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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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In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
[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 ...
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.
The dual of a formula is obtained by replacing each connective by its dual, [110] [111] e.g., for a formula containing only conjunction, disjunction, and negation (such as a formula in disjunctive normal form), its dual is the result of replacing each conjunction with a disjunction, and each disjunction with a conjunction. (For a formula in ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Disjunctive normal form; H. Head normal form;
Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) way.