HoldsAt(house(x),t)∧HoldsAt(house(y),t)→x=y,
a property that can be enforced by integrity constraints as introduced in chapter 8. Here we will simply assume that this can be done.
The scenario should be thought as being part of the lexical entry of ‘build a house’. The full entry will be much more complex, since it must add details concerning the building process. In fact, talking about ‘thefull entry’ is apt to be misleading, since it suggests uniqueness. What we mean is something more modest: the lexical information concerning the expression ‘build a house’ stored in someone’s brain at a particular moment. Thus variation from person to person, and from moment to moment is allowed to a certain extend.
2.2. Example of an achievement: ‘reach the top’. Here we need a terminating event type7reach, derived by (perfect) nominalization from the corresponding verb, and a fluentbe-at-the-top, related by
(1) Initiates(reach,be-at-the-top,t).
More may be said about the resulting state, but we reserve this for our dis- cussion of states below.
2.3. Example of an activity: ‘push a cart’. This is what we called an activity in the wide sense, characterized by a quadruple (+,+,−,−): a force is exerted (‘push’) and as a result an object changes position. Accord- ingly, the terms we need are the activity (in the narrow sense)push, derived by (imperfect) nominalization from the corresponding verb, a parametrized fluent position(x), and an injective real valued function g. In contrast to accomplishments, there is no canonical goal here, so the main component of the scenario is the dynamics given by
(1) HoldsAt(position(x),t)→
Trajectory(push,t,position(x+g(d)),d).
2.4. Examples of states: ‘know’, ‘love’, ‘be sad’. At first the distinc- tion between state and activity seems obvious: an activity involves change, and a state doesn’t. This characterization fits the perceived difference be- tween ‘run’ and ‘know’. In our setup, states and activities must both be rep- resented by fluents, and the question is how to account formally for the dif- ference. The formula we found for this difference is that ‘states are causally inert’, so that they cannot occur as first argument of the Trajectory predi- cate. The reader may well wonder whether this is really what is at issue: don’t we say things like: ‘His excitement caused him to write the paper overnight’? Or ‘Loving her caused him endless sadness’?
One does indeed say such things, but we submit that ‘cause’ is not used here in the sense formalized in the event calculus. Rather, it functions as a
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precondition, in this case having the effect of increased sensitivity, so that we get something like
HoldsAt(love,t)→Initiates(e,sadness,t)
where e is some action on the part of the female character (there may be many such actions, and corresponding statements in the scenario). Fur- thermore it must be noted again that we do not propose a fixed association between VPs and Aktionsarten. A state is primarily a cognitive category. Whether a state or an activity is associated to ‘love’ in the last resort de- pends on context. In fact we shall see below that there are contexts where ‘love’ is forced to be an activity.
A second point to be noted about states is that they usually are not that static after all. Sadness usually subsides without further aggravating events, and in democratic countries with a presidential system, one is president for an amount of time which is fixed beforehand. We must therefore investi- gate how this ‘decay’ of states (either continuous or discontinuous) can be modelled in the event calculus. One way to model continuous decay is to introduce the special fluent decay, which is syntactically an activity, and a monotone increasing function g, governing the decay rate. If we now conceive of ‘be sad’ as a parametrized fluentsad(x), we may write the fol- lowing formula for the dynamics of decay
HoldsAt(sad(x),t)→Trajectory(decay,t,sad(x−g(d)),d).
The fluentdecaywill be initiated as soon assadis initiated, and may be terminated by events increasing sadness. We thus do not agree entirely with Comrie’s characterization of states, when he writes
With a state, unless something happens to change that state, then the state will continue: this applies equally to standing and to knowing. With a dynamic situation [i.e. activity], on the other hand, the situation will only continue if it is continually subject to a new input of energy: this applies equally to run- ning and to emitting a pure tone8, since if John stops putting any effort into running, he will come to a stop, and if the os- cilloscope is cut off from its source of power it will no longer emit sound. To remain in a state requires no effort, whereas to remain in a dynamic situation requires effort, whether from the inside (in which case we have an agentive interpretation, e.g. John is running), or from the outside (in which case we have a nonagentive interpretation, e.g. the oscilloscope is emitting a pure tone) [17, p. 49].
On this characterization, ‘be excited’ and ‘be sad’ would not be states but activities, because their propensity to decay means that they require input of
8This refers to an example considered problematic by Comrie
(i) The oscilloscope is emitting a pure tone at 300 cycles per second.
The use of the progressive indicates an ongoing activity, or continuous change, but the lay- man who does not know about sinus waves may well believe a tone is a static phenomenon.
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