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A '''boolean-valued function''', in some usages a '''predicate''' or a '''proposition''', is a function of the type <math>f : X \to \mathbb{B}</math>, where <math>X</math> is an arbitrary set, where <math>\mathbb{B}</math> is a generic 2-element set, typically <math>\mathbb{B} = \left \{ 0, 1 \right \}</math>, and where the latter is frequently interpreted for logical applications as <math>\mathbb{B} = \left \{ false, true \right \}</math>. A '''boolean-valued function''', in some usages a '''predicate''' or a '''proposition''', is a function of the type <math>f : X \to \mathbb{B}</math>, where <math>X</math> is an arbitrary set, where <math>\mathbb{B}</math> is a generic 2-element set, typically <math>\mathbb{B} = \left \{ 0, 1 \right \}</math>, and where the latter is frequently interpreted for logical applications as <math>\mathbb{B} = \left \{ false, true \right \}</math>.


In the ]s, ], ], ], and their applied disciplines, a boolean-valued function may also be referred to as a ], ], ], or ]. Actually, boolean valued functions are stupid. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding ] sign or syntactic expression. In the ]s, ], ], ], and their applied disciplines, a boolean-valued function may also be referred to as a ], ], ], or ]. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding ] sign or syntactic expression.


In ] theories of ], a '''truth predicate''' is a predicate on the ]s of a ], interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value. In ] theories of ], a '''truth predicate''' is a predicate on the ]s of a ], interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.

==See also==

* ]

===Equivalent concepts===

* ]
* ]
* ], in some senses.
* ], in some senses.

===Related concepts===

* ]

]
]
]
]

Revision as of 06:58, 18 May 2006

A boolean-valued function, in some usages a predicate or a proposition, is a function of the type f : X → B {\displaystyle f:X\to \mathbb {B} } , where X {\displaystyle X} is an arbitrary set, where B {\displaystyle \mathbb {B} } is a generic 2-element set, typically B = { 0 , 1 } {\displaystyle \mathbb {B} =\left\{0,1\right\}} , and where the latter is frequently interpreted for logical applications as B = { f a l s e , t r u e } {\displaystyle \mathbb {B} =\left\{false,true\right\}} .

In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding semiotic sign or syntactic expression.

In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.

See also

Equivalent concepts

Related concepts

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