Glossary: G-Function - Revision history

Manfred: /* Examples */

2013-04-11T15:56:53Z

Examples

← Older revision		Revision as of 15:56, 11 April 2013
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	With the indicated definition of I and g, the two formulae have the same truth conditions, i.e.		With the indicated definition of I and g, the two formulae have the same truth conditions, i.e.

	<nowiki>[[</nowiki>'''like-watching-football-together'''('''alice''','''lisa''')]]<sup>g</sup>		<nowiki>[[</nowiki>'''like-watching-football-together'''('''alice''','''lisa''')]]<sup>g</sup> = <nowiki>[[</nowiki>'''like-watching-football-together'''(''x'',''y'')]]<sup>g</sup>


	== References ==		== References ==

Manfred: /* G-Function */

2013-04-11T15:56:12Z

G-Function

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	{{CreatedByStudents1213}} ''Involved participants: [[User:Lisa\| Lisa]], [[User:Marthe\| Marthe]], [[User:Elisabeth.krall\| Elisabeth]], [[User:IsaB\|Isabelle]].''		{{CreatedByStudents1213}} ''Involved participants: [[User:Lisa\| Lisa]], [[User:Marthe\| Marthe]], [[User:Elisabeth.krall\| Elisabeth]], [[User:IsaB\|Isabelle]].''

	= G-Function =		= g-Function =

	== Definition ==		== Definition ==

	The G-Function in Predicate Logic maps variables to individuals from the universe. ~~In natural, real~~-~~world language we use~~ variable~~, such as personal~~ pronouns, instead of repeating the names ~~constantly that are referred to. In order to, firstly, display and, then, interpret sentences with~~ pronouns ~~, the G-Function is applied~~.		The g-Function in Predicate Logic maps variables to individuals from the universe. The g-function is also called a ''variable assignment function''.
			Personal pronouns in natural language roughly correspond to variables in logic. So, instead of repeating the names we use pronouns.

	== Examples ==		== Examples ==

	The following examples refer to the scenario given in ~~the~~ online ~~exercises~~.		The following examples refer to the scenario given in an [[Exercise_First_Order_Models\|online exercise]].

	Alice likes watching footbal together with Lisa.		Sentence with proper names: ''Alice likes watching footbal together with Lisa.''

	~~-->~~ I-Function:		I-Function:

	I('''alice''') = <''alice''><br/ >		I('''alice''') = ''alice''<br/ >
	I('''lisa''') = <''lisa''>		I('''lisa''') = ''lisa''

	Formula: '''like-watching-football-together (alice, lisa)'''		Formula: '''like-watching-football-together'''('''alice''','''lisa''')

	~~But~~: She likes watching football together with her.		Sentence with pronouns: ''She likes watching football together with her.''

	~~--> G~~-Function: <br/ >		g-Function: <br/ >
	g('''x''')= <''alice''><br/ >
	g('''y''')= <''lisa''>		g(''x'')= ''alice''<br/ >
			g(''y'')= ''lisa''

			Formula with variables: '''like-watching-football-together'''(''x'',''y'')

			With the indicated definition of I and g, the two formulae have the same truth conditions, i.e.

			<nowiki>[[</nowiki>'''like-watching-football-together'''('''alice''','''lisa''')]]<sup>g</sup>

	~~--> Formula can be formed and interpreted: '''like-watching-football-together (x,y)'''~~

	== References ==		== References ==

Manfred at 15:49, 11 April 2013

2013-04-11T15:49:01Z

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	{{MaterialUnderConstruction}}		{{MaterialUnderConstruction}}

			{{CreatedByStudents1213}} ''Involved participants: [[User:Lisa\| Lisa]], [[User:Marthe\| Marthe]], [[User:Elisabeth.krall\| Elisabeth]], [[User:IsaB\|Isabelle]].''

	= G-Function =		= G-Function =

Lisa: /* Literature */

2013-02-27T19:45:28Z

Literature

← Older revision		Revision as of 19:45, 27 February 2013
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	== Literature ==		== Literature ==

	* Chapter 2 ~~of Manfred Sailer's textbook~~
			* Levine, Robert D., Frank Richter, and Manfred Sailer (in preparation): Formal Semantics. An Empirically Grounded Approach. Stanford: CSLI Publications. Draft of April 2012. Chapter 2.

Lisa: /* Examples */

2013-02-06T10:28:30Z

Examples

← Older revision		Revision as of 10:28, 6 February 2013
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	g('''y''')= <''lisa''>		g('''y''')= <''lisa''>

	--> Formula can be formed: '''like-watching-football-together (x,y)'''		--> Formula can be formed and interpreted: '''like-watching-football-together (x,y)'''

	== References ==		== References ==

Lisa: /* Examples */

2013-02-06T10:27:49Z

Examples

← Older revision		Revision as of 10:27, 6 February 2013
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	--> I-Function:		--> I-Function:

	I('''alice''') = ''alice''<br/ >		I('''alice''') = <''alice''><br/ >
	I('''lisa''') = ''lisa''		I('''lisa''') = <''lisa''>

	Formula: '''like-watching-football-together (alice, lisa)'''		Formula: '''like-watching-football-together (alice, lisa)'''
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	But: She likes watching football together with her.		But: She likes watching football together with her.

	--> G-Function:		--> G-Function: <br/ >
	g('''x''')= <''alice''><br/ >		g('''x''')= <''alice''><br/ >
	g('''y''')= <''lisa''>		g('''y''')= <''lisa''>

Lisa: /* Examples */

2013-02-06T10:27:07Z

Examples

← Older revision		Revision as of 10:27, 6 February 2013
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	--> I-Function:		--> I-Function:

	I('''alice''') = ''alice''		I('''alice''') = ''alice''<br/ >
	I('''lisa''') = ''lisa''		I('''lisa''') = ''lisa''

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	But: She likes watching football together with her.		But: She likes watching football together with her.

	--> G-Function: g('''x''')= <''alice''> ~~and~~ g('''y''')= <''lisa''>		--> G-Function:
			g('''x''')= <''alice''><br/ >
			g('''y''')= <''lisa''>

	--> Formula can be formed: '''like-watching-football-together (x,y)'''		--> Formula can be formed: '''like-watching-football-together (x,y)'''

Lisa: /* Examples */

2013-02-06T10:26:03Z

Examples

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	Alice likes watching footbal together with Lisa.		Alice likes watching footbal together with Lisa.

	--> I-Function: '''like-watching-football-together (alice, lisa)'''		--> I-Function:

			I('''alice''') = ''alice''
			I('''lisa''') = ''lisa''

			Formula: '''like-watching-football-together (alice, lisa)'''

	But: She likes watching football together with her.		But: She likes watching football together with her.

	--> G-Function: g('''x''')= <''alice'''> and g('''y''')= <''lisa''>		--> G-Function: g('''x''')= <''alice''> and g('''y''')= <''lisa''>

	--> Formula can be formed: '''like-watching-football-together (x,y)'''		--> Formula can be formed: '''like-watching-football-together (x,y)'''

Lisa: /* Examples */

2013-02-06T10:23:48Z

Examples

← Older revision		Revision as of 10:23, 6 February 2013
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	The following examples refer to the scenario given in the online exercises.		The following examples refer to the scenario given in the online exercises.

	Alice likes watching ~~soccer~~ together with Lisa.		Alice likes watching footbal together with Lisa.

	--> I-Function: '''like-watching-~~soccer~~-together~~-with~~ (alice, lisa)'''		--> I-Function: '''like-watching-football-together (alice, lisa)'''

	But: She likes watching ~~soccer~~ together with her.		But: She likes watching football together with her.

	--> G-Function: g('''x''')= <''alice'''> and g('''y''')= <''lisa''>		--> G-Function: g('''x''')= <''alice'''> and g('''y''')= <''lisa''>

	--> Formula can be formed: '''like-watching-~~soccer~~-together~~-with~~ (x,y)'''		--> Formula can be formed: '''like-watching-football-together (x,y)'''

	== References ==		== References ==

Elisabeth.krall: /* Examples */

2013-02-05T22:06:34Z

Examples

← Older revision		Revision as of 22:06, 5 February 2013
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	But: She likes watching soccer together with her.		But: She likes watching soccer together with her.

	--> G-Function: g('''x''')= <''alice'''> g('''y''')= <''lisa''>		--> G-Function: g('''x''')= <''alice'''> and g('''y''')= <''lisa''>

	--> Formula can be formed: '''like-watching-soccer-together-with (x,y)'''		--> Formula can be formed: '''like-watching-soccer-together-with (x,y)'''


	== References ==		== References ==