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In computer science, a binary decision diagram (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 representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed ...
A binary decision is a choice between two alternatives, for instance between taking some specific action or not taking it. [1] Binary decisions are basic to many fields. Examples include: Truth values in mathematical logic, and the corresponding Boolean data type in computer science, representing a value which may be chosen to be either true or ...
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.
A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to
Lewis's trilemma is a famous example of this type of argument involving three disjuncts: "Jesus was either a liar, a lunatic, or Lord". [3] By denying that Jesus was a liar or a lunatic, one is forced to draw the conclusion that he was God. But this leaves out various other alternatives, for example, that Jesus was a prophet. [3]
This table does not describe the logic operations necessary to implement this operation, rather it simply specifies the function of inputs to output values. With respect to the result, this example may be arithmetically viewed as modulo 2 binary addition, and as logically equivalent to the exclusive-or (exclusive disjunction) binary logic ...
Binary decision diagram, listing the truth table values at the bottom of a binary tree; Venn diagram, depicting the truth table values as a colouring of regions of the plane; Algebraically, as a propositional formula using rudimentary Boolean functions: Negation normal form, an arbitrary mix of AND and ORs of the arguments and their complements
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.