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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/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
All rules use the basic logic operators. A complete table of "logic operators" is shown by a truth table , giving definitions of all the possible (16) truth functions of 2 boolean variables ( p , q ):
In Boolean algebra, the consensus theorem or rule of consensus [1] is the identity: ¯ = ¯ The consensus or resolvent of the terms and ¯ is . It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.
If one replaces '=' in R1 and R2 with the biconditional, the resulting rules hold in conventional logic. However, conventional logic relies mainly on the rule modus ponens; thus conventional logic is ponential. The equational-ponential dichotomy distills much of what distinguishes mathematical logic from the rest of mathematics.
For a complete boolean algebra infinite de-Morgan's laws hold. A Boolean algebra is complete if and only if its Stone space of prime ideals is extremally disconnected. Sikorski's extension theorem states that if A is a subalgebra of a Boolean algebra B, then any homomorphism from A to a complete Boolean algebra C can be extended to a morphism ...
The second rule of unit propagation can be seen as a restricted form of resolution, in which one of the two resolvents must always be a unit clause.As for resolution, unit propagation is a correct inference rule, in that it never produces a new clause that was not entailed by the old ones.
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.
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.