Vague legal concepts and Fuzzy Logic. An attempt to Determine the Reuired Period of Waiting after Traffic Accidents

• Autore: Lothar Philipps
• Pagine: 37-51

Page 37

1.1. According to German law, a person involved in a traffic accident may not leave the site of the accident but is required to wait until somebody arrives who is willing to take Ms name and information on the car and the accident; otherwise he commits ´unerlaubtes Entfernen vom Unfalloro (leaving the scene of an accident; ß 142 I StGB). Of course nobody has to wait forever, but only for an ´amount of time adequate under the circumstancesª.

The statute, however, does not tell us what amount of time is adequate under what circumstances. That information is nowhere to be found. Fritjof Haft tells us¹: ´A rule of thumb might be: 'The more severe the accident, the longer the required wait'. More cannot be said. Even a lawyer cannot tell you more, not even for moneyª,

That is indeed very little. Comparative rules (the more severe - the longer) carry only little information. The rule does not say how bad an accident has to be to require a certain period of waiting.

Perhaps the rule of thumb given by Haft could be supplemented by another rule: ´A severe accident requires a long wait; a medium accident requires a medium wait; and a slight accident only requires a short wait, Very extensive damage, esp. if people are killed or severely injured, necessitates a very long wait². If the damage is merely a scratch, one can leave immediatelyª. This new rule joins a indeterminate time of required waiting with an equally open issue.

It does not give much more information, however. First, one has to take into account that terms like 'slight', 'severe', 'short', or 'long' arePage 38 dependent on the context (compare the duration of a long faculty meeting' to that of a 'short term of imprisonment'). In addition there are questions like: ´What is still "only a scratch", and what is light damage'? When does a 'medium wait' turn into a long wait'?ª.

In fact, one must be careful not to presuppose too much at this point. It should not be assumed the light damage stops at a certain point, at which medium damage starts. Or that a medium wait ends exactly when a long wait begins. Rather the terms run into one another, without clear boundaries; a fact long known to legal methodology³.

1.2. Traditional logic of course stipulates that an object either is or is not a member of a class - either totally or not at all. There is no room for gradual transitions. But for a quarter of a century fuzzy logic has existed, and has recently become a subject of general public interest⁴, triggered by a technological breakthrough the Japanese have achieved using it. They have managed to create appliances which adapt to their environment and live up to the unspoken expectations of their users. The advertisements promise ´intelligentª cameras and ´sensitive vacuum-cleanersª.

In fuzzy logic the either-or classification does not exist. It is based on the idea that an item may also be part of a class to a greater or lesser extent.

This concept is also found in every-day speech. Somebody-might not be ´oldª yet, but already ´a little oldª. If two classes are neighboring concepts, it will often happen that an item extends into both. One is not necessarily either ´youngª, ´middle-agedª or ´oldª, but perhaps ´still pretty young, but already middle-agedª. And somebody who is ´still middle-agedª could already be- called ´oldª, if with less justification.

It is possible to use precise numerical expressions instead of vague qualities. The age could be given in years instead of terms of ´youngª and ´oldª. But really, that is no solution to the problem. It will be possible toPage 39 establish many precise delineators, but they will be too rigid. There is much which only applies to ´youngª people, and much that only applies to ´oldª people; but there is nothing that applies only to twenty-five year-olds, and not to twenty-six year-olds or twenty-four year-olds⁵. In everyday speech numerical information is therefore often given with some vagueness, explicitly or implicitly: the number is a guide-line, not a delineator (´thirty-ishª, ´the woman of thirty yearsª).

Statements with vague terms are not only more flexible, but also more ´durableª. They can retain validity for a long time, even if their concrete significance varies with time. If indeed there is still a ´dangerous ageª for women, it would be much higher today than it was in Balzac's day.

2. Philipp Heck has found a metaphor for vague terms which has had great influence in publications on legal theory: ´The meaning [of a word] can be compared to a moon which is surrounded by a haloª. ´A nucleus of certain meaning is surrounded by a gradually fading halo of meaning⁶ª. That is a good metaphor. I would like to add another metaphor, even more expressive and precise: a mountain skyline before the evening sky. The meaning of a word has a peak, from which it slopes down into the valley. It may be a narrow summit or a high plateau, The slopes into the valley may be steep or gentle, jagged or straight. When two mountains lie adjacent, their skylines often run into each other. The closer the mountains are to each other, the more they melt together.

   The metaphor of a mountain skyline is more expressive and precise than that of nucleus and halo, because it translates directly to the graphs for the membership function of classes, and because a point in a graph is easier to define than a nuance of a fading hue. Also the relation of neighboring terms can be expressed more clearly.

3. The skyline for the required waiting period after a car accident might look like this⁷:

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   The meaning of the expression ´short waitª retains its peak up to twenty minutes; then it dips and finally ends at 40 minutes. Meanwhile the ´medium waitª has started - also at 20 minutes. It peaks between 40 and 80 minutes and ends at 100 minutes, deeply within the area of the ´long waitª.

   Thus, a remark by Adolf Merkels becomes directly evident: ´Very many terms in jurisprudence have a flowing quality... Their areas of application are not separated by insurmountable fences, but rather there are steady transitions into the area of neighboring terms⁸ª.

   I have designed these graphs intuitively⁹, it is a first suggestion which must be discussed by the specialists. But most of all, there have to be testsPage 41 to see whether such an understanding of the required waiting period will yield results which satisfy the sense of justice.

   Especially the trapezoid or triangle will have to be viewed as a simplification and stylization. In reality, a term's use will not be so rigid and linear. Rather one would expect a smoothly curved meaning. But how does the curve run? As long as that is unknown,, it is sensible to connect with straight lines the fixed points of one hypothesis - beginning, end and peak. It also has little impact whether an object belongs to a class at 0,4 or at 0.5 - and belongs to the neighbouring class to a certain degree. It does make a difference if an object totally belongs to one class and not at all to its neighbour.

   There is a hierarchy of categories in these diagrams: at the top there are the ´linguistic variablesª. In our case it is a term like ´duration of the required waitª.

   The values of the linguistic variables - one step lower in the hierarchy - are not numerical, but of natural speech: terms such as ´short waitª, ´medium waitª.

   Below these are the ´base variablesª, in our case ´minutes of waitingª, whose values are finally numerical.

   The numerical values are related to the values of natural speech, not in a definite way, but in the sense of a possible use in natural speech. Thus, there is an area where both are conceivable: a waiting period might be called ´shortª or ´mediumª. This relation is therefore called a possibility distribution.

4. The graphs of the membership functions are very illustrative - comparable to the Euler Circles that are commonly used to symbolize relations between terms.

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   The...