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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
Function returning one of only two values
vectorial or vector-valued Boolean function (an S-box in symmetric cryptography). There are 2 2 k {\displaystyle 2^{2^{k}}} different Boolean functions with
Boolean_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
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
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
System including an indeterminate value
A three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which
Three-valued_logic
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)
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
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
Logical connective AND
And-inverter graph AND gate Bitwise AND Boolean algebra Boolean conjunctive query Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_conjunction
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
Mathematical topics based on the works of George Boole
Boole is considered Boolean. Related to this, "Boolean" may refer to: Boolean data type, a form of data with only two possible values (usually "true" and
Boolean
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
Logical connective OR
come.' Affirming a disjunct Boolean algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_disjunction
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
Property that assigns truth values to k-tuples of individuals
and 1 = true. The characteristic function of R, denoted by χR, is the Boolean-valued function χR: X1 × ... × Xn → B, defined by χR((x1, ..., xn)) = 1 if
Finitary_relation
Formal semantics based on algebras
modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are
Algebraic semantics (mathematical logic)
Algebraic_semantics_(mathematical_logic)
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
Branch of mathematics that studies sets
theory, in which the value of an atomic formula embodying the membership relation is not simply True or False. The Boolean-valued models of ZFC are a related
Set_theory
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)
Dialect of Lisp
as '(), evaluate to the value true in a Boolean expression. (R5RS sec. 6.3.1) Where the constant representing the Boolean value of true is T in most Lisps
Scheme_(programming_language)
Type of propositional logic
allow second-order Boolean propositions, where quantifiers may range either just over the Boolean truth values, or over the Boolean-valued truth functions
Second-order propositional logic
Second-order_propositional_logic
Technique invented by Paul Cohen for proving consistency and independence results
explained in terms of Boolean-valued models. In these, any statement is assigned a truth value from some complete atomless Boolean algebra, rather than
Forcing_(mathematics)
Classical logic of two values, either true or false
classical logic. In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra, "true"
Principle_of_bivalence
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
In mathematical logic, a well-formed formula with no free variables
mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed
Sentence_(mathematical_logic)
Interchange. assertion In computer programming, a statement that a predicate (Boolean-valued function, i.e. a true–false expression) is always true at that point
Glossary_of_computer_science
Study of Boolean functions via discrete Fourier analysis
mathematics and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0,1\}^{n}}
Analysis_of_Boolean_functions
Probability distribution modeling a coin toss which need not be fair
yes–no question. Such questions lead to outcomes that are Boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero
Bernoulli_distribution
Statement that a predicate is always true at that point in code execution
the 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)
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
Set of rules defining correctly structured programs
new Boolean(false); // Object false {} const t = Boolean(b); // Boolean true const f = Boolean(b.valueOf()); // Boolean false let n = new Boolean(b);
JavaScript_syntax
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
Array data structure that compactly stores bits
commonly, they are used to represent a simple group of Boolean flags or an ordered sequence of Boolean values. Bit arrays are used for priority queues, where
Bit_array
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
non-standard analysis Standard part function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic First-order logic
List of mathematical logic topics
List_of_mathematical_logic_topics
novel type of semi-discrete dynamical systems, Boolean delay equations (BDEs) are models with Boolean-valued variables that evolve in continuous time. Since
Boolean_delay_equation
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 use of "for all" and "there exists"
interpreted 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
Quantifier_(logic)
Value indicating the relation of a proposition to truth
the Boolean domain. Assigning values for propositional variables is referred to as valuation. Whereas in classical logic truth values form a Boolean algebra
Truth_value
Finite field of two elements
elements of GF(2) may be identified with the two possible values of a bit and to the Boolean values true and false. It follows that GF(2) is fundamental and
GF(2)
Technical treatment of Boolean algebras
algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Various systems of symbolic logic
One of these semantics mirrors classical Boolean-valued semantics but uses Heyting algebras in place of Boolean algebras. Another semantics uses Kripke
Intuitionistic_logic
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
Symbolic boolean function representation, extension of BDDs
restricted to the Boolean values 0 (FALSE) and 1 (TRUE). The terminal nodes may take any value from a set of constants S. An ADD represents a Boolean function
Algebraic_decision_diagram
Expression language for XML documents
Consortium (W3C) in 1999, and can be used to compute values (e.g., strings, numbers, or Boolean values) from the content of an XML document. Support for
XPath
Method for constructing models of set theory
forcing notions indexed by some ordinals α, which give a family of Boolean-valued models VPα. If α+1 is a successor ordinal then Pα+1 is often constructed
Iterated_forcing
Mathematical-logic system based on functions
convention, the following two definitions (known as Church Booleans) are used for the Boolean values TRUE and FALSE: TRUE := λx.λy.x FALSE := λx.λy.y Then
Lambda_calculus
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)
Topics referred to by the same term
(logic) Propositional function Finitary relation, or n-ary predicate Boolean-valued function Syntactic predicate, in formal grammars and parsers Functional
Predicate
2009-09-12. Oren Ben-Kiki; Clark Evans; Brian Ingerson (2005-01-18). "Boolean Language-Independent Type for YAML Version 1.1". YAML.org. Clark C. Evans
Comparison of data-serialization formats
Comparison_of_data-serialization_formats
Programming language construct
or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is
Short-circuit_evaluation
Type of logical system
its 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
First-order_logic
Algebraic structure used in logic
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with
Heyting_algebra
Standard specifying ASN.1 encoding formats
encode data. X.680 defines a syntax for declaring data types, for example: Booleans, numbers, strings, and compound structures. Each type definition also includes
X.690
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
Formal specification language
Modules", which introduced the idea of describing state transitions as Boolean-valued functions of primed and unprimed variables. Work continued throughout
TLA+
Cloud storage standard
of configuration parameters known as capabilities. These are either boolean values that represent whether or not a system supports things such as queues
Cloud Data Management Interface
Cloud_Data_Management_Interface
meaning depending on whether they are used in a 'truth-value context' (i.e. when a Boolean value was expected, for example in if (a==b & c) {...} it behaved
Operators_in_C_and_C++
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
Russian mathematician (1945–2025)
of subdifferentials for vector-lattice valued functions, to whose study he introduced methods of Boolean-valued models and infinitesimals. He was professor
Semyon_Kutateladze
English mathematician and philosopher (1815–1864)
known as the author of The Laws of Thought (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping
George_Boole
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
Representation of data types in lambda calculus
are usually considered primitive in other notations (such as integers, Booleans, pairs, lists, and tagged unions) are not natively present. Hence the need
Church_encoding
British mathematician
influential papers in category theory entitled A category approach to boolean valued set theory, which introduced many students to topos theory. He was a
Denis_Higgs
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
Algebraic_normal_form
In mathematics, a 2-valued morphism is a homomorphism that sends a Boolean algebra B onto the two-element Boolean algebra 2 = {0,1}. It is essentially
2-valued_morphism
Transition system
structures.[citation needed] Let AP be a set of atomic propositions, i.e. boolean-valued expressions formed from variables, constants and predicate symbols.
Kripke structure (model checking)
Kripke_structure_(model_checking)
satisfy a given Boolean formula, introduced by Valiant in 1979. In other words, it asks in how many ways the variables of a given Boolean formula can be
♯SAT
Computer programming function
the original data structure for which a given predicate returns the Boolean value true. In Haskell, the code example filter even [1..10] evaluates to
Filter (higher-order function)
Filter_(higher-order_function)
1969 non-fiction book by G. Spencer-Brown
Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean
Laws_of_Form
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)
Algorithm from machine learning
{\displaystyle X=\{0,1\}^{n}} , that is, each instance is described as a set of Boolean-valued features. The algorithm maintains non-negative weights w i {\displaystyle
Winnow_(algorithm)
American logician (born 1932)
initial observation of Robert Solovay, Scott formulated the concept of Boolean-valued model, as Solovay and Petr Vopěnka did likewise at around the same time
Dana_Scott
System of formal mathematical logic
subscripted "o" is the type symbol for boolean values, and subscripted "i" is the type symbol for individual (non-boolean) values. Sequences of these represent
Q0_(mathematical_logic)
Control flow statement that branches according to a Boolean expression
program control flow based on the value of a condition; a Boolean expression. A conditional expression evaluates to a value without the side-effect of changing
Conditional (computer programming)
Conditional_(computer_programming)
Set of values which satisfy a given set of equations
and 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
Solution_set
countable choice Axiom of dependent choice Zorn's lemma Axiom of power set Boolean-valued model Burali-Forti paradox Cantor's back-and-forth method Cantor's diagonal
List_of_set_theory_topics
consisting of functions whose value is specified on less than λ elements of λ. Lévy 1963, p. 593. Bell, J. L. (1985). Boolean-Valued Models and Independence
Collapsing_algebra
Algorithmic paradigm for constraint satisfaction or enumeration problems
do 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
Data structure for Boolean functions
(BDD) or 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
Binary_decision_diagram
Programming language standard
predicates (answering a Boolean-valued question) and as returning a useful value for further computation, but in Scheme the value '() which is equivalent
Common_Lisp
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
Rules out assigning to arbitrary functions their computational complexity
then there exists a total computable predicate g {\displaystyle g} (a boolean valued computable function) so that for every program i {\displaystyle i} for
Blum's_speedup_theorem
Set theory concept
proposition. List of large cardinal properties Bell, J. L. (1985). Boolean-Valued Models and Independence Proofs in Set Theory. Oxford University Press
Large_cardinal
Basic notion of sameness in mathematics
certain properties. In computer science, an equation is defined as a boolean-valued expression, or relational operator, which returns 1 and 0 for true and
Equality_(mathematics)
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
Linux kernel security module
boolean value - Linux man page". Linux.die.net. Archived from the original on 3 June 2020. Retrieved 6 February 2013. "setsebool(8): set SELinux boolean value
SELinux
Typed lambda calculus
for the Boolean values T {\displaystyle \mathbf {T} } and F {\displaystyle \mathbf {F} } are used, extending the definition of Church Booleans: T = Λ α
System_F
Low-space search for a majority element
repeated elements Majority function, the majority of a collection of Boolean values Majority problem (cellular automaton), the problem of finding a majority
Boyer–Moore majority vote algorithm
Boyer–Moore_majority_vote_algorithm
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
Mathematical symbol of equality
0 === false is not, because the number 0 is an integer value whereas false is a Boolean value. JavaScript has the same semantics for ===, referred to
Equals_sign
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
Concept_learning
Software design pattern
Specification class has one function called IsSatisfiedBy that returns a Boolean value. After instantiation, the specification is "chained" with other specifications
Specification_pattern
Set of rules defining correctly structured C++ program
cannot: Start with a digit. Be equal to a reserved keyword, null literal or Boolean literal. The identifier nullptr is not a reserved word, but is a global
C++_syntax
Mathematical theory of data types
symbols could include the natural number 0 {\displaystyle 0} , the Boolean value true {\displaystyle {\texttt {true}}} , and functions such as the
Type_theory
Examples include: Truth values in mathematical logic, and the corresponding Boolean data type in computer science, representing a value which may be chosen
Binary_decision
Expression in propositional calculus
from the same set) and heterogeneous relations. Propositional formula Boolean-valued function Formula (logic) Sentence (logic) Truth function Open sentence
Propositional_function
BOOLEAN VALUED
BOOLEAN VALUED
Girl/Female
Indian
Flowering, Blooming, Flower
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 Bullen.
Boy/Male
Indian, Punjabi, Sikh
God's Spoken Word
Surname or Lastname
English
English : variant of Wool.Americanized form of Jewish Wollman or German Wollmann (see Wollman).
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.
Surname or Lastname
English
English : habitational name from places in Devon and Norfolk named Boyland. The Norfolk place name is derived from the Old English personal name Boia + lund ‘grove’ (Old Norse lundr).Irish : variant of Boylan.
Boy/Male
American, British, English
Lives at the Buck Meadow
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Telugu, Traditional
Flowering
Surname or Lastname
English
English : variant of Bullen.
Boy/Male
Irish
Puppy.
Surname or Lastname
North German form of Fries 1.Dutch
North German form of Fries 1.Dutch : variant of Frese.English : metonymic occupational name for a weaver of frieze, a coarse woolen cloth with a thick nap, Old French frise.
Surname or Lastname
English
English : variant of Boland.Irish : Anglicized form of Gaelic Ó Beólláin, ‘descendant of Bjolan’, a Norse personal name.
Girl/Female
Tamil
Foolan | பூலந, பூலà®
Flowering, Blooming, Flower
Foolan | பூலந, பூலà®
Surname or Lastname
English
English : possibly a variant of Woolen.
Boy/Male
English American German
Cuts the nap of woolen cloth. 'Shireman' In medieval times the shireman served as governor-judge...
Surname or Lastname
Czech
Czech : from a pet form of the personal names Boleslav or Bolebor.Polish (Boleń) : from a pet form of the personal name Bolesław.Variant spelling of German Bohlen.Swedish (Bolén) : ornamental name composed of an unexplained first element + the common surname suffix -én, a derivative of Latin -enius ‘descendant of’.English : variant of Bullen.
Surname or Lastname
English
English : variant spelling of Woolen.
Surname or Lastname
English
English : metonymic occupational name for a maker and seller of woolen cloth, from Old French drap ‘cloth’.
Surname or Lastname
English
English : variant of Bowerman.
BOOLEAN VALUED
BOOLEAN VALUED
Girl/Female
Tamil
Clove
Boy/Male
Hindu
The first Vedas, Lord Ganesh, Knower of the arthara Vedas
Boy/Male
Tamil
Moon (Lord of night
Boy/Male
Scottish
Speckled.
Male
Turkish
Variant spelling of Turkish Chagatai. Of unknown ÇAĞATAY means.
Girl/Female
Hindu
Deep pink
Girl/Female
Hindu, Indian, Marathi, Traditional
Goddess of Victory
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Leader of Men
Boy/Male
Hindu, Indian, Tamil
Canal
Girl/Female
Arabic, Muslim, Sindhi
Gift of God; Gift of Allah
BOOLEAN VALUED
BOOLEAN VALUED
BOOLEAN VALUED
BOOLEAN VALUED
BOOLEAN VALUED
a.
Alt. of Bollen
n.
A kind of woolen.
n.
A studious man; a scholar.
a.
Made of wool; consisting of wool; as, woolen goods.
n.
A kind of woolen stuff.
n.
One who deals in wool.
pl.
of Bookman
n.
A kind of woolen cloth.
n.
Cloth, or woolen stuffs in general.
a.
Swollen; puffed out.
n.
A kind of woolen cloth; tammy.
a.
Having the characteristic of Zoilus, a bitter, envious, unjust critic, who lived about 270 years before Christ.
a.
See Boln, a.
n.
Cloth made of wool; woollen goods.
n.
A woolen stuff thinner than ratteen.
a.
Of or pertaining to Sir Thomas Bodley, or to the celebrated library at Oxford, founded by him in the sixteenth century.
a.
Of or pertaining to wool or woolen cloths; as, woolen manufactures; a woolen mill; a woolen draper.
n.
A soft and delicate woolen, or woolen and silk, fabric, for ladies' dresses.
pl.
of Woolman