Any kind of logic, function, expression, or theory based on the work of

George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ...

is considered Boolean. Related to this, "Boolean" may refer to: *

Boolean data type 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 is intended to represent the two truth values of logic and Boolean algebra. It is named ...

, a form of data with only two possible values (usually "true" and "false") *

Boolean algebra 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 variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...

, a logical calculus of truth values or set membership *

Boolean algebra (structure) In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a ge ...

, a set with operations resembling logical ones *

Boolean domain In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include ''false'' and ''true''. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as ...

, a set consisting of exactly two elements whose interpretations include ''false'' and ''true'' *

Boolean circuit In computational complexity theory and circuit 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, one circuit for each possible inp ...

, a mathematical model for digital logical circuits. * Boolean expression, an expression in a programming language that produces a Boolean value when evaluated *

Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

, a function that determines Boolean values or operators *

Boolean model (probability theory) For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson ...

, a model in stochastic geometry *

Boolean network A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the sta ...

, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network *

Boolean processor The Intel MCS-51 (commonly termed 8051) is a single chip microcontroller (MCU) series developed by Intel in 1980 for use in embedded systems. The architect of the Intel MCS-51 instruction set was John H. Wharton. Intel's original versions were po ...

, a 1-bit variable computing unit *

Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean al ...

, a mathematical ring for which ''x''² = ''x'' for every element ''x'' *

Boolean satisfiability problem In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisf ...

, the problem of determining if there exists an interpretation that satisfies a given Boolean formula *

Boolean prime ideal theorem 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 for filters on sets is known as the ultrafilter lemma. Other theorems are obtained by cons ...

, a theorem which states that ideals in a Boolean algebra can be extended to prime ideals

See also