17.1.4 Inference and Variables

Continuing with the topic of the computational purposes that meaning representations should serve, we should consider more complex requests such as the following:

(17.10) Can vegetarians eat at Maharani?

Here, it would be a mistake to invoke canonical form to force our system to assign the same representation to this request as for the previous examples. The fact that this request results in the same answer as the others arises not because they mean the same thing, but because there is a commonsense connection between what vegetarians eat and what vegetarian restaurants serve. This is a fact about the world and not a fact about any particular kind of linguistic regularity. This implies that no approach based on canonical form and simple matching will give us an appropriate answer to this request. What is needed is a systematic way to connect the meaning representation of this request with the facts about the world as they are represented in a knowledge base.

We will use the term inference to refer generically to a system's ability to draw valid conclusions based on the meaning representation of inputs and its store of background knowledge. It must be possible for the system to draw conclusions about the truth of propositions that are not explicitly represented in the knowledge base, but are nevertheless logically derivable from the propositions that are present.

Now consider the following somewhat more complex request:

I'd like to find a restaurant where I can get vegetarian food.

Unlike our previous examples, this request does not make reference to any particular restaurant. The user is stating that they would like information about an unknown and unnamed entity that is a restaurant that serves vegetarian food. Since this request does not mention any particular restaurant, the kind of simple matching-based approach we have been advocating is not going to work. Rather, answering this request requires a more complex kind of matching that involves the use of variables. We can gloss a representation containing such variables as follows:

Serves(x, VegetarianFood)

Matching such a proposition succeeds only if the variable x can be replaced by some known object in the knowledge base in such a way that the entire proposition will then match. The concept that is substituted for the variable can then be used to fulfill the user's request. Of course, this simple example only hints at the issues involved in the use of such variables. Suffice it to say that linguistic inputs contain many instances of all kinds of indefinite references and it is therefore critical for any meaning representation language to be able to handle this kind of expression.