The Proof of the Pudding is in the Eating

Table of Contents

Exercise

1. Model Inspection

   Design a natural language-interface (using λ-calculus) to our revised model checker. The idea is that you can inspect some predefined model like

   
   example(4,[bird(tweety),siamesecat(mutzi),woman(mary),man(john),man(miles),
   	love(miles,mary),owner(mary),of(mary,mutzi),
   	love(miles,tweety),love(john,mary),walk(mary),
   	therapist(mary),eat(mutzi,tweety)]).
   
   

   by asking questions like

   • Does John love Mary?
   • Which owner of a siamese cat walks?

   Hint: For the time being, a cursory treatment of questions is enough for our purposes here. It should lead to the following representations of the questions given above: LOVE(JOHN,MARY) and λx∃y.SIAMESECAT(y)∧OWNER(x)∧of(x,y)∧WALK(x) The expected answer to the first question is yes in the example. The answer to the second question should consist of all values of x that make the scope of the abstraction true (in our case Mary).

2. Model Extension

   Use our tableaux-based model generation procedure to extend models like the one presented in » Beispiel: EX EX.PUTTING1EX_EX.PUTTING1. An example run could look like this:

   
   1 ?- extendModel(5,10).
   
    before: [bird(tweety), siamesecat(mutzi), woman(mary), man(john), man(miles) ,love(miles, mary), owner(mary), of(mary, mutzi), love(miles, tweety), love(john, mary), walk(mary), therapist(mary), eat(mutzi, tweety)] 
   
   > john loves every siamese cat.
   
    after: [eat(mutzi, tweety), therapist(mary), walk(mary), love(john, mary), love(miles, tweety), of(mary, mutzi), owner(mary), love(miles, mary), man(miles), ~siamesecat(miles), man(john), woman(mary), ~siamesecat(mary), siamesecat(mutzi), love(john, mutzi), ~siamesecat(john), bird(tweety), ~siamesecat(tweety), ~siamesecat(*)] 
   

   This example also gives you an impression of what direct, uncontrolled model generation does. First of all, if a speaker utters John loves every siamese cat. in the situation described by our input model, one thing she probably wants to communicate is that John loves Mutzi. But our system also has generated lots of other facts, such as ~siamesecat(john), that are not contradictory (up to now) although they probably weren't intended by the speaker. Moreover, the system has blindly chosen one of many possible extensions of the input model. Another possible extension would e.g. contain siamesecat(john), love(john,john) instead of ~siamesecat(john). Now what exactly makes the extension of mental models in human language understanding so much more focussed than what our implementation does? Do you have any ideas (speculate, you don't have to implement...)?

3. Informativity Checking

   Remember how we can use tableaux to check the informativity of a given formula with respect to some other formula(e) (see » An Application: Conversational Maxims). Implement a little program that checks the informativity of a natural language sentence with respect to some world knowledge. For example suppose you have some world knowledge that tells you that Every human works, that John is a man and that All men are human:

   wk(man(john) 
      & forall(x,human(x)>work(x)) 
      & forall(y,man(y)>human(y)) 
   
      & forall(z,woman(z)>human(z))).
   
   

   Now, your system should check the informativity of input sentences like this:

   
   1 ?- checkInf.
   
   
   > john works.
   
   *** Doesn´t interest me... ***
   Yes
   
   2 ?- checkInf.
   
   
   > john does not work.
   
   *** This is impossible! ***
   Yes
   
   3 ?- checkInf.
   
   
   > tweety works.
   
   *** Maybe... ***
   Yes