Controlled NOT gate - Revision history

88.105.161.172: Used square brackets for the matrices used to explain the CNOT Hadamard behaviour

2014-11-20T00:16:40Z

Used square brackets for the matrices used to explain the CNOT Hadamard behaviour

← Older revision		Revision as of 02:16, 20 November 2014
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	~~{{Unreferenced\|date=February 2007}}~~

	~~'''Preferential entailment'''~~ is ~~a [[non-monotonic logic]] based on selecting only [[model (logic)\|model]]s~~ that ~~are considered the most plausible. The plausibility of models is expressed by an ordering among models called a preference relation, hence the~~ name ~~preference entailment~~.

	~~Formally, given a~~ [~~[propositional formula]] <math>F<~~/~~math> and an ordering over propositional models <math>\leq<~~/~~math>, preferential [[entailment~~]~~] selects only the models of <math>F</math> that are minimal according~~ to ~~<math>\leq</math>~~. ~~This selection leads to a~~ [~~[non-monotonic inference relation]]~~: ~~<math>F \models_\text{pref} G<~~/~~math> holds if~~ and ~~only if all minimal models of~~ <~~math~~>F<~~/math~~> ~~according~~ to ~~<math>\leq<~~/~~math> are also models of <math>G<~~/~~math>~~.

	[[Circumscription (logic)\|Circumscription]] can be seen as the particular case of preferential entailment when the ordering is based on containment of the sets of variables assigned to true (in the propositional case) or containment of the extensions of predicates (in the first-~~order logic case).~~

	~~==See also==~~

	* [[Circumscription (logic)]]
	* [[Non-~~monotonic logic]]~~

	~~[[Category:Logic in computer science]]~~
	~~[[Category:Knowledge representation]]~~
	~~[[Category:Non~~-~~classical logic]~~]

en>RJFJR: remove {{cleanup|section|date=May 2008}}

2013-12-07T22:56:01Z

remove {{cleanup|section|date=May 2008}}

← Older revision		Revision as of 00:56, 8 December 2013
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			{{Unreferenced\|date=February 2007}}

			'''Preferential entailment''' is a [[non-monotonic logic]] based on selecting only [[model (logic)\|model]]s that are considered the most plausible. The plausibility of models is expressed by an ordering among models called a preference relation, hence the name preference entailment.

			Formally, given a [[propositional formula]] <math>F</math> and an ordering over propositional models <math>\leq</math>, preferential [[entailment]] selects only the models of <math>F</math> that are minimal according to <math>\leq</math>. This selection leads to a [[non-monotonic inference relation]]: <math>F \models_\text{pref} G</math> holds if and only if all minimal models of <math>F</math> according to <math>\leq</math> are also models of <math>G</math>.

			[[Circumscription (logic)\|Circumscription]] can be seen as the particular case of preferential entailment when the ordering is based on containment of the sets of variables assigned to true (in the propositional case) or containment of the extensions of predicates (in the first-order logic case).

			==See also==

			* [[Circumscription (logic)]]
			* [[Non-monotonic logic]]

			[[Category:Logic in computer science]]
			[[Category:Knowledge representation]]
			[[Category:Non-classical logic]]

en>Rubinbot: r2.5.4) (Robot: Adding hu:Vezérelt-NEM

2012-07-31T21:58:05Z

r2.5.4) (Robot: Adding hu:Vezérelt-NEM

New page

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