17.5.1 Categories

As we noted in Section 17.2, words with predicate-like semantics often express preferences for the semantics of their arguments in the form of selectional restrictions. These restrictions are typically expressed in the form of semantically-based categories where all the members of a category share a set of relevant features.

The most common way to represent categories is to create a unary predicate for each category of interest. Such predicates can then be asserted for each member of that category. For example, in our restaurant discussions we have been using the unary predicate VegetarianRestaurant as in:

VegetarianRestaurant (Maharani)

Similar logical formulas would be included in our knowledge base for each known vegetarian restaurant.

Unfortunately, in this method categories are relations, rather than full-fledged objects. It is, therefore, difficult to make assertions about categories themselves, rather than about their individual members. For example, we might want to designate the most popular member of a given category as in the following expression:

MostPopular(Maharani, VegetarianRestaurant)

Unfortunately, this is not a legal FOPC formula since the arguments to predicates in FOPC must be Terms, not other predicates.

One way to solve this problem is to represent all the concepts that we want to make statements about as full-fledged objects via a technique called reification. In this case, we can represent the category of VegetarianRestaurant as an object just as Maharani is. The notion of membership in such a category is then denoted via a membership relation as in the following:

ISA (Maharani, Vegetarian Restaurant)

The relation denoted by $ \text{ISA} $ (is a) holds between objects and the categories in which they are members. This technique can be extended to create hierarchies of categories through the use of other similar relations, as in the following:

AKO (Vegetarian Restaurant, Restaurant)

Here, the relation AKO (a kind of) holds between categories and denotes a category inclusion relationship. Of course, to truly give these predicates meaning they would have to be situated in a larger set of facts defining categories as sets.

Ch. 19 discusses the practical use of such relations in databases of lexical relations, in the representation of selectional restrictions, and in word sense disambiguation.