Glossary: G-Function

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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.
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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.