HYPO’S legacy: introduction to the virtual special issue

A major difficulty when thinking about how to reason with legal cases is that cases which are held to be similar appear to be very different when we consider their facts. Thus in a famous line of cases considered in Levi (1948), Bench-Capon et al. (2003) and Rissland and Xu (2011) a collection of very different things are seen to play the same role in the various cases² . These include a scaffold, an elevator, a bottle of aerated water and a coffee urn which were all held to be relevantly similar to an automobile for the purposes of the particular legal point under consideration. Similarly the series of property cases much studied in AI and Law consider a fox, wild ducks, a shoal of pilchards and a whale all to be relevantly similar to the baseball disputed in Popov v Hayashi (see Atkinson (2012)). Thus deciding whether two legal cases are relevantly similar does not seem to be a matter of considering facts in a simple manner using everyday notions of similarity.

For this reason HYPO introduced the notion of dimensions to match and compare cases. These are aspects of the case, ascribed on the basis of facts, which are relevant to the legal issues being considered. Thus what linked the scaffold, elevator, bottle of aerated water and coffee urn was that all were dangerous, but not visibly so. What links the animals and the baseball is that they were being pursued, and the relevant aspects include their value, and their connection to the land they were pursued on Bench-Capon and Bex (2015).

We can illustrate dimensions using the domain of the Automobile Exception to the 4th Amendment, discussed in Rissland (1989), Ashley et al. (2008) and Al-Abdulkarim et al. (2016c). This is a good illustration because it can be seen as having just two dimensions, privacy and exigency, which allows the space to be pictured, as in Fig. 1. Essentially the 4th Amendment provides that

[t]he right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, ...

The automobile exception permits search of an automobile without a warrant provided that there is probable cause, and that the search is sufficiently exigent. Exigency arises from the possibility that the delay in seeking a warrant might compromise the collection of evidence or public safety. If we consider the dimension of exigency, a completely immovable item would represent one end of the dimension and an automobile in transit on a highway the other. If we arrange our precedents along this dimension we will observe that at one extreme, where there is little exigency, all the cases will require a warrant, and at the other, where the matter is pressing, none of the cases will require a warrant. In between, some cases will need a warrant and some will not, suggesting that other relevant dimensions are in play. The situation is represented pictorially by the vertical grey lines in Fig. 1.³ Similarly for privacy, at one end (e.g. intimate body search) reasonable expectations of privacy will be such that a warrant will always be required, whereas at the other (in plain view in a public space) there may be little or no expectation of privacy so that a warrant may never be required. This situation is shown by the horizontal lines of Fig. 1. Putting the two dimensions together, the lines divide the space into 9 two-dimensional areas. In A, D and G, there is insufficient exigency to merit warrantless search, whereas in C and F the exigency is such (perhaps an immediate threat to the life of the President) that no expectations of privacy are sufficient to require a warrant. In A, B and C there are insufficient expectations of privacy to require a warrant given any degree of exigency, while in G and H the expectations of privacy are sufficiently high that no degree of exigency will permit the search. The interesting areas are E and I. In E there is a trade off between the two dimensions, so that some kind of balance must be struck (Lauritsen 2015). In area I, unless there is another dimension to consider, a preference needs to expressed, perhaps based on a preference between values (Bench-Capon and Sartor 2003). The dark line in Fig. 1 thus divides the space into areas where a warrant is required (to the left of the line) and those where it is not (to the right of the line).⁴ The line shown in Fig. 1 indicates an even trade off between privacy and exigency (giving the \(45^0\) line): other trade-offs are possible, which would require a curve rather than a line. It also includes area I in the no-warrant space, indicating a preference for exigency: a different preference would send the line horizontal, excluding I. Note also that trade-off could be possible throughout the range of the dimensions, so that areas A and I are squeezed. The right hand grey line effectively represents the point at which the dimension becomes decisive (subject to preference for a second dimension which is the decisive range for the other side), what (Bruninghaus and Ashley 2003a) call a knock-out factor. If both dimensions are such that the area E expands to consume the whole space, we have a situation where the dimensions are never decisive, but require to be balanced across their whole range.

If there is a third dimension the space will become a cube, with 27 partitions, and more dimensions will make visualisation very hard, although mathematicians can happily write equations relating to high dimensional spaces.⁵ If we now position the precedents in this dimensional space we can see the problem as being to divide the space into the plaintiff region and the defendant region. In the two dimensional case of Fig. 1, this could be achieved by the black line with the warrant cases on the left and the non-warrant cases on the right. The problem would seem to be the kind of line fitting problem which could be addressed by nearest neighbour or other statistical techniques. But there are two reasons why such techniques are not suitable here: first it is quite clear that this is not the way that people reason with cases, and so the point of the exercise, which was to model lawyer-like reasoning, would not be achieved. But more importantly there are not really sufficient cases to apply the statistical techniques, which depend heavily on having abundant examples. HYPO has 13 dimensions and many of the cases in fact only use some of these, typically no more than 4 or 5. The use of line fitting techniques would require hundreds or even thousands of cases (for a discussion of the required number of cases see Al-Abdulkarim et al. (2015b)). To obtain, let alone perform a dimensional analysis on, that many cases was far beyond what was sensible to ask from a nineteen-eighties PhD project. HYPO has 33 cases in its case base (Ashley 1990). It remains a task few would undertake, even if cases were available in this quantity.⁶

HYPO models argumentation, rather than using a purely statistical approach. Given a set of precedents located in the n-dimensional space, and a new case located in that space, the idea is to find arguments, based on the precedents, for and against a finding for the plaintiff (or defendant). Given a plaintiff precedent \(P_p\) and a defendant precedent \(P_d\) and a current case \(C_c\), the plaintiff’s task is to argue that \(C_c\) is on the same side of the line (or its n-dimensional equivalent) as \(P_p\) rather than \(P_d\). For example, in Fig. 1, if \(C_c\) is South East of \(P_p\), that is a strong argument for the plaintiff: if it is South West (or North East) we have arguments for and against the plaintiff, and if it is North West, it is of no help at all to the plaintiff.

In HYPO the arguments were deployed in a three-ply argumentation structure, as described in Sect. 2.2.

HYPO deploys its arguments within a three-ply structure. This structure is also found in the presentation of oral arguments in the US Supreme Court (Al-Abdulkarim et al. 2013), but in the Supreme Court the plies take the form of a dialogue between counsel and the Justices, whereas HYPO arguments are presented uninterruptedly (as if by the counsel), rather than in a dialogue. The three plies are:Each of these plies will be explained below.

As mentioned before, HYPO uses thirteen dimensions. But these are not homogeneous. The paradigmatic dimension is continuous, running from the extreme plaintiff to the extreme defendant location. But some of the dimensions in HYPO are not continuous: rather their range comprises a set of enumerable points. In other examples the dimension degrades to just two points: the extreme plaintiff and the extreme defendant point, and no intermediate points are recognised. Finally the dimension may degrade to a single point: for example if the defendant paid a bribe that is a strong point for the plaintiff, but if no bribe was paid that does not help the defendant’s case, rather it means that the dimension does not apply to the case. HYPO’s dimensions and their types are listed below:

After HYPO, Ashley moved to University of Pittsburgh (specifically to the School of Law and Learning, Research and Development Centre). At Pittsburgh, Ashley developed CATO, with Aleven (1997), and SMILE and Issue Based Prediction (IBP) with Ashley and Brüninghaus (2009). Meanwhile Rissland continued to develop the HYPO ideas at Amherst producing CABARET with Skalak and Rissland (1992), BankXX with Skalak and M. Timur Friedman Rissland et al. (1996) and SPIRE with Rissland and Daniels (1996). A major difference between these two strands was their use and understanding of factors. As explained in Rissland and Ashley (2002), both groups adopted the more legal sounding term “factors” in preference to the mathematical term “dimensions”. But whereas at Amherst, factors were just a different term for HYPO’s dimensions, a related but different notion was used in Pittsburgh. The Amherst systems will be discussed in Sect. 3 and the Pittsburgh systems, and the notion of factor as used there, in Sect. 4.

CABARET was described in conference papers, including Rissland and Skalak (1989b), Rissland and Skalak (1989a) and Skalak and Rissland (1991), before being consolidated in Rissland and Skalak (1991) and Skalak and Rissland (1992) (the very first paper to appear in this journal), which focussed in particular on strategies and argument moves. Because it took as its domain Home Office Deduction, there was a basis for the law in statutes, whereas HYPO had started from case law and its consolidation in the Restatement of Torts. This enabled CABARET to take as its focus the interpretation of terms found in the statutes, the idea being that the meaning of such terms is clarified and refined in case law. Thus while the statutes can be represented using rules, much in the manner of Sergot et al. (1986), when “the rules run out” (Gardner 1987), it is necessary to use case based techniques. The process is well explained by Ron Loui in his commentary on Skalak and Rissland (1991) in Bench-Capon et al. (2012). In this way the rules are able to focus the search and partition the case base so that there are fewer irrelevant distinctions made during the response (and the case base can provide precedents that govern more cases, since differences which relate to terms not at issue are not considered).⁸ This use of high level rules to focus and drive the lower level case based reasoning was a significant improvement, also used in IBP (Bruninghaus and Ashley 2003a) and still in use today (Al-Abdulkarim et al. 2016c).

Also CABARET developed a taxonomy of argument moves to represent patterns of actual legal argument, such as straw man and make-weight arguments, and showed how these were supported by the dimensional analysis of precedent cases. This was an important development since it enabled consideration of strategies for deploying arguments, an idea later developed through the use of dialogue games, such as The Pleadings Game (Gordon 1993), the game of Prakken and Sartor (1996), TDG (Bench-Capon et al. 2000), and PADUA (Wardeh et al. 2009), amongst others.

Both of the aspects introduced in CABARET represent significant developments of HYPO, allowing the dimensional analysis of cases to be employed in the context of rule interpretation, and for arguments with a more natural and familiar form to be used a strategic manner.

BankXX, which operates in the domain of personal bankruptcy (specifically Chapter 13 of the U.S. Bankruptcy Code), was most fully reported in Rissland et al. (1996) (in this issue) and its evaluation described in Rissland et al. (1997), an earlier conference version having appeared as Rissland et al. (1993). BankXX represents a considerable departure from HYPO and CABARET, since it uses the precedents (and other sources) to represent the domain knowledge as a highly interconnected network of building blocks which which is searched to gather argument pieces. The nodes in this network encompass a wide variety of ways of representing the domain knowledge including cases as collections of facts, cases as dimensionally-analyzed fact situations, cases as bundles of citations, and cases as prototypical factual scripts, as well as legal theories represented in terms of domain dimensions. Thus cases are represented in several ways. In particular, in its Domain Factor Space, cases are represented “by a vector composed of the magnitudes of the case on each dimension that applies to it; non-applicable factors are encoded as NIL. This ... represents a case as a point in an n-dimensional space.” Arguments are then formed by performing heuristic search over the network, using evaluation functions at the domain level, the argumentation piece level, and the overall argument level. The result is a highly sophisticated system which can blend the more Boolean nature of CATO’s factor-based approach with the more value-oriented nature of HYPO’s dimension-based approach. Further, the factors are grouped according to various theories, which, as in CABARET, gives some structure to the set of all factors.

The evaluation in Rissland et al. (1997) is one of the most (if not the most) detailed examples of evaluation in AI and Law. It considers several different forms of the BankXX program, and the evaluation is conducted from several perspectives, and a number of issues relating specifically to the evaluation of programs in the domain of law are noted.

BankXX has been rather unduly neglected⁹, and has no obvious descendants in current AI and Law research. This does scant justice to the importance of the work. Construction of cases by performing heuristic search was also carried out by AGATHA (Chorley and Bench-Capon 2005a), but the search tree was over only a collection of cases represented as bundles of CATO-style factors, rather than the highly sophisticated network of knowledge used in BankXX. Perhaps AI and Law should make more use of traditional AI techniques such as heuristic search. It is to be hoped that the appearance of BankXX in this special issue may revive interest in this work, and perhaps lead to more thorough evaluations of work in AI and Law. Evaluation remains an issue in AI and Law (Conrad and Zeleznikow 2015).

SPIRE Rissland and Daniels (1995), Rissland and Daniels (1996) and Daniels and Rissland (1997), which was applied to both the domain of home office deduction and the domain of personal bankruptcy, used case based reasoning to kick-start (seed) an information retrieval system. The idea was that in this way a large case base could be searched, but only a small number of these cases need be given the detailed analysis required for dimensional case based reasoning. From a case based reasoning view point this gives access to very much larger corpora of cases, while from an information retrieval point of view it enables the formulation of better queries.

The system operates in two stages (originally developed separately: the name SPIRE was not used in the earlier papers).

These two stages were put together as SPIRE (Daniels and Rissland 1997). For SPIRE, the input was a fact situation and the output was a set of relevant passages in each of the most relevant cases. It would then be possible to use these passages to query the main case base.

The engine used to query the main case base was INQUERY (Callan et al. 1992), developed by the University of Massachusetts Information Retrieval group in the Center for Intelligent Information Retrieval (CIIR). The use of HYPO is in selecting the seed cases: the top two layers of the case lattice proved to be a good choice for determining the cases to use.

Several different queries were tried , including bag of words, set of words and what was termed a “sum” query which required terms from within an excerpt to be found co-occurring in the passage, and some weighting methods. Among the results was that bag of words performed better than set of words, and bag of words and sum performed better than the other query types tried.

Although an interesting use of legal cased based reasoning, and with some encouraging results, SPIRE was not widely influential. This may be because Daniels went on to have a successful career in the US Army after finishing at Amherst, but in any case information retrieval is a hard field for research to make a lasting impact in because of the rapid development of technology. The tools now available for information retrieval are such as could only have been dreamed of in the mid-90s when the SPIRE research was carried out (which was before Google transformed the way we access information).

The task CATO was intended to address was to support teaching law students to distinguish cases. Not every difference between a case and a precedent represents a usable distinction. If we think think in two dimensions, as in Fig. 1, the plaintiff “owns” the area to the south-east of the precedent. Therefore a distinction has to place the current case to the north or west of the precedent since otherwise the difference actually strengthens the case, and the current case can be decided in the same way as the precedent using an a fortiori argument. Even if the distinction is usable, however, it may be that there are other differences between the current case and the precedent which can be used to compensate for or cancel out the identified distinction. Such a difference enables the distinction to be downplayed. If a distinction cannot be downplayed it may be considered significant, and so can be emphasised. Thus the task of CATO was to teach students:

Brüninghaus worked with Ashley on two projects, SMILE (SMart Index Learner) and IBP (Issue-Based Prediction) both of which are described in a paper included in this special issue (Ashley and Brüninghaus 2009). The two programs were supposed to act at different ends of the case based reasoning process: SMILE would take cases input as natural language and identify which factors were present, and then IBP would deploy CATO style reasoning, adapted for prediction rather than teaching, to predict the outcome of the case. Empirical evaluations are also reported in Ashley and Brüninghaus (2009), showing a strong performance from IBP, but a rather weaker performance from SMILE. Here we will concentrate on IBP, since SMILE draws mainly on classification techniques rather than the case based reasoning techniques we are focusing on here, albeit that SMILE was attempting to ascribe CATO’s factors to cases.

Another feature of IBP was that it was given a thorough empirical evaluation based on 184 cases (the 148 used in CATO together with another 36 analysed specifically for IBP). This evaluation was undertaken using versions of HYPO and CATO, a version of IBP with just the logical model, and several different machine learning approaches in addition to IBP itself. IBP performed best with a 91.8% success rate, and only a single abstention. The next best performer was a Rule Learning program which achieved 88%.¹⁰ The version of CATO achieved 77% (with 22 abstentions), and HYPO 67.9% with 50 abstentions. This is, of course, a little unfair on CATO and HYPO, since they were not designed to predict outcomes, and the abstentions count heavily against them. In fact, HYPO gets 93.3% of the cases for which it offers an opinion correct.

These results have been used as a basis for comparison when evaluating later programs, including AGATHA (Chorley and Bench-Capon 2005a), a program based on the approach of Chorley and Bench-Capon (2005b) in this issue, and ANGELIC (Al-Abdulkarimet al. 2015a), a project which produced a methodology for encapsulating case based domains, which was applied to several domains, including Trade Secrets. These programs were forced to use only a subset of the cases, since the majority of the case analyses have unfortunately not been made available to researchers, but evaluations showed them able to achieve 90+% on these cases. The results from Al-Abdulkarimet al. (2015a) are shown in Table 3. An earlier program based on neural networks (Bench-Capon 1993) was able to reach 98+%, on a different set of cases.¹¹ The full set of results for the IBP project are given as Table 3 of Ashley and Brüninghaus (2009). These results provide a useful benchmark for other programs attempting the task, and a success rate of 90% would seem a sensible aspiration.¹²

A number of different issues are addressed in Prakken and Sartor (1998), but here I will focus on its most influential idea, the movement from precedents represented as bundles of factors to sets of rules. The main aim of the translation was to enable the precedent to be used in a formal dialogue game, but the rules can equally be used as the basis of an executable logic program. Once rewritten as rules, the set of precedents are available in a form convenient for use in argumentation generally, as knowledge bases, and as the basis of formalisations of the reasoning involved.

The starting point is a set of cases represented as sets of factors together with their outcome. The factors can be divided into pro-plaintiff factors and pro-defendant factors, with each factor representing a reason to decide the case for the side they favour. It is assumed that an additional factor for a party will always strengthen the reasons to decide for that party. This may not be true in general (see Prakken (2005)), but is true of CATO, and can be imposed as a constraint on what is acceptable as a factor. Now the strongest pro-plaintiff reason will be the set of all the pro-plaintiff factors present in the case (\(F_p\)) and the strongest pro-defendant reason is the set of all the pro-defendant factors present in the case (\(F_d\)). We can express this as two rules:where p and d represent decisions for the plaintiff and defendant respectively. Now the outcome of the case will indicate which of these reasons was preferred, and so we add a rule expressing a priority between these two rules, so thatrepresents a preference for \(F_p\) over \(F_d\), and holds if the plaintiff won the case. Each of the precedent cases can be represent as three rules in this way, so that the whole case base can be rewritten as a set of rules to find for the plaintiff, a set of rules to find for the defendant, and an incomplete set of preferences between them. The result is a knowledge base with many similarities to the Reason Based Logic of Hage Hage (1993) and Hage (1996), further developed with his student Bart Verheij (Verheij 1995) and Verheij et al. (1998), but the timing and simplicity of the technique of Prakken and Sartor (1998), together with its strong connection to case based reasoning systems, meant that it made a more lasting impression on the AI and Law community.

The major limitation with the resulting knowledge base is that many possible rule conflicts will not be resolved by the priorities derived from the precedents. As noted in Al-Abdulkarim et al. (2015b), the 26 factors of CATO, split evenly as they are between plaintiff and defendant, give rise to more than 8000 sets of factors favouring each of the sides, and in excess of 67 million potential comparisons. Even allowing for subsumption of proper subsets, the number of required priorities to ensure that a conflict can be resolved with precedential authority will exceed the cases available (and most probably all the cases that have ever been decided). There is, however, a desire to go beyond what is contained in the set of precedent cases, so that we can say something about cases which are not decidable a fortori with respect to the precedents. In Prakken and Sartor (1998) this is achieved through rule broadening, allowing one or more factors to be removed from the antecedent, but then maintaining the priority of the original rule as established in the case from which it derived. The problem is that this lacks justification, unless or until endorsed by the judges in an actual case. Essentially, if the precedent does not provide a definitive answer, it can be distinguished by pointing to a factor missing from the plaintiff rule, or an additional factor in the rule in the precedent, and we need to rely on the user to say whether the distinction blocks the argument or not. Broadening, and several kinds of distinction, are fully discussed in Prakken and Sartor (1998). Although this is a difficult problem, addressed differently in Horty and Bench-Capon (2012), discussed in the following subsubsection, and in the value based theory construction approaches described in Sect. 6, the techniques of Prakken and Sartor (1998) at least enable a clean expression of the problem and potential solutions to it.

Although (Prakken and Sartor 1998) provides a formal dialogue game which can be regarded as a formalization of the aspects of legal theories on judicial reasoning discussed in that paper, it is very much tied to the dialogical context, and so to a process of argumentation. Horty’s main aim was to answer the question How is it, exactly, that precedents constrain future decisions?, and attempts to give a logic of precedent. Horty pursued this through a series of papers beginning with Horty (1999), moving through Horty (2004), Horty (2011a) and Horty (2011b) to its culmination in the paper included in this special issue, Horty and Bench-Capon (2012). Horty is motivated by a desire to counter the arguments of Alexander (1989). As Horty explains in Horty (2004), Alexander (who is working in Law rather than AI and Law) had identified three different models of precedent:

In Horty (2004) Horty wishes to defend the result model against the rule model advocated by Alexander. Both Horty and Alexander reject the natural model. To defend the result model, Horty draws extensively on AI and Law research, citing amongst others, Ashley (1989) and Ashley (1990), Aleven (1997) and Prakken and Sartor (1998).

The main idea of Horty is to represent precedents in rules, in much the same way as Prakken and Sartor (1998), but with one very important difference. Suppose the case was decided for the plaintiff. Now the defendant’s reason, in both Prakken and Sartor (1998) and Horty and Bench-Capon (2012) will be the strongest possible, that is the set of all pro-defendant factors present in the case, but the plaintiff’s reason is treated differently. Whereas in Prakken and Sartor (1998) it is the strongest pro-plaintiff reason, that is all the pro-plaintiff factors present in the case, Horty reasons that a weaker reason may have been enough to defeat the defendant. Thus the plaintiff rule in Horty and Bench-Capon (2012) can be a subset of the factors present in the case favouring the winner. The makes the resulting rule stronger, because it constrains future cases to a greater extent. The effect is the same as rule broadening, but is is done at the theory level rather than the case level, and is supposed to apply to all the cases in the case base. The situation is illustrated using the pictorial notation of Bench-Capon (1999) (which followed Prakken and Sartor (1998) in using narrow preferences) in Fig. 6.

The figure shows a Factor Lattice for a domain with six factors: three pro-plaintiff and three pro-defendant. These are grouped into two lattices one pro-plaintiff and one pro-defendant. These contain every possible combination of factors favouring the appropriate party, arranged in a partial order embodying the assumption that more factors beat fewer factors. A precedent provides a link between one node from each lattice, and so enables comparison between sets of factors from the two different lattices. Thus a narrow interpretation of the precedent with all six factors decided for the plaintiff, (shown in Fig. 6) will indicate a preference for {P1, P2, P3} over {D1 D2 D3}. This will not constrain any of the subsets. There are, however, several broad interpretations possible in the manner of Horty and Bench-Capon (2012): any of the two member or single member sets could be said to be preferred to {D1 D2 D3}, one of which, {P3}, is shown in Fig. 6. This means that {P3} is preferred to every combination of pro-defendant factors (since {D1 D2 D3} is preferred to every subset). Now only three pro-plaintiff subsets ({P1, P2}, {P1} and {P2}) are not constrained, and so await future decisions. For example a case with factors {P1, P2, D1} would, if decided for the defendant, now fully determine all subsequent cases. This would incidentally mean that {P3} was preferred to {P1, P2}, but this is not significant, since these subsets are never competing.

With these mechanisms Horty can formally characterise what it is for a case base with the given (broad or less broad) interpretations to be consistent. Now cases must be decided so as to maintain consistency of the case base: this may constrain the outcome, or just how broad the rule taken for the winner of the case can be. The open question is how the subset of pro-winner factors is to be determined. Horty does not specify this, although one suggestion might be that it should be the ratio deciendi of the case (see Branting (1993)), which can often be discovered by an examination of the text of the decision. Horty also envisages the subset being determined when the precedent is decided. A possible alternative might be that the theory is built anew for each new case, the constraint being that a consistent theory explaining the previous precedents would need to be produced. This might well, especially when there are relatively few precedents available, lead to some considerable revision of the rules to be taken from the precedent cases, but as the number of precedents increases the scope to revise rules while maintaining consistency with cases already decided will decrease. This view of reasoning with cases has some strong similarities with the theory construction approaches found in McCarty (1995) and Bench-Capon and Sartor (2003), and with the notion of a life cycle of case law found in Levi (1948) in which a period of turbulence is followed by a period of stability.

Horty is the starting point for Rigoni (2015), who likes the rule based representation of cases, especially because it is able to maintain the venerable distinction between ratio deciendi and obiter dicta. Rigoni associates Horty’s broadened rules with ratio deciendi. Rigoni, however, offers a number of improvements to Horty’s account. First he allows for multiple rules to be associated with a single precedent in order to handle over-determined cases. This would also allow the incorporation of obiter dicta. Second he recognises that not all precedents serve the same purpose: identifying a class of precedents he calls framework cases. His example of a framework precedent is Lemon v. Kurtzman.¹⁴ Rigoni summarises the case:

In that case the US Supreme Court addressed the question of whether Pennsylvania’s and Rhode Island’s statutes that provided money to religious primary schools subject to state oversight violated the Establishment Clause of the First Amendment. The court introduced a three-pronged test and ultimately ruled that both programs did violate the Establishment Clause.

It is a feature of HYPO and CATO that all the precedent cases play the same role: to express a preference or, in HYPO, to constrain the n-dimensional space in some way. Thus cases are analysed against a framework of dimensions and factors developed with respect to the whole set of cases. In practice, however, the dimensions, factors and issues have developed over time, and some of the cases that introduced a factor, issue or dimension may well be in the case base. For example, if we consider the cases related to the Automobile Exception to the Fourth Amendment described in Rissland (1989), Bench-Capon (2011) and Al-Abdulkarim et al. (2016c), we see that no mention was made of privacy issues in the case which is seen as introducing the exception, Carroll v US.¹⁵ The need to consider privacy is stressed in South Dakota v. Opperman.¹⁶ Thus the issue of privacy must have been introduced in Opperman, or some earlier framework precedent. The much discussed Califormia v Carney,¹⁷ which, especially in the oral argument (Rissland 1989; Ashley et al. 2008; Al-Abdulkarim et al. 2013) was important for its identification of the factors needed to distinguish between an automobile being used as a vehicle and an automobile being used as a residence. This was extensively discussed in the Oral Argument for that case (Rissland 1989; Al-Abdulkarim et al. 2013) and a number of new factors made their way into the decision. Such factors are rarely considered as present in previous cases, and so it may be a mistake to analyse earlier cases in terms of dimensions, factors and issues introduced subsequently. Understanding a body of cases as a sequence, although the topic of Henderson et al. (2001) and Rissland and Xu (2011), is perhaps a topic which merits further exploration. Keeping a representation current in the face of changes in case law is also explored in Al-Abdulkarim et al. (2016a).

The motivation for expressing a set of precedents as rules in Prakken and Sartor (1998) was so that the precedents could be used to deploy arguments in a dialogue game. At the time, following Gordon (1993), dialogue games were a popular way of expressing legal procedures, such as particular forms of legal argumentation. Since their introduction to explain fallacies in propositional logic Hamblin (1970) and Mackenzie (1979), such games handed tended to be built on an underlying rule base. An excellent overview of such systems is given in Prakken (2006). As this century has progressed, however, the use of dialogue games has tended to make way for argumentation schemes Walton (1996) and Walton et al. (2008). Although argument schemes had been used before in AI and Law: arguably the three ply argumentation of HYPO is a scheme, CABARET certainly uses schemes and Toulmin’s argumentation scheme (Toulmin 1958) was widely used (e.g Marshall (1989)), often to drive dialogues as in Bench-Capon et al. (2000), explicit use of argumentation schemes moved to the forefront when Walton’s understanding of them in terms of premises, conclusions and critical questions, as expressed in Walton (1996), became prevalent.

A particular argumentation scheme (originally designed for value based practical reasoning) was applied to reasoning with legal cases in Greenwood et al. (2003), and argumentation schemes were used to model a particular case in Gordon and Walton (2006). The explicit use of CATO’s argumentation moves was carried out in Wyner and Bench-Capon (2007). These schemes were used to model particular cases in Bench-Capon (2012), and formalised, further developed and extended to include dimensions in Wyner et al. (2011), Atkinson et al. (2013) and Prakken et al. (2015). The last of these, in particular, offers a set of schemes designed to model HYPO/CATO style reasoning in a formal framework, ASPIC+ Modgil and Prakken (2014).

Interest in Berman et al. (1993) and examination of the purpose of laws, interpreted as the values they were intended to promote and protect, was revived by a group of three articles that appeared in Artificial Intelligence and Law, volume 10 numbers 1–3: Bench-Capon (2002), Prakken (2002) and Sartor (2002). Following this Sartor and Bench-Capon developed the ideas in a series of papers, including Bench-Capon and Sartor (2000) and Bench-Capon and Sartor (2001), culminating in Bench-Capon and Sartor (2003). These papers gave an account of theory construction with disagreements resolved according to the value preferences of the audience (here society, as represented by the judges).

The overall idea is shown in Fig. 7. The starting point is at the bottom left where we have a set of cases (described as bundles of factors) and their outcomes. These outcomes reveal preferences between sets of factors, which will explain the case outcomes. The preferences are essentially the priority rules of Prakken and Sartor (1998). Each factor is associated with a value: a value that will be promoted by deciding the case for the side favoured by that factor. This enables us to rewrite sets of factors as sets of values, and transfer the preferences to these sets of values. The heart of the theory is this set of value preferences. This takes us to the top of the diagram, and we have constructed a theory and so we can start to apply the theory and work our way down the right hand side. The value preferences determine and explain preferences between sets of factors which are not to be found in the existing precedents. These preferences can then be used to determine the outcomes of as yet undecided cases which have these sets of factors.

The theories are constructed using a set of operators, defined in Bench-Capon and Sartor (2003). The theory starts from nothing and construction begins by including a case from the background. This will bring with it a set of factors and their associated values. Each factor is associated with a simple rule stating that the factor is a reason to decide for the side favoured by the factor. The theory can then be extended by including more cases, combining simple rules into rules with multiple antecedents and establishing preferences between rules and between values. This continues until the theory can be applied to give an outcome for the case under consideration. At this point the onus moves to the other party who must attempt to extend the theory to produce a better theory with an outcome for its favoured side, whereupon, it is again the turn of the original side. This process of extending and refining the theory continues until there is no possible extension of the theory which changes the outcome. The paper illustrates the process with the wild animals cases introduced in Berman et al. (1993). The paper also includes a discussion of how the theory operators relate to the argument moves of CATO.

This approach was tested empirically in Chorley and Bench-Capon (2005b) (included in this issue) and Chorley and Bench-Capon (2005a). The paper included in this special issue explored the use of CATE (CAse Theory Editor) in a series of experiments intended to explore a number of issues relating to the theories constructed using the operators of Bench-Capon and Sartor (2003), including how the theories should be constructed, how sets of values should be compared, and the representation of cases using structured values (which are akin to dimensions) as opposed to factors. In CATE, the construction of theories is done by the user, supported by the CATE toolset. The second paper described AGATHA (Argument Agent for Theory Automation) which is designed to automate the theory construction process, by constructing the theory first as a search over the space of possible theories, and then as a two player dialogue game (which could be played with the AGATHA program playing both sides). A set of search operators and argument moves are defined in terms of the theory constructors and the resulting theories are evaluated according to their explanatory power and their simplicity. The search or game continues until it is not possible to produce a better theory. Several search methods were investigated: brute force and heuristic search using A* and adversarial search using \(\alpha\)/\(\beta\) pruning. The results proved to be good: they were reported in Chorley and Bench-Capon (2005a):

AGATHA produces better theories that the hand constructed theories reported in Chorley and Bench-Capon (2005b), and theories comparable in explanatory power to the best performing reported technique, IBP (Ashley and Brüninghaus 2009). Note also that AGATHA can be used even when there is no accepted structural model of the domain, whereas IBP relies on using the structure provided by the Restatement of Torts.

Table 3 of this introduction includes the results of some versions of AGATHA.

Apart from their pivotal role in the approach to theory construction advocated in Bench-Capon and Sartor (2000), values have been applied to case based reasoning in several other ways. Their original use, to tailor an argumentation framework to the preferences of an audience using Value based Argumentation Frameworks (VAF) (Bench-Capon 2003a) was applied to reasoning with cases in Atkinson and Bench-Capon (2005), Wyner and Bench-Capon (2007) and Atkinson and Bench-Capon (2007), but recent work by Atkinson and her colleagues has placed moved away from this use of values in Al-Abdulkarim et al. (2015b) and Al-Abdulkarim et al. (2016d). They continue to use the VAF approach for legislative law making and e-democracy Atkinson et al. (2006), Atkinson et al. (2011) and Bench-Capon et al. (2015), and in the justification of norms (Bench-Capon and Modgil 2017).

Values have also been used for reasoning with cases in Araszkiewicz (2011), which recognised that values could be used to justify rules (their traditional role in VAF based systems) and also the inclusion of particular antecedents in rules, and in Grabmair and Ashley (2011), from which developed a different formalism intended to capture dynamic aspects of reasoning with legal cases (Grabmair and Ashley 2013). The most recent work in this strand is Grabmair (2017). Finally, another approach to using values in the representation of cases can be found in Verheij (2016).

One issue relating to values that has yet to be fully explored is that it seems that they can be used in a variety of ways. Sometimes they appear to give rise to conflicting positions which can be resolved by preferring one value to another, which is essentially the approach of VAF based systems, At others they appear to be better regarded a sets of reasons, for which issues such as accrual are pertinent (Prakken 2005; Modgil and Bench-Capon 2010; Bench-Capon et al. 2011, which seems applicable in domains such as US Trade Secrets, when a number of different aspects of the case must be considered. Also, however, there seem to be situations where a balance (Lauritsen 2015; Gordon and Walton 2016) must be struck between two values: it cannot be said that one is preferred to another, but rather both must be respected to an appropriate degree. This is perhaps the case with the Automobile Exception cases, where a balance must be struck between exigency and privacy, Bench-Capon and Prakken (2010). Unpicking these different aspects is something that AI and Law may need to address in future work.

In the Restatement of Torts (quoted in Atkinson and Bench-Capon (2005)) we find (italics mine):

Some factors to be considered in determining whether given information is one’s trade secret are: 1. the extent to which the information is known outside of his business; 2. the extent to which it is known by employees and others involved in his business; 3. the extent of measures taken by him to guard the secrecy of the information; 4. the value of the information to him and to his competitors; 5. the amount of effort or money expended by him in developing the information; 6. the ease or difficulty with which the information could be properly acquired or duplicated by others.

Although we can identify all of these “factors to consider” with factors in CATO, the language here is, as the italicised phrases show, not really consistent with the all or nothing, present or absent, nature of CATO-style factors. Each of them seems to require some kind of quantitative estimate of how much?. Thus F16, ReverseEngineerable, a CATO factor which has presented a number of difficulties for subsequent systems attempting to use CATO’s analysis, such as that reported in Al-Abdulkarimet al. (2015a), cries out for a more nuanced representation. Reverse Engineerable could mean that a person could build a version after a cursory inspection, or could require many person years of expert effort. Arguably, anything is reverse engineerable with sufficient effort, expertise and ingenuity. There are three ways in which issues requiring dimensions can arise:

The first two of these concern what can be argued about. When using factors, the decisions are made by the analyst and once made cannot be debated when attempting to resolve the case. (1) is effectively decided when defining the factors: thus whether Justinian, who demands actual physical possession for the animal to count as caught should be chosen over other authorities who make less stringent demands, such as mortal wounding or certain capture, is something that the analyst needs to be told along with the existence of caught as a factor. Once the definition has been chosen, ascription to cases is relatively easy. (2) relates to the analysis of particular cases. Given that the information was not in fact reverse engineered (in which case F25 would apply instead), the analyst must decide whether “the ease or difficulty with which the information could be properly acquired or duplicated by others” is such that F16 can be deemed to be present. (3) rather concerns computation, and allows mapping onto numbers to facilitate accrual and comparison. We need to be able to argue about whether a factor applies to a case and which side is favoured, but using CATO-style factors these issues are resolved by the analyst and so outside the scope of systems which begin with cases represented as bundles of factors.

The computation aspect is key in Chorley and Bench-Capon (2005b). The main concern in that paper is values, but there is a section on what it terms structured values. The 26 CATO factors are associated with one of five values: CA for respect for confidentiality agreements, QM for questionable methods used by the defendant, LM for legitimate methods used by the defendant, RE for reasonable efforts to maintain secrecy of the part of the plaintiff, and MW for material worth of the information.. A structured value runs from an extreme pro-plaintiff point to an extreme pro-defendant point, and the various CATO factors relating to the value are assigned positions along this line according to how strongly they promote or demote the value. They are thus dimensions in all but name. The values can themselves be ordered, and to the contribution of the factor becomes a function of the importance of the value and the extent to which the particular factor promotes it. The empirical consequences of the additional degrees of freedom this enables are given as part of the results in Al-Abdulkarim et al. (2016b)¹⁹ and Table 3 of this paper.

This approach is also adopted in Bench-Capon and Bex (2015) which provides dimensions for the wild animal cases of Berman et al. (1993) and Al-Abdulkarim et al. (2016b) which applies the same process to CATO’s factors. In Al-Abdulkarim et al. (2016b) seven dimensions are used rather than the five structured values of Chorley and Bench-Capon (2005b), and the dimension runs from 10 (extreme pro-plaintiff) to 0 (extreme pro-defendant) rather than from +10 to −10, as used by Chorley and Bench-Capon (2005b).

The seven dimensions in Al-Abdulkarim et al. (2016b) are:

The distribution of the 26 CATO factors is shown in Table 4.

These dimensions allowed computation of predictions of case outcomes using propositions with truth values between 0 and 1 to represent the dimension points, and interpreting the logical operators in the manner of fuzzy logic (Zadeh 1965), as proposed in Bench-Capon and Gordon (2015). The results of the dimensional version of Angelic Secrets reported in Al-Abdulkarim et al. (2016b) showed an improvement on previously reported versions which had used boolean factors (Al-Abdulkarimet al. 2015a). This seemed to centre in particular on a better handling of the vague factor F16, reverse engineerability. Two other cases with factors which it had been suggested in Al-Abdulkarim et al. (2016c) were wrongly ascribed, were wrongly decided by the program, but when the factors in these cases were corrected in the ways suggested in that earlier paper a success rate of 96.8% was achieved. This suggests that it is possible to achieve better results if we allow for degrees of support, rather than insisting on the all or nothing choices required by the use of factors. Note, however, that even with the dimensional approach of Al-Abdulkarim et al. (2016b), the description of the cases in terms of factors/dimensions is still a matter for the analyst: it cannot be disputed within the program. This relates to issues (1) and (2) above and will be discussed in Sect. 7.3. Note, however, that that there is no obligation for the computer system to cover the whole process: as discussed in Al-Abdulkarim et al. (2016d) a system may be scoped so as to start with factors or dimensions. It may be preferable to allow an analyst to represent the case in terms of dimensions and factors rather than attempt to enable their derivation from the brute facts. There is a degree of trade off here: see also Ashley (2009) and the commentary on it by Thorne McCarty in Bench-Capon et al. (2012).

The use of dimensions can also be used to generate case narratives, as described in Bench-Capon and Bex (2015), using methods akin to the scripts of Schank and Abelson (1977). These narratives can then be used to recast the story of the case in terms of legally significant facts, and to support improved explanations.²⁰

The transition from the facts of a case as reported using “world facts” to a set of legally significant “legal facts” has long been as issue in AI and Law, at least since Breuker and Den Haan (1991). The difficulty is that the world facts are diverse and peculiar to particular cases, whereas the legal facts exhibit more uniformity and have a more definite relation to the issues to decided. It is often said that once the world facts have been qualified into legal facts, the decision itself is often obvious. This clearly relates to issues (1) and (2) from Sect. 7.1. Both these questions need to be able to be made the subject of argument.

As can be seen from the use of structured values in Chorley and Bench-Capon (2005b) and the Tables in this paper, especially Table 4, factors can be regarded as points (or ranges) on dimensions. So the first move is to see the legal facts of a case as a bundle of dimension points. Then a case description can be seen as a frame with slots corresponding to dimensions and fillers as points/ranges of those dimensions. This is precisely the structure advocated in Bench-Capon and Bex (2015) and Al-Abdulkarim et al. (2016b). It is also the method of representing cases in Prakken et al. (2015) to enable argumentation about the how the factors present in a case relate to facts and dimensions.

The matter is made more explicit in Al-Abdulkarim et al. (2016d), which distinguishes various types of statements in the journey from evidence to verdict, with a particular emphasis of how we can move from the world facts to the legal facts. It is important not to confuse issues of fact and issues of law. Table 6 shows the different types of statement used in that paper.

Note that the points/ranges on dimensions play three roles. First, they are the conclusion of the reasoning about the world, and the input to the legal reasoning. Thus we start with a mass of evidence from which we need to arrive at a set of well structured legal facts which will relate to the law governing the case. As such they are typically not certain but established with a certain degree of belief. The methods used here will be the standard ways in which people reason about the world: evidence takes many forms: witness testimony, documents, forensics, video footage etc. Each of these are associated with their own kind of reasoning, coherence (Bex 2011), probability (Timmer et al. 2015), etc, and the courts should make use of these established ways of reasoning. There is nothing distinctively legal in this phase, and the decisions are often made by lay juries, and often facts cannot be revisited at the Appeal stage. At his point the appropriate standard of proof (Farley and Freeman 1995; Gordon and Walton 2009) is applied. The appropriate proof standard will depend on the jurisdiction and the nature of the case: typically criminal cases impose a higher standard of proof than civil cases.

Those factual conclusions that meet the required standards become legal facts. At this point they become either true or false: all factual conclusions that meet the proof standard are “equally true”: the question is not the extent to which they are believed, but whether they are believed sufficiently to be taken as true in the legal reasoning. This is the bridge between the world and realm of law: the proof standard is the toll which gives entry to the bridge. On leaving the bridge the legal facts assume their third role: they become base level factors. As such they again become associated with a number: 1 for extreme pro-plaintiff factors, \(-1\) for extreme pro-defendant factors and somewhere in between otherwise. Note that the number is entirely independent of the degree of belief with the factual conclusion was established: the base level factor number is determined by the dimension and the position of the factor on that dimension. Conflation of these roles can lead to problems: perhaps applying the standard of proof during legal reasoning, or allowing the degree of belief to contaminate the contribution of the factor.

All this is quite recent work and nothing like the consensus about, let alone the understanding of, reasoning with CATO-style factors has emerged with respect to dimensions. None the less, this is an active area of work, and points to a direction which may serve to enhance our understanding of reasoning with legal cases.