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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.
{{Normal forms in logic | state = collapsed}} will show the template collapsed, i.e. hidden apart from its title bar. {{Normal forms in logic | state = expanded}} will show the template expanded, i.e. fully visible. This template organizes various normal forms used in logic, split into three categories: propositional logic, predicate logic, and ...
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 ...
For some versions of the SAT problem, it is useful to define the notion of a generalized conjunctive normal form formula, viz. as a conjunction of arbitrarily many generalized clauses, the latter being of the form R(l 1,...,l n) for some Boolean function R and (ordinary) literals l i. Different sets of allowed Boolean functions lead to ...
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
[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 ...
A logical formula is considered to be in CNF if it is a conjunction of one or more disjunctions of one or more literals.As in disjunctive normal form (DNF), the only propositional operators in CNF are or (), and (), and not ().
The stroke is named after Henry Maurice Sheffer, who in 1913 published a paper in the Transactions of the American Mathematical Society [10] providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by Huntington employing the familiar operators of propositional logic (AND, OR, NOT).