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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
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
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
Algebraic structure modeling logical operations
In mathematics, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Data having only values "true" or "false"
In computer science, the Boolean is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the
Boolean_data_type
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all clopen subsets
Cantor_algebra
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
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
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
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
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
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
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
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)
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
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
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
Mathematical structure combining Boolean algebra with additional residuation operations
mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the
Residuated_Boolean_algebra
Topics referred to by the same term
ASCII symbol for the boolean "or" operator, formed with a backslash and a slash The ALGOL 68 boolean "or" operator \/, the boolean "or" operator in early
\/
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
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)
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
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
Representation of data of various 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
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
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
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
Symbolic boolean function representation, extension of BDDs
(MTBDD), is a data structure that is used to symbolically represent a Boolean function whose codomain is an arbitrary finite set S. An ADD is an extension
Algebraic_decision_diagram
Type of topological space
mathematics, a Stone space, also known as a profinite space, profinite set, or Boolean space, is a compact Hausdorff totally disconnected space. Stone spaces
Stone_space
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
graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph
Propositional directed acyclic graph
Propositional_directed_acyclic_graph
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
Computer program for the Boolean satisfiability problem
computer program which aims to solve the Boolean satisfiability problem (SAT). On input a formula over Boolean variables, such as "(x or y) and (x or not
SAT_solver
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
Russian mathematician (1932–2006)
finite-state automata, Boolean circuits and multi-valued logic circuits. Ingo Wegener, in his book The Complexity of Boolean Functions, credits O. B
Oleg_Lupanov
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)
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
Topics referred to by the same term
ASCII symbol for boolean "and" operator, formed with a slash and a backslash /\, an ALGOL 68 boolean "and" operator /\, the boolean "and" operator in
/\
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
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)
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)
Information retrieval technique
Fuzzy retrieval techniques are based on the Extended Boolean model and the Fuzzy set theory. There are two classical fuzzy retrieval models: Mixed Min
Fuzzy_retrieval
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
or false. A Boolean expression may be composed of a combination of the Boolean constants true or false, Boolean-typed variables, Boolean-valued operators
Glossary_of_computer_science
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
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
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
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
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
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
Extremely basic data type
hardware, such as integers of various sizes, floating-point numbers, and Boolean logical values. Operations on such types are usually quite efficient. Primitive
Primitive_data_type
is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra
Measure_algebra
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
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
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
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
Canadian computer scientist
Carnegie Mellon University. He is known for his work on the analysis of Boolean functions and for authoring the textbook on this subject. He is also known
Ryan O'Donnell (computer scientist)
Ryan_O'Donnell_(computer_scientist)
Country within the United Kingdom
Boole created the binary logic underlying all digital systems, known as boolean logic. Alan Turing defined the foundations of computing and pioneered artificial
England
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