CHAPTER 24

Representing Events

24.1 Scenarios

We have already introduced the ideas to be presented here. An event is regarded as a set of states, each with a time-stamp. These time-stamps are represented by parameters tI, t2, t3, etc. and they are related by expressions such as tl < t2, which indicates that the state with time-stamp tl is (or was, or will be) perceived before the state with time-stamp t2. We have also discussed how the causal connectivity of such a set of states might be represented. In this chapter we shall tackle some of the outstanding problems which we have so far avoided.

24.2 Repetitive Events

We can return now to the problem of finding an appropriate representation for 'tennis ball' (see section 23.4). We noted in section 16.5 that repetitive operations are hard to represent, and that a looping mechanism is unsatisfactory because each state requires a separate time-stamp, and the re-use of states on an iterative loop would make this impossible.

How might we attempt to represent the game of tennis? The following is an illustration of a possible way to represent a single rally in the game of tennis.

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participants  in  game  their  properties  and  relative  positions
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1.  {player-I} 
2.  {player-2}
3.  {tenniscourt}
4.  {court-I}
5.  {court-2}
6.  {(4)  and  (5)  are  constituent  parts  of  (3)} 
7.  {net}
8.  {(7)  separates  (4)  and  (5»
9.  {tennisball}
10.  {properties  of  (9)  }
11.  {racket-I}
12.  {racket-2}
13.  {properties  of  (11)  and  (12)  } 
14.  {location  (1)  within  (4)  } 
15.  {location  (2)  within  (5)  }
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        (1)  plays-a-stroke
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16.  {movement  of  (11)  }  swing  of  racket-l
17.  {  (1)  causes  (16)  }  by  player-l
18.  {  (11)  contacts  (9)  }  hit  of  ball
19.  {  (16)  causes  (18)  }  by  racket-l
20.  {  movement  of  (9)  }  ball  moves
21.  {  location  of  (9)  within  (5)  }  ball  in  court-2
22.  {  location  of  (9)  =  (ouLoLcourt)  }  out
23.  {  location  of  (9)  =  (7)  }  in  net
24.  {  (18)  causes  (21)  or  (22)  or  (23)  }  three  outcomes  25.  {  point  scored  by  (2)  }  player-2  scores
26.  {  (22)  or  (23)  causes  (25)  }  if  out  or  in  net
          (21)  causes:
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          (2)  plays-a-stroke
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27.  {  movement  of  (12)  }  swing  of  racket-2
28.  {  (2)  causes  (27)  }  by  player-2
29.  {  (12)  contacts  (9)  }  hit  of  ball
30.  {  NOT(  (12)  contacts  (9)  }  miss
31.  {  (27)  causes  (29)  or  (30)  }  miss  or  strike  by  racket-2
32.  {  point  scored  by  (I)  }  player-I  scores
33.  {  (30)  or  (37)  or  (38)  causes  (32)  }miss  or  net  or  out  -}  score  34.  {  movement  of  (9)  }  ball  moves
35.  {  (29)  causes  (34)  }  hit  causes  movement  of  ball
36.  {  location  of  (9)  within  (4)  }  ball  in  court-I
37.  {  location  of  (9)  =  (outofcourt)  }  out
38.  {  location  of  (9)  =  (7)  }  net
            (36)  causes:
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            (1)  plays  a  stroke
-------------------------­



The reader is invited to trace this representation by writing in the names of entities against the numerical references, and then translating the representation into the graphical form in order to confirm that it is a very crude representation of a tennis rally. It omits a great deal of detail. There is no reference to the line markings, and the additional restriction placed on the server to place the ball into a smaller area of the court. There is no mention offoot faults or net-cords, and above all there is no mention of the motivation of the players for carrying out this strange ritual. It is hoped that the reader will be convinced that if we had the time and patience we could incorporate the additional rules and regulations of tennis which have been omitted.

The question we wish to address is - how do we go on? A rally in tennis is potentially infinite, although it seldom continues beyond four or five strokes. One method is to use a form of recursion in which the states 16-26 are bundled up and used to define the statement 'player-1 plays a stroke'. The states from 27-­38 are also bundled up and used to define the statement 'player-2 plays a stroke'. We now append the statement 'player-2 plays a stroke' to the end of the definition of 'player-l plays a stroke', and vice-versa. These are conditional extensions, because they depend upon the disjunction of causal connections. The extensions act like macro expansions and generate the next section of representation as required.

The idea is similar to our proposal for the representation of plural entities, which uses a generation function or structure to create more and more examples of an entity as required. The iterative operation is similarly generated repeatedly, and each repetition generates a new example of the event with new time-stamps. The process is terminated if one of the causal connection options is chosen which results in a point being scored. In many cases, however, there will be no requirement for the representation to be exploded. It will be sufficient for the recursive structure to indicate that repetition is present. The main problem with such a form of representation would be that of writing appropriate pattern­matching functions.

24.3 Occasional Events

In section 16.5 we also noted the problem of representing events which occur from time to time. We say that a person 'plays tennis,' or 'He smokes' meaning that he plays a game occasionally or that he smokes a cigarette occasionally. We do not mean that the person concerned does these things continuously. The tense of the verb is present tense, but not present continuous.

In the case of 'He plays tennis', the representation will consist of the kind of structure described in the previous section. The time-stamp of the states within that structure should remain uninstantiated (or unrelated to 'now'). The difference between this representation and that of the statement 'He is playing tennis' is that the association between the representation of the person referred to by 'He' and that of one of the players must be given the condition value 'possible' instead of 'true'.

The implication of this (and it is an important implication) is that the association between an entity and its role must be represented by a state in its own right, and be given a time-stamp. It is then possible for us to distinguish between 'He plays tennis' and 'He used to play tennis'.