17.5.2 Events

The representations for events that we have used until now have consisted of single predicates with as many arguments as are needed to incorporate all the roles associated with a given example. For example, the representation for making a reservation discussed in Section 17.2 consisted of a single predicate with arguments for the person making the reservation, the restaurant, the day, the time, and the number of people in the party, as in the following:

Reservation(Hearer,Maharani,Today,8PM,2)

In the case of verbs, this approach simply assumes that the predicate representing the meaning of a verb has the same number of arguments as are present in the verb's syntactic subcategorization frame.

Unfortunately, there are four problems with this approach that make it awkward to apply in practice:

• Determining the correct number of roles for any given event.

Representing facts about the roles associated with an event.

• Ensuring that all the correct inferences can be derived directly from the representation of an event.

• Ensuring that no incorrect inferences can be derived from the representation of an event.

We will explore these, and other related issues, by considering a series of representations for events. This discussion will focus on the following examples of the verb eat:

(17.26) I ate.

(17.27) I ate a turkey sandwich.

(17.28) I ate a turkey sandwich at my desk.

(17.29) I ate at my desk.

(17.30) I ate lunch.

(17.31) I ate a turkey sandwich for lunch.

(17.32) I ate a turkey sandwich for lunch at my desk.

Clearly, the variable number of arguments for a predicate-bearing verb like eat poses a tricky problem. While we would like to think that all of these examples denote the same kind of event, predicates in FOPC have fixed $ \underline{\text{arity}} $—they take a fixed number of arguments.

One possible solution is suggested by the way that examples like these are handled syntactically. The solution given in Ch. 16 was to create one subcategorization frame for each of the configurations of arguments that a verb allows. The

semantic analog to this approach is to create as many different eating predicates as are needed to handle all of the ways that eat behaves. Such an approach would yield the following kinds of representations for examples (17.26) through (17.26).

Eating $ _{1} $(Speaker)

Eating $ _{2} $(Speaker, TurkeySandwich)

Eating $ _{3} $(Speaker, TurkeySandwich, Desk)

Eating_{4}(Speaker,Desk)

Eating $ _{5} $(Speaker, Lunch)

Eating $ _{6} $(Speaker, Turkey Sandwich, Lunch)

Eating7(Speaker, TurkeySandwich, Lunch, Desk)

This approach simply sidesteps the issue of how many arguments the Eating predicate should have by creating distinct predicates for each of the subcategorization frames. Unfortunately, this approach comes at a rather high cost. Other than the suggestive names of the predicates, there is nothing to tie these events to one another even though there are obvious logical relations among them. Specifically, if example (17.32) is true then all of the other examples are true as well. Similarly, if example (17.31) is true then examples (17.26), (17.27), and (17.30) must also be true. Such logical connections can not be made on the basis of these predicates alone. Moreover, we would expect a commonsense knowledge base to contain logical connections between concepts like Eating and related concepts like Hunger and Food.

One method to solve these problems involves the use of what are called meaning postulates. Consider the following example postulate:

$$ \forall w,x,y,z Eating_{7}(w,x,y,z)\Rightarrow Eating_{6}(w,x,y) $$

This postulate explicitly ties together the semantics of two of our predicates. Other postulates could be created to handle the rest of the logical relations among the various Eatings and the connections from them to other related concepts.

Although such an approach might be made to work in small domains, it clearly has scalability problems. A somewhat more sensible approach is to say that examples (17.26) through (17.32) all reference the same predicate with some of the arguments missing from some of the surface forms. Under this approach, as many arguments are included in the definition of the predicate as ever appear with it in an input. Adopting the structure of a predicate like Eating $ _{7} $ as an example would give us a predicate with four arguments denoting the eater, thing eaten, meal being eaten and the location of the eating. The following formulas would then

capture the semantics of our examples:

$ \exists w, x, y \, Eating(Speaker, w, x, y) $

$ \exists w, x $ Eating (Speaker, TurkeySandwich, w, x)

∃w Eating(Speaker,TurkeySandwich,w,Desk)

$ \exists w, x \text{ Eating}(Speaker, w, x, Desk) $

$ \exists w, x \text{ Eating}(Speaker, w, Lunch, x) $

$ ∃w $ Eating(Speaker, TurkeySandwich, Lunch, w)

Eating(Speaker,TurkeySandwich,Lunch,Desk)

This approach directly yields the obvious logical connections among these formulas without the use of meaning postulates. Specifically, all of the sentences with ground terms as arguments logically imply the truth of the formulas with existentially bound variables as arguments.

Unfortunately, this approach still has at least two glaring deficiencies: it makes too many commitments, and it does not let us individuate events. As an example of how it makes too many commitments, consider how we accommodated the for lunch complement in examples (17.30) through (17.32); a third argument, the meal being eaten, was added to the Eating predicate. The presence of this argument implicitly makes it the case that all eating events are associated with a meal (i.e., breakfast, lunch, or dinner). More specifically, the existentially quantified variable for the meal argument in the above examples states that there is some formal meal associated with each of these eatings. This is clearly silly since one can certainly eat something independent of it being associated with a meal.

To see how this approach fails to properly individuate events, consider the following formulas.

$ \exists w, x \text{ Eating}(Speaker, w, x, Desk) $

$ \exists w, x \text{ Eating}(Speaker, w, Lunch, x) $

$ \exists w, x \text{ Eating}(Speaker, w, Lunch, Desk) $

If we knew that the first two formulas were referring to the same event, they could be combined to create the third representation. Unfortunately, with the current representation we have no way of telling if this is possible. The independent facts that I ate at my desk and I ate lunch do not permit us to conclude that I ate lunch at my desk. Clearly what is lacking is some way of referring to the events in question.

As with categories, we can solve these problems if we employ reification to elevate events to objects that can be quantified and related to other objects via sets of defined relations (Davidson, 1967; Parsons, 1990). Consider the representation of example (17.27) under this kind of approach.

$$ \begin{array}{c}\exists w ISA(w,Eating)\\\land Eater(w,Speaker)\land Eaten(w,TurkeySandwich)\end{array} $$

This representation states that there is an eating event where the Speaker is doing the eating and a TurkeySandwich is being eaten. The meaning representations for examples (17.26) and (17.31) can be constructed similarly.

$ \exists w \text{ ISA}(w, Eating) \land Eater(w, Speaker) $

$ \exists w \text{ ISA}(w, Eating) $

$ \land Eater(w, Speaker) \land Eaten(w, TurkeySandwich) $

$ \land MealEaten(w, Lunch) $

Under this reified-event approach:

There is no need to specify a fixed number of arguments for a given surface predicate; rather as many roles and fillers can be glued on as appear in the input.

• No more roles are postulated than are mentioned in the input.

• The logical connections among closely related examples are satisfied without the need for meaning postulates.