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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 in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
Boolean algebras canonically defined. Boolean algebras are models of the equational theory of two values; this definition is equivalent to the lattice and ring definitions. Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with ...
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 {-1,1}). [ 1][ 2] Alternative names are switching function, used especially in older computer science literature, [ 3][ 4] and truth function (or logical function), used in logic.
Boolean expression. In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/Yes or False/No, Boolean-typed variables, Boolean-valued operators ...
Boolean-valued model. Boolean satisfiability problem. Boolean differential calculus. Indicator function (also called the characteristic function, but that term is used in probability theory for a different concept) Espresso heuristic logic minimizer. Logical matrix. Logical value. Stone duality. Stone space.
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [ 1][ 2][ 3] also known as De Morgan's theorem, [ 4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British ...
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 generalization of a power set algebra or a field of sets, or its elements can ...
The Karnaugh map ( KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 [ 1][ 2] as a refinement of Edward W. Veitch 's 1952 Veitch chart, [ 3][ 4] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram[ 5][ 6] aka Marquand diagram[ 4] but now with a focus set on its ...
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