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2015-01-09T02:45:21Z

Output resistance

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	~~In [[mathematical logic]], a formula is in '''negation normal form''' if~~ the ~~[[negation]] operator (<math>\lnot</math>, {{smallcaps\|not}})~~ is only applied to variables and the only other allowed [[Boolean algebra\|Boolean operators]] are [[logical conjunction\|conjunction]] (<math>\land</math>, {{smallcaps\|and}}) and [[logical disjunction\|disjunction]] (<math>\lor</math>, {{smallcaps\|or}}).		Anybody who wrote the blog is called Eusebio. South Carolina is michael's birth place. The most beloved hobby for him and as well his kids is up to fish and he's been really doing it for a while. Filing has been his profession although. Go to his website to identify a out more: http://prometeu.net<br><br>My web-site; [http://prometeu.net clash of clans unlimited gems]

	~~Negation normal form~~ is ~~not a canonical form:~~ for ~~example, <math>a \land (b\lor \lnot c)</math>~~ and ~~<math>(a \land b) \lor (a \land \lnot c)</math> are equivalent, and are both in negation normal form.~~

	~~In classical logic and many [[modal logic]]s, every formula can be brought into this form by replacing implications~~ and ~~equivalences by their definitions, using [[De Morgan~~'s ~~laws]] to push negation inwards, and eliminating double negations~~. ~~This process can be represented using the following [[rewrite rule]]s:~~

	~~:<math>\lnot (\forall x~~. ~~G) \~~to ~~\exists x. \lnot G</math>~~
	~~:<math>\lnot (\exists x. G) \~~to ~~\forall x. \lnot G</math>~~
	:~~<math>\lnot \lnot G \to G</math>~~
	~~:<math>\lnot (G_1 \land G_2) \to (\lnot G_1) \lor (\lnot G_2)</math>~~
	~~:<math>\lnot (G_1 \lor G_2) \to (\lnot G_1) \land (\lnot G_2)</math>~~

	~~A formula in negation normal form can be put into the stronger [[conjunctive normal form]] or [[disjunctive normal form]] by applying [[Distributive property\|distributivity]].~~

	~~==Examples and counterexamples==~~
	~~The following formulae are all in negation normal form:~~
	~~:<math>(A \vee B) \wedge C</math>~~
	~~:<math>(A \wedge (\lnot B \vee C) \wedge \lnot C) \vee D</math>~~
	:~~<math>A \vee \lnot B<~~/~~math>~~
	~~:<math>A \wedge \lnot B<~~/~~math>~~

	~~The first example is also in [[conjunctive normal form]] and the last two are in both [[conjunctive normal form]] and [[disjunctive normal form]], but the second example is in neither~~.

	~~The following formulae are not in negation normal form:~~
	~~:<math>A \Rightarrow B</math>~~
	~~:<math>\lnot (A \vee B)</math>~~
	~~:<math>\lnot (A \wedge B)</math>~~
	~~:<math>\lnot (A \vee \lnot C)</math>~~

	~~They are however respectively equivalent to the following formulae in negation normal form:~~
	~~:<math>\lnot A \vee B</math>~~
	~~:<math>\lnot A \wedge \lnot B</math>~~
	:<~~math~~>~~\lnot A \vee \lnot B~~<~~/math~~>
	~~:<math>\lnot A \wedge C</math>~~

	~~==References==~~

	* Alan J.A. Robinson and Andrei Voronkov, ''Handbook of Automated Reasoning'' '''1''':203''ff'' (2001) ISBN 0444829490.

	~~==External links==~~
	* [http://~~www~~.~~izyt.com/BooleanLogic/applet.php Java applet for converting logical formula to Negation Normal Form, showing laws used]~~

	~~[[Category:Propositional calculus]]~~
	~~[[Category:Normal forms (logic)]~~]

en>DavidLeighEllis: Reverted edits by 175.110.86.40 (talk) to last version by Sv1xv

2013-10-23T18:02:00Z

Reverted edits by 175.110.86.40 (talk) to last version by Sv1xv

← Older revision		Revision as of 20:02, 23 October 2013
Line 1:		Line 1:
			In [[mathematical logic]], a formula is in '''negation normal form''' if the [[negation]] operator (<math>\lnot</math>, {{smallcaps\|not}}) is only applied to variables and the only other allowed [[Boolean algebra\|Boolean operators]] are [[logical conjunction\|conjunction]] (<math>\land</math>, {{smallcaps\|and}}) and [[logical disjunction\|disjunction]] (<math>\lor</math>, {{smallcaps\|or}}).

			Negation normal form is not a canonical form: for example, <math>a \land (b\lor \lnot c)</math> and <math>(a \land b) \lor (a \land \lnot c)</math> are equivalent, and are both in negation normal form.

	~~Your individual Tribe is the lots of strong of all~~ and ~~you will probably have~~ the ~~planet~~ (~~virtual~~) ~~at your toes, as well as the all that with single a brief on-line video that may direct you step by step back in how~~ to ~~get our cheat code for Mismatch of Tribes~~.<br><br>~~Use the web for help~~. ~~Nearly all game has its actually own legion of devoted devotees, lots of which waste countless hours crafting effective maps and guides. Additionally there are newsgroups where you are able~~ to ~~speak one on with other players~~. ~~Benefit from this goldmine and it is easy~~ to ~~eventually get past that level you have been stuck on forever.~~<br><br>~~To [http~~:/~~/Www.dict.cc/?s=enjoy+unlimited enjoy unlimited~~] ~~points, resources, gold and silver coins~~ or ~~gems, you is required to download the clash of clans hack tool~~ by ~~clicking throughout the button~~. ~~Depending around operating system that you~~ are ~~using, you will should run the downloaded doc as administrator. Give you log~~ in ~~ID and choose the device. Promptly after this, you are ought enter the number behind gems or coins that you would like to get.~~<br><br>~~Daily check several distinct [http~~://~~www.britannica.com~~/~~search?query=locations locations~~] ~~before purchasing a on~~ the ~~internet. Be sure - look~~ both ~~online~~ and ~~as well in genuine brick and mortar stores in your amazing region. If you enjoyed this post and you would like to receive more details regarding~~ [~~http://circuspartypanama.com clash of clans hack cydia~~] ~~kindly go to our webpage~~. The ~~costs of a video online may differ widely, certain if a game is considered~~ not ~~brand new. By performing a modest additional leg work, it is possible to gain clash of clans.~~<br><br>You might be looking Conflict of The entire family Jewels Free, or you can find yourself just buying a Steal Conflict of Tribes, currently has the smartest choice at the internet, absolutely free and also only takes a jiffy to get all all these.<br><br>~~You will notice for yourself that all of our Money Compromise of Clans i fairly effective, fully invisible by the manager of the game, predominantly absolutely no price!~~<br><br>~~You don''t necessarily have~~ to ~~one of~~ the ~~reliable troops to win wins~~. A ~~mass volume~~ of ~~barbarians, your first-level troop, could well totally destroy an enemy village, and strangely it~~''~~s quite enjoyable~~ to ~~examine the virtual carnage.~~		In classical logic and many [[modal logic]]s, every formula can be brought into this form by replacing implications and equivalences by their definitions, using [[De Morgan's laws]] to push negation inwards, and eliminating double negations. This process can be represented using the following [[rewrite rule]]s:

			:<math>\lnot (\forall x. G) \to \exists x. \lnot G</math>
			:<math>\lnot (\exists x. G) \to \forall x. \lnot G</math>
			:<math>\lnot \lnot G \to G</math>
			:<math>\lnot (G_1 \land G_2) \to (\lnot G_1) \lor (\lnot G_2)</math>
			:<math>\lnot (G_1 \lor G_2) \to (\lnot G_1) \land (\lnot G_2)</math>

			A formula in negation normal form can be put into the stronger [[conjunctive normal form]] or [[disjunctive normal form]] by applying [[Distributive property\|distributivity]].

			==Examples and counterexamples==
			The following formulae are all in negation normal form:
			:<math>(A \vee B) \wedge C</math>
			:<math>(A \wedge (\lnot B \vee C) \wedge \lnot C) \vee D</math>
			:<math>A \vee \lnot B</math>
			:<math>A \wedge \lnot B</math>

			The first example is also in [[conjunctive normal form]] and the last two are in both [[conjunctive normal form]] and [[disjunctive normal form]], but the second example is in neither.

			The following formulae are not in negation normal form:
			:<math>A \Rightarrow B</math>
			:<math>\lnot (A \vee B)</math>
			:<math>\lnot (A \wedge B)</math>
			:<math>\lnot (A \vee \lnot C)</math>

			They are however respectively equivalent to the following formulae in negation normal form:
			:<math>\lnot A \vee B</math>
			:<math>\lnot A \wedge \lnot B</math>
			:<math>\lnot A \vee \lnot B</math>
			:<math>\lnot A \wedge C</math>

			==References==

			* Alan J.A. Robinson and Andrei Voronkov, ''Handbook of Automated Reasoning'' '''1''':203''ff'' (2001) ISBN 0444829490.

			==External links==
			* [http://www.izyt.com/BooleanLogic/applet.php Java applet for converting logical formula to Negation Normal Form, showing laws used]

			[[Category:Propositional calculus]]
			[[Category:Normal forms (logic)]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-09T08:09:10Z

ISBNs (Build KE)

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