textit{predicate} or a \textit{proposition}. In other contexts these terms may be used to describe the syntactic entities that denote or express Boolean-valued functions, or that have Boolean-valued functions among their canonical or intended \PMlinkname{models}{Model}. When necessary to avoid confusion, terms like \textit{propositional expression} or \textit{predicate formula} may be used to distinguish \PMlinkname{signs}{SignRelation} from their objects.