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Algebraic manipulation of "true" and "false"
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the
Boolean_algebra
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
Expression in a computer program
Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed
Boolean_expression
Data having only values "true" or "false"
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which
Boolean_data_type
Algebraic structure modeling logical operations
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Difficulty measures for computer science problems
The Boolean hierarchy is the hierarchy of Boolean combinations (intersection, union and complementation) of NP sets. Equivalently, the Boolean hierarchy
Boolean_hierarchy
Algebraic structure in mathematics
In mathematics, a Boolean ring R is a ring for which x2 = x for all x in R, that is, a ring that consists of only idempotent elements. An example is the
Boolean_ring
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
Topics referred to by the same term
Look up Boolean algebra in Wiktionary, the free dictionary. Boolean algebra is the algebra of truth values and operations on them. Boolean algebra may
Boolean algebra (disambiguation)
Boolean_algebra_(disambiguation)
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
Problem of determining if a Boolean formula could be made true
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY
Boolean satisfiability problem
Boolean_satisfiability_problem
Concept in mathematical logic
In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic
Boolean_domain
Model of computation
complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits
Boolean_circuit
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
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
Index of articles associated with the same name
Off, 1 or 0) referring to two-element Boolean algebra (the Boolean domain), e.g. Boolean-valued function or Boolean data type in mathematics: something
Boolean-valued
Boolean analysis was introduced by Flament (1976). The goal of a Boolean analysis is to detect deterministic dependencies between the items of a questionnaire
Boolean_analysis
mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called
Boolean_matrix
The Scannerless Boolean Parser is an open-source scannerless GLR parser generator for boolean grammars. It was implemented in the Java programming language
Scannerless_Boolean_Parser
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
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem
Cook–Levin_theorem
of the Extended Boolean model is to overcome the drawbacks of the Boolean model that has been used in information retrieval. The Boolean model doesn't consider
Extended_Boolean_model
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
Order-preserving mathematical function
be proven optimal provided that the heuristic they use is monotonic. In Boolean algebra, a monotonic function is one such that for all ai and bi in {0
Monotonic_function
Boolean grammars, introduced by Okhotin [Wikidata], are a class of formal grammars studied in formal language theory. They extend the basic type of grammars
Boolean_grammar
Subject field of Boolean algebra discussing changes of Boolean variables and functions
Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean
Boolean_differential_calculus
Type of geometry processing
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR, ...) operating on one or more sets of polygons in computer graphics
Boolean operations on polygons
Boolean_operations_on_polygons
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
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
A Boolean Delay Equation (BDE) is an evolution rule for the state of dynamical variables whose values may be represented by a finite discrete numbers
Boolean_delay_equation
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
Analysis 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
Logical connective OR
will come.' Affirming a disjunct Boolean algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction
Logical_disjunction
Boolean algebra with all operators and laws forming a complete logical system
mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to
Complete_Boolean_algebra
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
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
Study of Boolean functions via discrete Fourier analysis
In mathematics and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0
Analysis_of_Boolean_functions
Set of rules defining correctly structured programs
const t = Boolean(b); // Boolean true const f = Boolean(b.valueOf()); // Boolean false let n = new Boolean(b); // Not recommended n = new Boolean(b.valueOf());
JavaScript_syntax
Network that allows computers to share resources and communicate with each other
Blockmodeling Maximum entropy Soft configuration LFR Benchmark Dynamics Boolean network agent based Epidemic/SIR Lists Categories Topics Software Network
Computer_network
Search using the full text of documents
within a stored data record, such as "Title" or "Author." Boolean queries: Searches using Boolean operators (for example, "encyclopedia" AND "online" NOT
Full-text_search
Classical information retrieval model
The (standard) Boolean model of information retrieval (BIR) is a classical information retrieval (IR) model where documents are retrieved based on whether
Boolean model of information retrieval
Boolean_model_of_information_retrieval
Creating a complex 3D surface or object by combining primitive objects
geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex
Constructive_solid_geometry
Logic constructed only from NAND gates
The NAND Boolean function has the property of functional completeness. This means that any Boolean expression can be re-expressed by an equivalent expression
NAND_logic
Ideals in a Boolean algebra can be extended to prime ideals
In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement
Boolean_prime_ideal_theorem
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
Process in digital electronics and integrated circuit design
structures on an integrated circuit. In terms of Boolean algebra, the optimization of a complex Boolean expression is a process of finding a simpler one
Logic_optimization
Can one split the integers into two sets such that every Pythagorean triple spans both?
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean
Boolean Pythagorean triples problem
Boolean_Pythagorean_triples_problem
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
Outline_of_logic
Algebraic structure
of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras
Interior_algebra
Model of computation
computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits
Circuit_(computer_science)
Technical treatment of Boolean algebras
Boolean algebras are models of the equational theory of two values; this definition is equivalent to the lattice and ring definitions. Boolean algebra
Boolean algebras canonically defined
Boolean_algebras_canonically_defined
Computational problem
problem) is the computational problem of computing the output of a given Boolean circuit on a given input. The problem is complete for P under uniform AC0
Circuit_value_problem
Every Boolean algebra is isomorphic to a certain field of sets
In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem
Stone's representation theorem for Boolean algebras
Stone's_representation_theorem_for_Boolean_algebras
Value indicating the relation of a proposition to truth
languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions
Truth_value
Boolean algebra generated by a set with no relations beyond Boolean laws
a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can
Free_Boolean_algebra
Geometric property of a pair of sets of points in Euclidean geometry
{\displaystyle N>2K} . A Boolean function in n variables can be thought of as an assignment of 0 or 1 to each vertex of a Boolean hypercube in n dimensions
Linear_separability
Model of computational complexity
computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related
Circuit_complexity
Graphical method to simplify Boolean expressions
Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as
Karnaugh_map
Set theory concept
mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the
Boolean-valued_model
Topics referred to by the same term
Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been
Topological_Boolean_algebra
In mathematics and computer science, a balanced Boolean function is a Boolean function whose output yields as many 0s as 1s over its input set. This means
Balanced_Boolean_function
Mathematical set of all subsets of a set
prototypical example of a Boolean algebra. In fact, one can show that any finite Boolean algebra is isomorphic to the Boolean algebra of the power set
Power_set
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
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
In Boolean algebra, the inclusion relation a ≤ b {\displaystyle a\leq b} is defined as a b ′ = 0 {\displaystyle ab'=0} and is the Boolean analogue to the
Inclusion_(Boolean_algebra)
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
Attribute of data
floating-point numbers (which approximate real numbers), characters and Booleans. A data type may be specified for many reasons: similarity, convenience
Data_type
Locating information online
Most search engines offer advanced search options using Boolean expressions (also known as Boolean operations). These expressions allow searches to produce
Online_search
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
System including an indeterminate value
the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false. Emil Leon Post is credited
Three-valued_logic
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
Topics referred to by the same term
arithmetic) 1 (number) (in Boolean algebra with a notation where '+' denotes a logical disjunction) 0 (number) (in Boolean algebra with a notation where
1+1
Algebraic ring that need not have additive negative elements
lattices. The smallest semiring that is not a ring is the two-element Boolean algebra, for instance with logical disjunction ∨ {\displaystyle \lor }
Semiring
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 (SoP
Canonical_normal_form
Typed lambda calculus
x^{\mathsf {Boolean}}\lambda y^{\mathsf {Boolean}}{.}x\,{\mathsf {Boolean}}\,y\,\mathbf {F} \\\mathrm {OR} &=\lambda x^{\mathsf {Boolean}}\lambda y^{\mathsf
System_F
Boolean algebra
two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain
Two-element_Boolean_algebra
Configuration file format
Non-standard Boolean, Number, String Read + Write *BSD, Linux, macOS, Windows PSFL C (implementation), Python (usage) 3.9.7 GLib Yes Yes No No Boolean, Number
INI_file
Representation of natural numbers and other 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
Logical problem studied in computer science
determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers
Satisfiability modulo theories
Satisfiability_modulo_theories
Problem in computational complexity theory
is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment
Maximum satisfiability problem
Maximum_satisfiability_problem
Pair of logical equivalences
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid
De_Morgan's_laws
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
Mathematical assumptions
mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus)
Minimal axioms for Boolean algebra
Minimal_axioms_for_Boolean_algebra
Mathematical table used in logic
mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional
Truth_table
Standard form of Boolean function
In Boolean logic, a formula for a Boolean function f is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum
Blake_canonical_form
Array data structure that compactly stores bits
arrays are composed with matrix multiplication where the arithmetic is Boolean, and such a composition represents composition of relations. Although most
Bit_array
Cryptographic attack
registers (LFSRs) using a Boolean function. Correlation attacks exploit a statistical weakness that arises from the specific Boolean function chosen for the
Correlation_attack
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
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)
For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously)
Boolean model (probability theory)
Boolean_model_(probability_theory)
Theorem about complexity measures of Boolean functions
theorem, proved by Hao Huang in 2019, states that the sensitivity of a Boolean function f : { 0 , 1 } n → { 0 , 1 } {\displaystyle f\colon \{0,1\}^{n}\to
Sensitivity_theorem
solves types of the Boolean satisfiability problem despite there being no known efficient algorithm in the general case. The Boolean satisfiability (or
Boolean satisfiability algorithm heuristics
Boolean_satisfiability_algorithm_heuristics
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
Symbol representing a property or relation in logic
Validity Syllogism Square of opposition Venn diagram Propositional Boolean algebra Boolean functions Logical connectives Propositional calculus Propositional
Predicate_(logic)
List of symbols used to express logical relations
if P then Q, it is not the case that P and not Q propositional logic, Boolean algebra, Heyting algebra A ⇒ B {\displaystyle A\Rightarrow B} is false
List_of_logic_symbols
Logical gate whose output is false if all its inputs are true
inverters followed by an OR gate. The NAND gate is significant because any Boolean function can be implemented by using a combination of NAND gates. This
NAND_gate
Set of computational problems stated by Richard Karp (1973)
Combinatorial Problems", Richard Karp used Stephen Cook's 1971 theorem that the Boolean satisfiability problem is NP-complete (also called the Cook–Levin theorem)
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
American mathematician (1904–1994)
theory of Boolean algebras and Boolean rings and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory. Subsequently
Alfred_Foster_(mathematician)
Boolean algebra extended with a unary operator representing existential quantification
monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, ', 0, 1⟩ is a Boolean algebra
Monadic_Boolean_algebra
Bound lattice in which every element has a complement
distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra. A complemented lattice is a bounded lattice (with least element
Complemented_lattice
BOOLEAN
BOOLEAN
BOOLEAN
BOOLEAN
Male
Greek
(Αἴσωπος) Original Greek form of Latin Æsop, the name of the author of Æsop's Fables, said to be a hump-backed slave of African descent; therefore, the name has taken on the AISOPOS means "hump-backed," but in Greek it means "Ethiop."Â
Girl/Female
Arabic, Australian
The First Lady who Obtained Shahadat in Islam
Boy/Male
Indian
Joy, Happiness, Unripe dates
Girl/Female
Arabic, Muslim
Full Moon of the Women
Boy/Male
Tamil
Kirtinath | கீரà¯à®¤à¯€à®¨à®¾à®¤
Famous person
Surname or Lastname
English
English : variant spelling of Bibby.
Boy/Male
Hindu, Indian, Traditional
Lord Brahma
Girl/Female
Assamese, Indian
Singer; Love; To Flow; Earth; River; Happy; In Bengal is for Fragrance of a Flower; Drop of Water
Girl/Female
American, Australian, British, Christian, Danish, English, Jamaican
Fortunate; Short Form of Alicia; Felicia; Letitia; Happy; Joy; Truth
Boy/Male
Muslim
Bright, Shining, Sparkling, Luminous
BOOLEAN
BOOLEAN
BOOLEAN
BOOLEAN
BOOLEAN