Booleanvalued function
☞ This page belongs to resource collections on Logic and Inquiry.
A booleanvalued function is a function of the type where is an arbitrary set and where is a boolean domain.
In the formal sciences — mathematics, mathematical logic, statistics — and their applied disciplines, a booleanvalued 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 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.
Examples edit
A binary sequence is a booleanvalued function , where . In other words, is an infinite sequence of 0's and 1's.
A binary sequence of length is a booleanvalued function , where
References edit
 Brown, Frank Markham (2003), Boolean Reasoning : The Logic of Boolean Equations, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
 Kohavi, Zvi (1978), Switching and Finite Automata Theory, 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978.
 Korfhage, Robert R. (1974), Discrete Computational Structures, Academic Press, New York, NY.
 Mathematical Society of Japan, Encyclopedic Dictionary of Mathematics, 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM.
 Minsky, Marvin L., and Papert, Seymour, A. (1988), Perceptrons, An Introduction to Computational Geometry, MIT Press, Cambridge, MA, 1969. Revised, 1972. Expanded edition, 1988.
Syllabus edit
Focal nodes edit
Peer nodes edit
 BooleanValued Function @ InterSciWiki
 BooleanValued Function @ Subject Wikis
 BooleanValued Function @ Wikiversity
 BooleanValued Function @ Wikiversity Beta
Logical operators edit


Related topics edit



Relational concepts edit



Information, Inquiry edit




Related articles edit
Document history edit
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.