Características del Mercado Alemán

The actual time point assigned to the time variable should be able to be ordered with other time points in time domain. The system cannot simply assign ‘T1’ to ‘T_’ in the middle of interpreting the problem statement because there can be other events occurring before it. Thus, a time index is assigned to the time variable first, and the final time value is assigned after all time variables are assigned with a time index. Time index is internal representation of time generated by the system.

The time index refers to the location of an event exposed in a sentence. For example in the problem statement Figure 25 , the event ‘throwing upward’ is exposed at the verb ‘thrown’. Thus, the time index should refer to the verb ‘thrown’. The time index has a form of a head, ‘t’, followed by the sentence number and the word number exposing the event. A type tag distinguishing a time point from a time interval is attached at the end.

t:<sentence number>:<word number>:<type tag> sentence number={0, 1, …n}

word number={0, 1, …n}

type tag = {point, left, right, initial, final, interval, wholeInterval} Examples: t:0:3:point, t:2:5:left, t:2:5:right, t:1:2:initial, t:1:2:final, t:3:3:interval, t:5:2:wholeInterval, …

Figure 27: The form of time index and examples.

In the example Figure 25, the sentence number of the event throwing upward is 0, and the word number for the verb ‘thrown’ is 3. The type of the time is point, not interval. Thus the time index for the event is t:0:3:point, and it will be assigned to the time variable T_.

In case of an event such as a projectile movement continuing over time, two time points (left and right time points) are needed to represent a time interval. The left time point refers to the beginning of the interval, and the right time point refers to the end of the interval. In the same way that a time point

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is created, a time interval can be created by creating the two time points. The time variable for a left time point is ‘Ti_’, and for a right time point is ‘Tj_’. In Figure 28, the two time variables were used only in the right side of the rule, so a new time index is assigned to each time variable. If the problem statement of throwing upward (Figure 25) matches this rule, t:0:3:left will be assigned to Ti_, and t:0:3:right will be assigned to Tj_.

‘An object_ is thrown_’

Implies ‘the object_ moves at the interval between Ti_ and Tj_’. Figure 28: creating a new time interval

The resulting facts generated so far are as following: ‘the ball starts to move at t:0:3:point.’

‘the magnitude of the velocity of the ball is 3 m/s at t:0:3:point.’ ‘the ball moves at the interval between t:0:3:left and t:0:3:right.’ Figure 29: generated facts with a time index assigned

This method creating a time index referring to a verb in a sentence allows to assign multiple time points when more than one event is described in a problem statement. For example, there are two physics events in Figure 30. The one is the ball’s throwing upward, and the other is the bug’s freefall. The background rule in Figure 28 and a corresponding rule for freefall (not shown here) will match the two input sentences creating two time intervals. One time index will be assigned to the point of the verb ‘thrown’ in the first sentence, and another time index will be assigned to point of the verb ‘free-fall’ in the second sentence. In this way, the system can recognize that the first event occurs before the second event.

A Startled Bug:

‘A ball was thrown straight upward at 3 m/s inside a building. The ball hits the ceiling one second later, and a startled bug on the ceiling starts to free-fall. How long does it take for the bug to hit the floor?’ Figure 30: an example with two time intervals

In most cases, a time index can be assigned to a generated fact when a background rule with a new time variable is triggered. But, there are cases that a time index should be assigned based on a word in a sentence. Some sentence expresses a type of time in an adjective. For example, ‘the initial velocity of the ball is 3 m/s’ provides a value of the initial velocity, and the adjective ‘initial’ has a role to determine the type of the time. In this case, a time index of initial type is assigned to the fact, and the final time value for it is assigned after all time points are generated. In the similar way, a time index of ‘interval’ type is assigned to a fact describing an event with a time interval. It will be explained in details in the chapter 8.3.

In many physics problems, it is required to represent an event occurring between two events. For example, the event of an object reaching the apex of projectile occurs between the event throwing upward and the event hitting the ground. The internal representation of time in the middle of two time points is t:mid(Ti_, Tk_). It will be explained in mental model extension again (chapter 0).

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