Generalized linear array model - Revision history

en>Bender235: /* Overview */

2014-09-26T04:31:42Z

Overview

← Older revision		Revision as of 06:31, 26 September 2014
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	~~In [[mathematical logic]], a '''literal'''~~ is an [~~[atomic formula]] (atom) or its [[negation]].~~		Nestor is the name my [http://Autos.aol.com/article/whats-in-car-warranty/ mothers] and fathers gave [http://ssdpro.com.ng/web/index.php?do=/GreggMaitland/blog/improve-your-auto-repair-knowledge-with-this-particular-advice/ car warranty] me but I don't like when [http://Www.Carbuyingtips.com/warranty.htm individuals] use my full title. He currently lives in Idaho and his parents reside close by. What he really enjoys performing is to perform handball but he is having difficulties to discover time for it. His day occupation is a monetary officer but he ideas on [http://family.ec-win.ir/index.php?do=/profile-2088/info/ extended auto warranty] car auto warranty warranty changing it.<br><br>Also visit my web site; [http://changbai.newdrycleaning.com/photo/54180 extended car warranty]
	~~The definition mostly appears in [[proof theory]] (of [[classical logic]]), e~~.g. in ~~[[conjunctive normal form]~~] and ~~the method of~~ [~~[resolution (logic)\|resolution]].~~

	~~Literals can be divided into two types~~:
	* A '''positive literal''' is just an atom.
	* A '''negative literal''' is the negation of an atom.

	~~For a literal <math>l<~~/~~math>, the '''complementary literal''' is a literal corresponding to the negation of <math>l<~~/~~math>,~~
	~~we can write <math>\bar{l}<~~/~~math> to denote the complementary literal of <math>l<~~/~~math>. More precisely, if <math>l\equiv x<~~/~~math> then <math>\bar{l}<~~/~~math> is <math>\lnot x</math> and if <math>l\equiv \lnot x<~~/~~math> then <math>\bar{l}<~~/~~math> is <math>x<~~/~~math>~~.

	~~In the context of a formula in the [[conjunctive normal form~~]~~], a literal is '''pure''' if the literal's complement does not appear~~ in ~~the formula~~.

	~~== Examples ==~~
	~~In [[propositional calculus]] a literal~~ is ~~simply a [[propositional variable]] or its negation~~.

	~~In [[predicate calculus]] a literal is an [[atomic formula]] or its negation, where an atomic formula~~ is a [~~[Predicate (mathematical logic)\|predicate]] symbol applied to some [[term (logic)\|terms]], <math>P(t_1,\ldots,t_n)<~~/~~math> with the terms [[recursive definition\|recursively defined~~]~~] starting from constant symbols, variable symbols, and [[function (mathematics)\|function]] symbols~~. ~~For example,~~ <~~math~~>~~\neg Q(f(g(x), y, 2), x)~~<~~/math~~> ~~is a negative literal with the constant symbol 2, the variable symbols ''x'', ''y'', the function symbols ''f'', ''g'', and the predicate symbol ''Q''.~~

	~~==References==~~
	*{{cite book \| author = Samuel R. Buss \| chapter= An introduction to proof theory \| editor = Samuel R. Buss \| title=Handbook of proof theory \| pages = 1–78 \| url = http://~~math~~.~~ucsd~~.~~edu/~sbuss~~/~~ResearchWeb~~/~~handbookI/ \| publisher = Elsevier \| date = 1998 \| id = ISBN 0-444-89840-9 }}~~

	~~[[Category:Propositional calculus~~]]
	~~[[Category:Logic symbols]]~~

	~~{{logic-stub}}~~

2001:630:12:10D2:E5C1:54FA:599B:F3E9: Misprint fixed.

2013-11-09T19:30:35Z

Misprint fixed.

← Older revision		Revision as of 21:30, 9 November 2013
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	~~Friends call him Royal Seyler~~. ~~His working day job~~ is a ~~cashier~~ and ~~his salary has been truly fulfilling~~. ~~Alabama has always been his house and his family members enjoys it~~. ~~Playing crochet~~ is a ~~thing that I'm totally addicted~~ to.<br><br>~~Here~~ is ~~my web page [~~http://~~Www~~.~~Thehubermangroup~~.~~com~~/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/~~60/userId/24292/Default.aspx car warranty~~]		In [[mathematical logic]], a '''literal''' is an [[atomic formula]] (atom) or its [[negation]].
			The definition mostly appears in [[proof theory]] (of [[classical logic]]), e.g. in [[conjunctive normal form]] and the method of [[resolution (logic)\|resolution]].

			Literals can be divided into two types:
			* A '''positive literal''' is just an atom.
			* A '''negative literal''' is the negation of an atom.

			For a literal <math>l</math>, the '''complementary literal''' is a literal corresponding to the negation of <math>l</math>,
			we can write <math>\bar{l}</math> to denote the complementary literal of <math>l</math>. More precisely, if <math>l\equiv x</math> then <math>\bar{l}</math> is <math>\lnot x</math> and if <math>l\equiv \lnot x</math> then <math>\bar{l}</math> is <math>x</math>.

			In the context of a formula in the [[conjunctive normal form]], a literal is '''pure''' if the literal's complement does not appear in the formula.

			== Examples ==
			In [[propositional calculus]] a literal is simply a [[propositional variable]] or its negation.

			In [[predicate calculus]] a literal is an [[atomic formula]] or its negation, where an atomic formula is a [[Predicate (mathematical logic)\|predicate]] symbol applied to some [[term (logic)\|terms]], <math>P(t_1,\ldots,t_n)</math> with the terms [[recursive definition\|recursively defined]] starting from constant symbols, variable symbols, and [[function (mathematics)\|function]] symbols. For example, <math>\neg Q(f(g(x), y, 2), x)</math> is a negative literal with the constant symbol 2, the variable symbols ''x'', ''y'', the function symbols ''f'', ''g'', and the predicate symbol ''Q''.

			==References==
			*{{cite book \| author = Samuel R. Buss \| chapter= An introduction to proof theory \| editor = Samuel R. Buss \| title=Handbook of proof theory \| pages = 1–78 \| url = http://math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ \| publisher = Elsevier \| date = 1998 \| id = ISBN 0-444-89840-9 }}

			[[Category:Propositional calculus]]
			[[Category:Logic symbols]]

			{{logic-stub}}

en>Melcombe: revise cats

2012-05-31T20:30:26Z

revise cats

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