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en>Mild Bill Hiccup: /* References */ layout

2014-08-17T05:15:17Z

References: layout

← Older revision		Revision as of 07:15, 17 August 2014
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	~~{{Transformation rules}}~~		Fascinated to meet you! My current name is Eusebio Ledbetter. It's not a [http://photobucket.com/images/common+stuff common stuff] but what I desire doing is bottle top [http://answers.yahoo.com/search/search_result?p=collecting&submit-go=Search+Y!+Answers collecting] and now I have time to consume on new things. Software developing is how My wife and i support my family. My house is now in Vermont. I've been working on my website during some time now. Study it out here: http://circuspartypanama.com<br><br>
	~~{{other uses}}~~

	In [[propositional calculus\|propositional logic]], '''simplification'''<ref>Copi and Cohen</ref><ref>Moore and Parker</ref><ref>Hurley</ref> (equivalent to '''conjunction elimination''') is a [[validity\|valid]] [[immediate inference]], [[argument form]] and [[rule of inference]] which makes the [[inference]] that, if the [[Logical conjunction\|conjunction]] ''A and B'' is true, then ''A'' is true, and ''B'' is true. The rule makes it possible to shorten longer [[formal proof\|proofs]] by deriving one of the conjuncts of a conjunction on a line by itself.		Also visit my website: [http://circuspartypanama.com clash of clans cheats no survey]

	~~An example in [[English language\|English]]:~~
	~~:It's raining and it's pouring.~~
	~~:Therefore it's raining.~~

	~~The rule can be expressed in [[formal language]] as:~~

	~~:<math>\frac{P \land Q}{\therefore P}</math>~~

	~~or as~~

	~~:<math>\frac{P \land Q}{\therefore Q}</math>~~

	~~where the rule is that whenever instances of "<math>P \land Q</math>" appear on lines of a proof, either "<math>P</math>" or "<math>Q</math>" can be placed on a subsequent line by itself.~~

	~~== Formal notation ==~~
	~~The ''simplification'' rule may be written in [[sequent]] notation~~:

	~~: <math>(P \land Q) \vdash P</math>~~
	~~or as~~
	~~: <math>(P \land Q) \vdash Q</math>~~

	where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>P</math> is a [[logical consequence\|syntactic consequence]] of <math>P \land Q</math> and <math>Q</math> is also a syntactic consequence of <math>P \land Q</math> in [[formal system\|logical system]];

	~~and expressed as a truth-functional [[tautology (logic)\|tautology]] or [~~[~~theorem]] of propositional logic:~~

	~~:<math>(P \land Q) \to P</math>~~
	~~and~~
	:~~<math>(P \land Q) \to Q</math>~~

	~~where <math>P<~~/~~math> and <math>Q<~~/~~math> are propositions expressed in some logical system~~.

	~~== References ==~~
	~~{{reflist}}~~

	~~[[Category:Rules~~ of ~~inference]]~~
	~~[[Category:Theorems in propositional logic]]~~

	~~[[sv:Matematiskt uttryck#Förenkling]~~]

en>Addbot: Bot: Migrating 8 interwiki links, now provided by Wikidata on d:q901492 (Report Errors)

2013-02-26T15:56:11Z

Bot: Migrating 8 interwiki links, now provided by Wikidata on d:q901492 (Report Errors)

← Older revision		Revision as of 17:56, 26 February 2013
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	~~Her name~~ is ~~Felicidad Ahmad. Bookkeeping~~ is ~~what she does. The favorite pastime for my children and me~~ is ~~dancing~~ and ~~now I~~'~~m attempting~~ to ~~make money with~~ it. ~~For years she~~'s ~~been living~~ in ~~Kansas~~.<br><br>~~Here~~ is ~~my website~~; [~~http~~://~~Yugiohgames.net~~/~~index~~.~~php?task~~=~~profile&id~~=~~527944 Yugiohgames.net~~]		{{Transformation rules}}
			{{other uses}}

			In [[propositional calculus\|propositional logic]], '''simplification'''<ref>Copi and Cohen</ref><ref>Moore and Parker</ref><ref>Hurley</ref> (equivalent to '''conjunction elimination''') is a [[validity\|valid]] [[immediate inference]], [[argument form]] and [[rule of inference]] which makes the [[inference]] that, if the [[Logical conjunction\|conjunction]] ''A and B'' is true, then ''A'' is true, and ''B'' is true. The rule makes it possible to shorten longer [[formal proof\|proofs]] by deriving one of the conjuncts of a conjunction on a line by itself.

			An example in [[English language\|English]]:
			:It's raining and it's pouring.
			:Therefore it's raining.

			The rule can be expressed in [[formal language]] as:

			:<math>\frac{P \land Q}{\therefore P}</math>

			or as

			:<math>\frac{P \land Q}{\therefore Q}</math>

			where the rule is that whenever instances of "<math>P \land Q</math>" appear on lines of a proof, either "<math>P</math>" or "<math>Q</math>" can be placed on a subsequent line by itself.

			== Formal notation ==
			The ''simplification'' rule may be written in [[sequent]] notation:

			: <math>(P \land Q) \vdash P</math>
			or as
			: <math>(P \land Q) \vdash Q</math>

			where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>P</math> is a [[logical consequence\|syntactic consequence]] of <math>P \land Q</math> and <math>Q</math> is also a syntactic consequence of <math>P \land Q</math> in [[formal system\|logical system]];

			and expressed as a truth-functional [[tautology (logic)\|tautology]] or [[theorem]] of propositional logic:

			:<math>(P \land Q) \to P</math>
			and
			:<math>(P \land Q) \to Q</math>

			where <math>P</math> and <math>Q</math> are propositions expressed in some logical system.

			== References ==
			{{reflist}}

			[[Category:Rules of inference]]
			[[Category:Theorems in propositional logic]]

			[[sv:Matematiskt uttryck#Förenkling]]

en>Cydebot: Robot - Speedily moving category Centimetre gram second system of units to :Category:Centimetre–gram–second system of units per CFDS.

2012-02-16T15:41:52Z

Robot - Speedily moving category Centimetre gram second system of units to Category:Centimetre–gram–second system of units per CFDS.

New page

Her name is Felicidad Ahmad. Bookkeeping is what she does. The favorite pastime for my children and me is dancing and now I'm attempting to make money with it. For years she's been living in Kansas.<br><br>Here is my website; [http://Yugiohgames.net/index.php?task=profile&id=527944 Yugiohgames.net]