iPedia Free Information Center

Information about Boolean Valued Function

A boolean-valued function, in some usages a predicate or a proposition, is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain.

A boolean domain B is a generic 2-element set, say, B = {0, 1}, whose elements are interpreted as logical values, for example, 0 = false and 1 = true.

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.

References

  • 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.

See also

Equivalent concepts

Related concepts

proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
..... Click the link for more information.
function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
..... Click the link for more information.
SET may stand for:
  • Sanlih Entertainment Television, a television channel in Taiwan
  • Secure electronic transaction, a protocol used for credit card processing,

..... Click the link for more information.
A boolean domain B is a generic 2-element set, say, B = , whose elements are interpreted as logical values, typically 0 = false and 1 = true.

A boolean variable x is a variable that takes its value from a boolean domain, as x ∈
..... Click the link for more information.
In logic and mathematics, a logical value, also called a truth value, is a value indicating the extent to which a proposition is true.

In classical logic, the only possible truth values are true and false.
..... Click the link for more information.
A formal science is an academic study that is predominantly concerned with abstract formal systems, for instance, logic, mathematics, and the theoretical branches of computer science, information theory, and statistics.
..... Click the link for more information.
Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
..... Click the link for more information.
Mathematical logic is a branch of mathematics, which grew out of symbolic logic. Subfields include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic has contributed to, and been motivated by, the study of foundations of mathematics, but
..... Click the link for more information.
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
..... Click the link for more information.
In mathematics, characteristic function can refer to any of several distinct concepts:
  • The most common and universal usage is as a synonym for indicator function, that is the function
:
which for every subset A of X

..... Click the link for more information.
indicator function or a characteristic function is a function defined on a set that indicates membership of an element in a subset of .

The indicator function of a subset of a set is a function



defined as


..... Click the link for more information.
common. We use the notation P(x) to denote a sentence or statement P concerning the variable object x. The set defined by P(x) written , is just a collection of all the objects for which P is sensible and true.

For instance, is the set .
..... Click the link for more information.
proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
..... Click the link for more information.
Semiotics, semiotic studies, or semiology is the study of sign processes (semiosis), or signification and communication, signs and symbols, both individually and grouped into sign systems. It includes the study of how meaning is constructed and understood.
..... Click the link for more information.
The introduction to this article provides insufficient context for those unfamiliar with the subject matter.
Please help [ improve the introduction] to meet Wikipedia's layout standards.

..... Click the link for more information.
truth extends from honesty, good faith, and sincerity in general, to agreement with fact or reality in particular.[1] The term has no single definition about which the majority of professional philosophers and scholars agree.
..... Click the link for more information.
In mathematical logic, a sentence of a predicate logic is a formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an assertion, potentially concerning any structure of L.
..... Click the link for more information.
This article is about the term formal language as it is used in mathematics, logic and computer science. For information about a mode of expression that is more disciplined or precise than everyday speech, see Register (linguistics).

..... Click the link for more information.
Marvin Lee Minsky

Marvin Minsky in 2006
Born July 9 1927 (1927--) (age 80)
New York City
..... Click the link for more information.
Seymour Papert

Born March 1 1928 (1928--) (age 79)
Pretoria, South Africa
..... Click the link for more information.
''For alternate meanings see Perceptron (disambiguation).
The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt.
..... Click the link for more information.

..... Click the link for more information.
A boolean domain B is a generic 2-element set, say, B = , whose elements are interpreted as logical values, typically 0 = false and 1 = true.

A boolean variable x is a variable that takes its value from a boolean domain, as x ∈
..... Click the link for more information.

..... Click the link for more information.
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules
..... Click the link for more information.
A truth table is a mathematical table used in logic — specifically in connection with Boolean algebra, boolean functions, and propositional calculus — to compute the functional values of logical expressions on each of their functional arguments, that is, on each
..... Click the link for more information.
Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate calculus, propositional calculus, or sentential calculus.
..... Click the link for more information.
Boolean minimization may refer to:
  • Karnaugh map
  • Quine-McCluskey algorithm
  • Espresso heuristic logic minimizer

..... Click the link for more information.
In mathematics, characteristic function can refer to any of several distinct concepts:
  • The most common and universal usage is as a synonym for indicator function, that is the function
:
which for every subset A of X

..... Click the link for more information.
indicator function or a characteristic function is a function defined on a set that indicates membership of an element in a subset of .

The indicator function of a subset of a set is a function



defined as


..... Click the link for more information.


This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus


page counter