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In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
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[8] [9] This provides a procedure for converting between conjunctive normal form and disjunctive normal form. [10] Since the Disjunctive Normal Form Theorem shows that every formula of propositional logic is expressible in disjunctive normal form, every formula is also expressible in conjunctive normal form by means of effecting the conversion ...
It was Jean Nicod who first used the stroke as a sign for non-conjunction (NAND) in a paper of 1917 and which has since become current practice. [ 11 ] [ 12 ] Russell and Whitehead used the Sheffer stroke in the 1927 second edition of Principia Mathematica and suggested it as a replacement for the "OR" and "NOT" operations of the first edition.
From a classical semantic perspective, material implication is the binary truth functional operator which returns "true" unless its first argument is true and its second argument is false. This semantics can be shown graphically in a truth table such as the one below.
Download QR code; Print/export ... This category concerns the various normal forms used in logic. Pages in category "Normal forms (logic)" ... Disjunctive normal form; H.
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]