Glossary: G-Function: Difference between revisions
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{{CreatedByStudents1213}} ''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], [[User:IsaB|Isabelle]].'' | |||
= | = g-Function = | ||
== Definition == | == Definition == | ||
The | 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 following examples refer to the scenario given in an [[Exercise_First_Order_Models|online exercise]]. | ||
Alice likes watching | Sentence with proper names: ''Alice likes watching footbal together with Lisa.'' | ||
I-Function: | |||
I('''alice''') = ''alice''<br/ > | |||
I('''lisa''') = ''lisa'' | |||
-- | Formula: '''like-watching-football-together'''('''alice''','''lisa''') | ||
- | Sentence with pronouns: ''She likes watching football together with her.'' | ||
g-Function: <br/ > | |||
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> = <nowiki>[[</nowiki>'''like-watching-football-together'''(''x'',''y'')]]<sup>g</sup> | |||
== References == | == References == | ||
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== Literature == | == Literature == | ||
* Chapter 2 | |||
* 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. | |||
Latest revision as of 15:56, 11 April 2013
Warning:
The material on this page has been created as part of a seminar. It is still heavily under construction and we do not guarantee its correctness. If you have comments on this page or suggestions for improvement, please contact Manfred Sailer.
This note will be removed once the page has been carefully checked and integrated into the main part of this wiki.
The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS). Involved participants: Lisa, Marthe, Elisabeth, Isabelle.
g-Function
Definition
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
The following examples refer to the scenario given in an online exercise.
Sentence with proper names: Alice likes watching footbal together with Lisa.
I-Function:
I(alice) = alice
I(lisa) = lisa
Formula: like-watching-football-together(alice,lisa)
Sentence with pronouns: She likes watching football together with her.
g-Function:
g(x)= alice
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.
[[like-watching-football-together(alice,lisa)]]g = [[like-watching-football-together(x,y)]]g
References
Literature
- 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.