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The essential idea of a truth assignment is that the propositional variables are mapped to elements of a fixed Boolean algebra, and then the truth value of a propositional formula using these letters is the element of the Boolean algebra that is obtained by computing the value of the Boolean term corresponding to the formula.
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 Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
In computer science, a Boolean expression (also known as logical 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 ...
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]
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
In realizability truth values are sets of programs, which can be understood as computational evidence of validity of a formula. For example, the truth value of the statement "for every number there is a prime larger than it" is the set of all programs that take as input a number n {\displaystyle n} , and output a prime larger than n ...
The truth values of the atomic formulas can be used to reconstruct the truth values of more complicated formulas, using the structure of the Boolean algebra. For propositional connectives, this is easy; one simply applies the corresponding Boolean operators to the truth values of the subformulae.