Negation normal formFrom Wikipedia, the free encyclopediaIn mathematical logic, a formula is in negation normal form if the negation operator ( , not) is only applied tovariables and the only other allowed Boolean operators are conjunction ( , and) and disjunction ( , or).Negation normal form is not a canonical form: for example, a (b c) and (a b) (a c) are equivalent, andare both in negation normal form.In classical logic and many modal logics, every formula can be brought into this form by replacing implications andequivalences by their denitions, using De Morgans laws to push negation inwards, and eliminating double negations.This process can be represented using the following rewrite rules:(x.G) x.G(x.G) x.GG G(G1 G2) (G1) (G2)(G1 G2) (G1) (G2)A formula in negation normal form can be put into the stronger conjunctive normal form or disjunctive normal formby applying distributivity.1 Examples and counterexamplesThe following formulae are all in negation normal form:(A B) C(A (B C) C) DA BA BThe rst example is also in conjunctive normal form and the last two are in both conjunctive normal form anddisjunctive normal form, but the second example is in neither.The following formulae are not in negation normal form:A B(A B)(A B)(A C)They are however respectively equivalent to the following formulae in negation normal form:12 3 EXTERNAL LINKSA BA BA BA C2 ReferencesAlan J.A. Robinson and Andrei Voronkov, Handbook of Automated Reasoning 1:203 (2001) ISBN0444829490.3 External linksJava applet for converting logical formula to Negation Normal Form, showing laws used34 Text and image sources, contributors, and licenses4.1 Text Negationnormalform Source: https://en.wikipedia.org/wiki/Negation_normal_form?oldid=665947556 Contributors: Vkuncak, Sil-versh, Olathe, Macrakis, Starblue, Obradovic Goran, Pearle, Oleg Alexandrov, Linas, Kbdank71, Mets501, CRGreathouse, CBM,Gregbard, Cydebot, Christian75, Amikake3, Brian Geppert, Addbot, Luckas-bot, Tomdwrightenator, Kejia, Mogism, Ayush3292 andAnonymous: 64.2 Images File:Text_document_with_red_question_mark.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg License:Public domain Contributors:Created by bdesham with Inkscape; based upon Text-x-generic.svgfrom the Tango project. Original artist: Benjamin D. Esham (bdesham)4.3 Content license Creative Commons Attribution-Share Alike 3.0