9.2.2 A first Example

An example of tableaux for discourse modeling.

Let us now look at an example of tableaux-based discourse processing. Assume that we hear the sentence ``If Mary smokes, Mary looks pale and feels sick.'' Let us further assume that we process this sentence without any further knowledge whatsoever. This is cognitively implausible, but it facilitates the presentation: We simply start with an empty tableaux. Understanding this sentence gives us the following tableaux:

This tableaux has two branches, both saturated and open. So, there are two models that make this discourse true. In other words, there are two situations that are described by this sentence. Either Mary does not smoke, or Mary is pale and feels sick. As we argued above, we now have to decide which model we prefer.

?- Question!

It is an open question what kind of information influences such decisions. Do you have any ideas? (We encourage you to speculate!)

Let's take the second model (on the right branch) to be our preferred model (without any compelling reasons), and assume that the sentence ``Mary does not feel sick, Mary is hungry.'' is uttered next. We proceed as follows: First, we add the corresponding formula to all branches of our tableaux:

We then start further expanding our preferred branch:

But what has happened? Our preferred branch has become inconsistent. So, we backtrack and expand the other branch (which is still open). As a result, we get the following tableaux:

The left branch (which is the new preferred branch) is saturated. So we've ``understood'' our little discourse by building a model where Mary is hungry, and where she's neither smoking nor feeling sick. Note that the tableaux would close altogether if it would turn out later in the discourse that Mary is indeed smoking. In this case, there would be no model for the discourse at all, and we would know that at least one of the previous utterances must have been false.