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Function returning one of only two values
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1
Boolean_function
Function that outputs either true or false
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B
Boolean-valued_function
Index of articles associated with the same name
two-element Boolean algebra (the Boolean domain), e.g. Boolean-valued function or Boolean data type in mathematics: something taking values over an arbitrary
Boolean-valued
of Boolean functions Balanced Boolean function Bent function Boolean algebras canonically defined Boolean function Boolean matrix Boolean-valued function
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Expression in a computer program
True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. Boolean expressions correspond to propositional formulas
Boolean_expression
Set theory concept
Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of
Boolean-valued_model
Logical connective AND
graph AND gate Bitwise AND Boolean algebra Boolean conjunctive query Boolean domain Boolean function Boolean-valued function Conjunction/disjunction duality
Logical_conjunction
Algebraic manipulation of "true" and "false"
logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true
Boolean_algebra
Algebraic structure modeling logical operations
List of Boolean algebra topics Boolean domain Boolean function Boolean logic Boolean ring Boolean-valued function Canonical form (Boolean algebra) Complete
Boolean_algebra_(structure)
Study of Boolean functions via discrete Fourier analysis
and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} or {
Analysis_of_Boolean_functions
Function in logic
In two-valued logic, there are sixteen possible truth functions, also called Boolean functions, of two inputs P and Q. Any of these functions corresponds
Truth_function
Data having only values "true" or "false"
defined to test Boolean-valued expressions. Languages with no explicit Boolean data type, like C90 and Lisp, may still represent truth values by some other
Boolean_data_type
Concept in mathematical logic
value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true. Boolean-valued
Boolean_domain
Property that assigns truth values to k-tuples of individuals
typically 0 = false and 1 = true. The characteristic function of R, denoted by χR, is the Boolean-valued function χR: X1 × ... × Xn → B, defined by χR((x1, ..
Finitary_relation
Mathematical topics based on the works of George Boole
Look up Boolean, Booleans, or boolean in Wiktionary, the free dictionary. Any kind of logic, function, expression, or theory based on the work of George
Boolean
Overview of and topical guide to logic
form (Boolean algebra) Boolean conjunctive query Boolean-valued model Boolean domain Boolean expression Boolean ring Boolean function Boolean-valued function
Outline_of_logic
Mathematical table used in logic
logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on
Truth_table
Generalization of binary functions
pseudo-Boolean function is a function of the form f : B n → R , {\displaystyle f:\mathbf {B} ^{n}\to \mathbb {R} ,} where B = {0, 1} is a Boolean domain
Pseudo-Boolean_function
Statement that a predicate is always true at that point in code execution
imperative programming paradigm, an assertion is a predicate (a Boolean-valued function over the state space, usually expressed as a logical proposition
Assertion (software development)
Assertion_(software_development)
Topics referred to by the same term
logic: Predicate (logic) Propositional function Finitary relation, or n-ary predicate Boolean-valued function Syntactic predicate, in formal grammars
Predicate
Symbol connecting formulas in logic
Psychology portal Boolean domain Boolean function Boolean logic Boolean-valued function Catuṣkoṭi Dialetheism Four-valued logic List of Boolean algebra topics
Logical_connective
Logical connective OR
' Affirming a disjunct Boolean algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_disjunction
System including an indeterminate value
Boolean algebra (structure) Boolean function Digital circuit Four-valued logic Homogeneity (linguistics) Paraconsistent logic § An ideal three-valued
Three-valued_logic
Technical treatment of Boolean algebras
infinite Boolean algebras whose topology is neither discrete nor compact. Boolean domain Boolean function Boolean-valued function Boolean-valued model Cartesian
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Expression in propositional calculus
heterogeneous relations. Propositional formula Boolean-valued function Formula (logic) Sentence (logic) Truth function Open sentence Tiles, Mary (2004). The philosophy
Propositional_function
Subject field of Boolean algebra discussing changes of Boolean variables and functions
of Boolean algebra discussing changes of Boolean variables and Boolean functions. Boolean differential calculus concepts are analogous to those of classical
Boolean_differential_calculus
Function in Boolean algebra
In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function
Parity_function
Special type of Boolean function
bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when
Bent_function
Boolean function whose output depends only on the number of true inputs
In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on
Symmetric_Boolean_function
Concept in mathematical logic
connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression.
Functional_completeness
Boolean function
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are
Majority_function
Topics referred to by the same term
Boolean operation or Boolean operator may refer to: Boolean function, a function whose arguments and result assume values from a two-element set Boolean
Boolean_operation
Order-preserving mathematical function
Graphically, this means that an n-ary Boolean function is monotonic when its representation as an n-cube labelled with truth values has no upward edge from true
Monotonic_function
assertion In computer programming, a statement that a predicate (Boolean-valued function, i.e. a true–false expression) is always true at that point in
Glossary_of_computer_science
In mathematics, an evasive Boolean function f {\displaystyle f} (of n {\displaystyle n} variables) is a Boolean function for which every decision tree
Evasive_Boolean_function
Many-valued logic in which truth values comprise a continuous range
forms can further encompass finite-valued logic. For example, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification
Infinite-valued_logic
Real-valued mathematical function
Interpreting positive values as true and negative values as false, an R-function is transformed into a "companion" Boolean function (the two functions are called
Rvachev_function
Algorithmic paradigm for constraint satisfaction or enumeration problems
backtrack(P, s) s ← next(P, s) The reject procedure should be a Boolean-valued function that returns true only if it is certain that no possible extension
Backtracking
Set of rules defining correctly structured programs
value. For explicit coercion to the Boolean type, Mozilla recommends that the Boolean() function (without new) be used in preference to the Boolean object
JavaScript_syntax
Data structure for Boolean functions
branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation
Binary_decision_diagram
Programming language construct
OR function evaluates to true, the overall value must be true. In programming languages with lazy evaluation (Lisp, Perl, Haskell), the usual Boolean operators
Short-circuit_evaluation
Value indicating the relation of a proposition to truth
This set of two values is also called the Boolean domain. Corresponding semantics of logical connectives are truth functions, whose values are expressed
Truth_value
Boolean polynomials as sums of monomials
Algebraic normal form (ANF) is a representation of functions in boolean algebra. Formulas written in ANF are also known as ring sum normal form (RSNF or
Algebraic_normal_form
Term in educational psychology
applied in training computer programs. Concept learning: Inferring a Boolean-valued function from training examples of its input and output. A concept is an
Concept_learning
Model of computation
Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for
Boolean_circuit
Attribute of data
-> Bool denoting functions taking an integer and returning a Boolean. In C, a function is not a first-class data type but function pointers can be manipulated
Data_type
Set of values which satisfy a given set of equations
the solution set is the inverse image of the Boolean value true by the associated Boolean-valued function.) The above meaning is a special case of this
Solution_set
Model of computation
input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits
Circuit_(computer_science)
Propositional calculus in which there are more than two truth values
Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in
Many-valued_logic
Type of propositional logic
second-order Boolean propositions, where quantifiers may range either just over the Boolean truth values, or over the Boolean-valued truth functions. The most
Second-order propositional logic
Second-order_propositional_logic
Problem of determining if a Boolean formula could be made true
satisfies a given Boolean formula. In other words, it asks whether the formula's variables can be consistently replaced by the values TRUE or FALSE to
Boolean satisfiability problem
Boolean_satisfiability_problem
Class of mathematical functions
(supermodular) functions can be found in "Maximization of submodular functions: Theory and enumeration algorithms", B. Goldengorin. Pseudo-Boolean function Topkis's
Supermodular_function
Concept in mathematics or computer science
as an operator that evaluates to the logical conjunction of the Boolean-valued function P {\displaystyle P} applied to each element in the (possibly infinite)
Free variables and bound variables
Free_variables_and_bound_variables
Mathematical model for data types
removal. A complete abstract stack definition includes also a Boolean-valued function empty(S) and a create() operation that returns an initial stack
Abstract_data_type
Geometric property of a pair of sets of points in Euclidean geometry
whether a Boolean function given in disjunctive or conjunctive normal form is linearly separable. A linear threshold logic gate is a Boolean function defined
Linear_separability
Type of logical system
second argument. Equivalently, predicate symbols may be assigned Boolean-valued functions from Dn to { t r u e , f a l s e } {\displaystyle \{\mathrm {true
First-order_logic
Branch of logic
Higher-order logic Boolean algebra (logic) Boolean algebra (structure) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Categorical
Propositional_logic
Computer science topic
each bit represents an individual Boolean state. This technique is an efficient way to store a number of Boolean values using as little memory as possible
Bitwise_operation
Process in digital electronics and integrated circuit design
simplifies) a Boolean function. The Boolean function carried out by the circuit is directly related to the algebraic expression from which the function is implemented
Logic_optimization
Boolean algebra with all operators and laws forming a complete logical system
Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion
Complete_Boolean_algebra
Mathematical use of "for all" and "there exists"
as a Boolean-valued function F(v1, ..., vn) of n arguments, where each argument ranges over the domain X. Boolean-valued means that the function assumes
Quantifier_(logic)
Coding guidelines by Gerald J. Holzmann
Boolean tests. When an assertion fails, an explicit recovery action must be taken such as returning an error condition to the caller of the function that
The Power of 10: Rules for Developing Safety-Critical Code
The_Power_of_10:_Rules_for_Developing_Safety-Critical_Code
Binary operation that is true if and only if both operands are false
operators of propositional logic are: Bitwise NOR Boolean algebra Boolean domain Boolean function Functional completeness NOR gate Propositional logic
Logical_NOR
Representation of data types in lambda calculus
are functions, represented by lambda abstraction terms. Types that are usually considered primitive in other notations (such as integers, Booleans, pairs
Church_encoding
Function computable with bounded loops
functions are the basic functions and those obtained from the basic functions by applying these operations a finite number of times. A (vector-valued)
Primitive_recursive_function
English mathematician and philosopher (1815–1864)
false) Boolean expression, an expression in a programming language that produces a Boolean value when evaluated Boolean function, a function that determines
George_Boole
Discrete set of Boolean variables
A Boolean network consists of a discrete set of Boolean variables each of which has a Boolean function (possibly different for each variable) assigned
Boolean_network
Combinatorial sequence of numbers
9 {\displaystyle n\leq 9} . A Boolean function is a function that takes as input n Boolean variables (that is, values that can be either false or true
Dedekind_number
Logic with discrete truth values
typically not considered forms of finite-valued logic. However, finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification
Finite-valued_logic
Property of operations
to be. As an example for the latter, the negation function ¬ {\displaystyle \neg } on the Boolean domain is not idempotent, but ¬ ∘ ¬ {\displaystyle
Idempotence
Formal specification language
which introduced the idea of describing state transitions as Boolean-valued functions of primed and unprimed variables. Work continued throughout the
TLA+
A Boolean flag, truth bit or truth flag in computer science is a Boolean value represented as one or more bits, which encodes a state variable with two
Boolean_flag
Mathematical function that can be computed by a program
is computable if there is an algorithm that computes the value of the function for every value of its argument. Because of the lack of a precise definition
Computable_function
Computational Formula that can be measured in terms of True or False
a formal language consisting of the true quantified Boolean formulas. A (fully) quantified Boolean formula is a formula in quantified propositional logic
True quantified Boolean formula
True_quantified_Boolean_formula
Yes/no problem in computer science
characterize complexity classes of decision problems. For example, the Boolean satisfiability problem is complete for the class NP of decision problems
Decision_problem
Function that is its own inverse
algebra of truth values. Examples of logics that have involutive negation are Kleene and Bochvar three-valued logics, Łukasiewicz many-valued logic, the fuzzy
Involution_(mathematics)
Feature of some programming languages
NullableInteger, NullableBoolean). A Boolean variable makes the effect more clear. Its values can be either "true" or "false", while a nullable Boolean may also contain
Nullable_type
Algorithm for supervised learning of binary classifiers
separable Boolean function, or threshold Boolean function. The sequence of numbers of threshold Boolean functions on n inputs is OEIS A000609. The value is only
Perceptron
Properties of mathematical relationships
F) = F, and these functions correspond to linear maps over the Boolean vector space. In every row in which the value of the function is T, there is an
Linearity
Axioms in computational complexity theory
computable functions with a complexity less than f {\displaystyle f} . C 0 ( f ) {\displaystyle C^{0}(f)} is the set of all boolean-valued functions with a
Blum_axioms
Probability distribution
independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q
Binomial_distribution
Device performing a Boolean function
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output
Logic_gate
Assignment of meaning to the symbols of a formal language
Interpretations used to study non-classical logic include topological models, Boolean-valued models, and Kripke models. Modal logic is also studied using Kripke
Interpretation_(logic)
Logical operation
truth-value of the operation, or it never makes a difference. Negation is a linear logical operator. In Boolean algebra, a self dual function is a function
Negation
Relationship where one statement follows from another
penguin}. Abstract algebraic logic Ampheck Boolean algebra (logic) Boolean domain Boolean function Boolean logic Causality Deductive reasoning Logic gate
Logical_consequence
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Computer programming function
2, …, 10 for which the predicate even returns the Boolean value false (with . being the function composition operator). Below, you can see a view of
Filter (higher-order function)
Filter_(higher-order_function)
Symbolic description of a mathematical object
expressions that can be evaluated to the Boolean values true or false. To evaluate an expression means to find a numerical value equivalent to the expression. Expressions
Expression_(mathematics)
Any logic with four truth values
contradictions in two-valued logic: contradictions are never isolated, infecting as they do the whole system." Belnap proposed a four-valued logic as a means
Four-valued_logic
Standard forms of Boolean functions
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products
Canonical_normal_form
Graphical method to simplify Boolean expressions
also known as minterms, while each cell value represents the corresponding output value of the Boolean function. Optimal groups of 1s or 0s are identified
Karnaugh_map
Boolean function which has monotonic properties
unate function is a type of boolean function which has monotonic properties. They have been studied extensively in switching theory. A function f ( x
Unate_function
Provides lower bounds on the circuit complexity of boolean functions
mathematical notion of "discrepancy" or "scatter" or "variation" of the values of a Boolean function, or of an associated polytope or other structure. [...] Show
Natural_proof
Algorithm for the minimization of Boolean functions
implicants or the tabulation method, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward
Quine–McCluskey_algorithm
In logic, a statement which is always true
is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies
Tautology_(logic)
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Class of formal logics
semantics. In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra; "true"
Classical_logic
Theorem in Boolean algebra
In Boolean algebra, the consensus theorem or rule of consensus is the identity: x y ∨ x ¯ z ∨ y z = x y ∨ x ¯ z {\displaystyle xy\vee {\bar {x}}z\vee
Consensus_theorem
Notation for representing a fixed value in source code
strings, and usually for Booleans and characters; some also have notations for elements of enumerated types and compound values such as arrays, records
Literal (computer programming)
Literal_(computer_programming)
Theories in mathematical logic
used for Boolean algebras: The signature has two constants, 0 and 1, and two binary functions ∧ and ∨ ("and" and "or"), and one unary function ¬ ("not")
List_of_first-order_theories
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Female
Spanish
Spanish name SALUD means "health."
Girl/Female
Indian
Flowering, Blooming, Flower
Surname or Lastname
English
English : variant of Bullen.
Boy/Male
American, British, English
Lives at the Buck Meadow
Girl/Female
British, English, Finnish, French, Latin
Valley; Usually with a Stream; Strong
Surname or Lastname
English
English : topographic name for someone who lived on a curved or irregularly shaped piece of land, from Old English wÅh ‘curved’, ‘crooked’ + land ‘land’, ‘estate’, or a habitational name from Woolland in Dorset, named from an Old English winn, wynn ‘meadow’, ‘pasture’ + land ‘land’, ‘estate’.
Surname or Lastname
English
English : variant of Boland.Irish : Anglicized form of Gaelic Ó Beólláin, ‘descendant of Bjolan’, a Norse personal name.
Male
Welsh
Welsh name ALED means "offspring."
Surname or Lastname
English
English : variant of Bowerman.
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Telugu, Traditional
Flowering
Boy/Male
Irish
Puppy.
Boy/Male
Anglo, British, English, Finnish, French, Swedish
Lives in the Valley; Valley; Usually with a Stream; Strong; Healthy
Surname or Lastname
English
English : variant of Wool.Americanized form of Jewish Wollman or German Wollmann (see Wollman).
Male
Scandinavian
Scandinavian form of German Walther, VALTER means "ruler of the army."
Surname or Lastname
English
English : variant of Bullen.
Surname or Lastname
Irish
Irish : Anglicized form of Gaelic Ó Baoighealláin. It was the name of a sept of Dartry, County Monaghan.English : variant of Boyland.
Boy/Male
English
Lives in the valley.
Male
English
Variant spelling of Middle English Alvred, ALURED means "elf counsel."
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English valeye.
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
Boy/Male
Hindu
King Nala, A hero from the mahabharata who was king of nishadha, A open
Male
Greek
(ΧείÏων) Greek name KHEIRON means "surgeon." In mythology, this is the name of a wise centaur, the son of Kronos and the nymph Philyre. He himself fathered Okyrhoe with the nymph Khariklo. He was said to be a great healer, oracle and astrologer.
Boy/Male
Tamil
Battle maiden
Female
English
 Feminine form of English August, AUGUSTA means "August (the month)." Compare with another form of Augusta.
Boy/Male
German
Blessed and Brave
Male
Yiddish
(מָ×רְדְכֶע) Yiddish form of Hebrew Mordekay, MORDCHE means "devotee of Marduk (Mars)" or "little man."
Boy/Male
Hindu
Polite
Boy/Male
Arabic
Good News
Boy/Male
Hebrew
God will judge.
Girl/Female
Arabic, Gujarati, Indian, Kannada, Muslim
A Beautiful Portrait
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
BOOLEAN VALUED-FUNCTION
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.
n.
Value.
a.
Of or pertaining to wool or woolen cloths; as, woolen manufactures; a woolen mill; a woolen draper.
a.
Not valued; not appraised; hence, not considered; disregarded; valueless; as, an unvalued estate.
imp. & p. p.
of Value
n.
In an artistical composition, the character of any one part in its relation to other parts and to the whole; -- often used in the plural; as, the values are well given, or well maintained.
n.
One who values; an appraiser.
a.
Changed; altered; various; diversified; as, a varied experience; varied interests; varied scenery.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.
a.
Made of wool; consisting of wool; as, woolen goods.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
a.
Having a valve or valve; valvate.
a.
Having the form of a volume, or roil; as, volumed mist.
a.
Arched; concave; as, a vaulted roof.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
a.
Having inestimable value; invaluable.
v. t.
To be worth; to be equal to in value.
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
a.
Consisting of, or having, three valves; opening with three valves; as, a three-valved pericarp.