«,QWURGXFWLRQ In this paper we attempt to describe and model a type of analogy which we believe is commonly used in legal reasoning. The basic ...»
A model of the development of
distinctions in case law
John Henderson and Trevor Bench-Capon
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$EVWUDFW. In this paper we put forward a way of modelling reasoning with cases as it
is described by writers such as Levi. This style of reasoning concentrates on finding
and refining particular distinctions amongst cases which bear on the outcome. It thus
contrasts with work such as HYPO in which such distinctions are the product of initial analysis of the domain, and so come already fixed. We provide a detailed walk through of a specific example to show how a legal distinction can develop, assuming initially the availability of a limited ontology and then show how a richer ontology can be used to capture increased subtlety of argument.
,QWURGXFWLRQ In this paper we attempt to describe and model a type of analogy which we believe is commonly used in legal reasoning. The basic purpose of the mechanism is to find a feature within the facts in a set of cases by which that set can be divided into two subsets. One of those subsets contains all the cases that exhibit the feature, the other those cases where the feature is absent. Ideally, all the cases in each subset will share the same outcome (for example, all the cases in the first subset are decided in favour of the claimant), although, in practice, there will be exceptions. We refer to such a feature as a GLVWLQFWLRQ and the idea is that considering this distinction in relation to a case is a useful part of reasoning about the decision that should be made. Broadly the reasoning process is that described in Levi , and our account is also informed by the discussion of  in Smith .
The mechanism consists of a method that identifies the similarity between the facts in two cases and a method for combining similarities between more than two cases into a single composite similarity.
We will use a running example in the paper. The example is based on the following simplification of reality. Each case in the example concerns the same single question and contains a single fact. The legal question in the example arises out of a fictional rule of common law which states that whether or not a person owes a duty of care to others depends on the job that person does. For example, under the fictional rule a racing tipster does not owe a duty of care but an investment adviser does. All cases are considered to be of equal authority (ie there is nor priority rules between them).
The example will be based on 14 cases, in each of which the defendant has a different occupation. Table 1 lists the cases with their outcomes. The question need not be stated as it is the same in every case namely whether a duty of care was owed.
In section 2 we give a brief explanation of the mechanism try to give some foundation for our model, and discuss how one could use it to construct an H[ SRVW rule, once all the cases have been decided. In section 3 we show how this analogy mechanism John Henderson and Trevor Bench-Capon, ‘A model of the development of distinctions in case law’, in: Joost Breuker, Ronald Leenes and Radboud Winkels (eds.), /HJDO.QRZOHGJH DQG,QIRUPDWLRQ 6\VWHPV -XUL[ 7KH 7KLUWHHQWK $QQXDO &RQIHUHQFH Amsterdam: IOS Press, 2000, pp. 23-34.
could be used as the cases are presented to develop the distinctions which appear in the H[ SRVW rule dynamically as the cases are decided. Both sections 2 and 3 make use of an abstraction hierarchy-like ontology, of the kind of which Wordnet  provides the best known example. We use a simplified example ontology of our own as illustration. In section 4 we consider what can be done with a richer ontology, of the sort that CYC  exemplifies. We assume that such an ontology will contain facets to identify GLVFULPLQDWLQJ and SURWRW\SLFDO attributes of classes, along the lines of . Again for illustration of the mechanism we use our own ontology fragment, tailored for the example and with no pretence to correctness.
$QDORJ\ LQ RXU 0RGHO The analogy mechanism we propose finds a similarity between cases which is asserted to be a JURXQG for analogy between them. The analogy can then be expressed as a general rule, giving the grounds of the analogy as its antecedent and one outcome (ie, either ‘claimant’ or ‘defendant’) as its consequent. This rule is, however, defeasible, and the group of analogous cases so defined will contain exceptions (ie, cases that have an outcome that is the opposite to that given by following the rule). An analogy between these exceptions is then found, and the rule grounding the analogy between these exceptions can be used to refine the general rule by including the negation of its antecedent as an additional term in the antecedent of the original rule. Since “analogy” has been given a variety of interpretations, we will begin by making precise what we mean by it.
First consider an analogy between a pair of situations. One will be the VRXUFH situation, about which all features are known. The other will be the WDUJHW situation, about which only some features are known. We must first identify some similarity between the corresponding features of the two situations which are known. What is it to find a similarity between corresponding features? Our idea is that two features are similar if they have a common ancestor in an abstraction hierarchy. To reach this common ancestor it may be necessary to go through several abstraction steps. For example, a lion is analogous to a tiger because they are both wild cats, to a domestic tabby because they are both cats, to a dog because they are both mammals, to a parrot because they are both animals, to a tree because they are both living things and to a stone because they are both physical objects. A lion is thus closely analogous to a tiger because only a single abstraction step is required, but only distantly to a stone where (in the abstraction hierarchy as conceived here) there are six abstraction steps. The common ancestor we call the JURXQG of the analogy: thus the ground of the analogy between lions and tigers is that they are wild cats, between lions and stones that they are physical objects. If we regard the similarity as being sufficiently close, we then transfer the known values of the source situation to the corresponding features of the target situation whose values are unknown.
Suppose we are trying to use the analogy to find the value of some unknown feature, of the target situation, say disposition. Our source situation is that lions have a fierce disposition. Given a target situation with an unknown animal or thing, we can use the analogy to lions to say that a target situation with the same ground will also have a fierce disposition. This argument can be encapsulated as a rule of the form “,I JURXQG WKHQ GLVSRVLWLRQ ILHUFH”; here, for tigers, “LI ZLOG FDW WKHQ GLVSRVLWLRQ ILHUFH”, and, for stones, “LI SK\VLFDO REMHFW WKHQ GLVSRVLWLRQ ILHUFH”. Obviously the closer the analogy the more plausible the rule.
Similarly with two legal cases: here the source situation is the precedent case, the target situation is the new, undecided, case the known features are the facts of the two cases and the unknown feature is the outcome of the new case.
To illustrate the method for combining similarities, we will consider analogy between a group of cases, some with a decision for the plaintiff, and some for the defendant. We believe that there are two approaches to generating the single similarity from a mixed set of cases. The first is ‘top down’ in which a general rule is asserted for a whole subset of cases and then refined by finding an exception and an exception to the exception etc, until the facts of all the precedent cases have been subsumed into the single similarity. The second is ‘bottom up’ in which a rule is asserted to cover two cases and then extended one case at a time until all the cases in the set are subsumed. In this paper we illustrate the top down approach Consider an abstraction $ that will cover some subset of these cases. This subset can be said to be analogous with respect to A. Suppose that c is the number of cases, sA is the number of cases in the subset with A as a common ancestor, cp is the number of cases for the plaintiff, cd is the number of cases for the defendant, sAp the number of cases for the plaintiff in the subset and sAd the number of cases for the defendant in the subset. Let us suppose we are trying to find an analogy for pro-plaintiff cases. Now A is the ideal ground
for such an analogy if sAd = 0 and sAp = cp. There is, however, unlikely to be such an A:
typically the subset will contain some pro-defendant cases, and miss some pro-plaintiff cases. So let us introduce two measures, which we will term FRYHUDJH and SUHFLVLRQ.
Coverage is intended to express the ability of A to explain a decision in favour of the
plaintiff, and will be the proportion of pro-plaintiff cases “caught” by A. Thus:
Coverage = sAp / cp.
Precision is intended to represent the degree of confidence in the analogy and is given
by the proportion of cases in the subset which are pro-plaintiff. Thus:
Precision = sAp / sA.
In the ideal case both coverage and precision will be equal to 1. Typically also there will be a trade-off; moving up an abstraction step from A to A’ is likely to both increase coverage and decrease precision. Our aim therefore will be to choose an A such that coverage is high enough for the analogy to be worth making, while precision is high enough to make the analogy useful. As a rule of thumb we will attempt to maximise coverage, subject to some threshold on precision. Any precision below 0.5 is clearly too low: we would be wrong more often that we were right. Something about two thirds seems a likely minimum for precision.
If precision and coverage are acceptable we will get a rule, R1, “,I $ WKHQ SODLQWLII”, which will be defeasible to the extent of the pro-defendant cases covered by the rule. Next consider the subset caught by A.
We now look for an analogy between the exceptions to R1 in this subset. That is we attempt to find a specialisation of A, B, such that the coverage and precision of the pro-defendant cases in the subset generated by B is acceptable. This will give us a modification of R1, R2 ³,I $ DQG QRW % WKHQ SODLQWLII”.
We can now consider the coverage and precision of the complement of B with respect to A. Coverage will have decreased to the extent that B has caught pro-plaintiff cases, but precision will have increased. We can then repeat this process by finding an analogy for the pro-plaintiff cases caught by B, say C, and get a further modification of the rule, R3, ³,I $ DQG QRW % DQG QRW & WKHQ SODLQWLII”. This will increase the coverage and precision for the subset A – (B – C).
Let us consider a example. Figure 1 shows a sample abstraction hierarchy for the occupations and outcomes of Table 1. We can calculate the coverage and precision of each node in the hierarchy and produce Table 2. All leaf nodes will have coverage of 0.143 and precision of 1, where the decision was for the plaintiff and 0 and 0 otherwise.
What is the best ground for analogy here? In order to get complete coverage we must
as far as worker: but precision is then only 0.5. Since a rule based on an analogy with such precision is wrong as often as it is right, this may be taken as unacceptably low.
White collar and professional have the same, reasonably high coverage, but the precision of the latter is better at 0.667. So let us take professional as our initial ground, and our first defeasible rule as “,I SURIHVVLRQDO WKHQ SODLQWLII”.
Within professional there are three exceptions to this rule. If we now try to ground an analogy giving these exceptions we get the results in Table 3. Here the pro-defendant leaf nodes will have coverage of 0.333 and precision of 1 and the others 0 and 0.
7DEOH Precision and coverage for non-leaf nodes with professional as root
The most useful ground here is medical professional, which has acceptable coverage and precision. We can thus modify our rule to “,I SURIHVVLRQDO DQG QRW PHGLFDO SURIHVVLRQDO WKHQ SODLQWLII” The coverage for this rule remains 0.857, but the precision is now increased to 0.857.
Overall, there remain three exceptions: the pro-plaintiff builder and the pro-plaintiff consultant, who is an exception to our exception, and the pro-defendant barrister who remains an exception to our rule. These cases must be treated as VXL JHQHULV, since the lowest abstraction is too abstract in the case of the builder, and the first available abstraction already used for the other side in the case of the consultant. We therefore add these specific exceptions to our rule to get the final form of our rule: “,I EXLOGHU RU
SURIHVVLRQDO DQG QRW EDUULVWHU RU PHGLFDO SURIHVVLRQDO DQG QRW FRQVXOWDQW WKHQSODLQWLII”. Although a little complicated, this is the most economical description of the situation of Figure 1.
'HYHORSLQJ WKH 'LVWLQFWLRQ :LWK DQ $EVWUDFWLRQ +LHUDUFK\ Section 2 describes the situation SRVW KRF, when all decisions are known. But we are interested in the GHYHORSPHQW of such distinctions. Let us therefore consider how such a situation might develop case by case.
Suppose the first case (C1) that comes to judgement involves an accountant.