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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. [1] Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. [2]
Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences. [6] An argument is a set of premises together with a conclusion.
In logic, a set of symbols is commonly used to express logical representation. ... (“variable”) expressions; [4] also used for denoting Gödel number; [5] ...
Logic sentences that can be expressed in classical propositional calculus have an equivalent expression in Boolean algebra. Thus, Boolean logic is sometimes used to denote propositional calculus performed in this way. [14] [15] [16] Boolean algebra is not sufficient to capture logic formulas using quantifiers, like those from first order logic.
A form of logical expression where all quantifiers are moved to the front, standardizing the structure of first-order logical statements. primitive recursion A form of recursion where a function is defined in terms of itself, using simpler cases, with a base case to stop the recursion. primitive recursive function
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.
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
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.