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(1) Not all knowledge can be stated symbolically.
(2) Developing and maintaining the system is time consuming.
The problem of trying to symbolically formalise knowledge can be enormous.
It has been found that where there are 'grey areas' to a problem, the resolution
of which involves the weighing of a multitude of factors, experts often
reach a conclusion and then ex post facto justify it according to
their hierarchy of symbolic rules. Rules then do not seem to capture all
that is involved in expert knowledge. [3]
Secondly the actual construction and maintenance of the system is complex
and time consuming; there is a 'knowledge acquisition bottleneck'. The
system's creators have to explicitly code every rule and predicate manipulated
by a symbolic reasoner. The system then has to be 'debugged' to ensure
the database is free of errors and operates as predicted. Any changes made
to the database, either through changes in or expansion of the knowledge
of the system, have to be incorporated through the same time-consuming
process. To make these systems 'intelligent' requires much work by a domain
expert working in conjunction with a knowledge engineer. [4]
Neural nets adopt an alternative approach to modelling intelligence.
In neural nets, the relations between pieces of information do not have
to be explicitly specified. Instead the neural net 'learns' the relationships
between the information. For this reason neural nets are sub-symbolic reasoners;
the system's designers do not have to explicitly state the relationship
between pieces of information in the form of symbols. These aspects of
neural nets have lead to resurgent interest in their use in 'intelligent'
computer systems.
Neural nets mimic this structure. Neural nets are composed of 'neurodes'.
A neurode is a mathematical model of a biological neuron. Neurodes are
connected through synaptic weights to other neurodes; to create a network.
What group of neurodes each neurode accepts input from, what output a neurode
generates from its inputs and to which other group of neurodes the output
is sent to, all determine the way the neural net will behave.
One of the major goals in neural net research has been to construct
neural nets capable of learning. In biological systems, experiments show
that one of the most important effects of learning at the cellular level
is the modification of the strength of the synaptic connection between
two neurons. Analogously, training a neural net, is a matter of modifying
the values of the synaptic weights in the system. Unfortunately, training
is a complex task and the method used depends on the architecture of the
network being used.Contrary to the optimistic hopes of early neural net
researchers, it is not possible to simply connect many neurodes in a random
fashion and hope that they will perform a meaningful task; as in biology
the neurodes must be connected in a particular structure.All neural nets
however, operate as some form of pattern classifier. During its training
the neural net learns to associate a certain pattern presented on its input
with a certain pattern on its output, what is known as 'pattern association'.
Further, neural nets have the property that they can generalise their input,
'pattern generalisation'. Neural nets can learn the characteristics of
a general category of objects based on a series of specific examples from
that category. This ability to classify patterns is retained even when
the neural net is presented with partial patterns, the neural net will
infer which general category the partial input belongs to. [6]
Researchers have experimented with various structures for
constructing neural nets ranging from the simplest single neurode to complex
hybrid networks. The major drawback in simple networks is that they can
only classify 'linearly separable' problems; [7]
they cannot be trained to correctly classify every possible
collection of patterns.This problem of linear separability can be overcome
by using networks of three or more layers; it has been proved that such
networks can map any input set to any output set, [8]
subject to one limitation. All neural nets including these
multi-layer neural nets, can only map contradictory input patterns by reaching
a compromise between those input patterns. Neural nets cannot take one
input pattern and map it to two separate outputs. The consequence of this
will be discussed in chapter five.Adaptive filter networks are multi-layer
neural nets, and are trained using 'back-propagation' techniques. [9]
Although adaptive filter networks must undergo supervised
learning [10]
they are perhaps the most common form of neural net used.
While much more sophisticated neural nets than adaptive filter networks exist, many are extremely complex and are difficult to implement and tune. For this reason such networks remain largely at the research stage. Unless otherwise specified, general reference to neural nets in this paper will thus concern adaptive filter networks.
(1) deductive reasoning,
(2) inductive reasoning, and(3) analogical reasoning.
Detailed expositions of each type of reasoning have been given elsewhere, [12] however a short explanation is worthwhile.
Deductive reasoning is a strict logical method of reasoning. Deductive
arguments take the general form
(A) In any case, if p then q.
(B) In the present case p.
(C) Therefore, in the present case, q.
In this form of reasoning, one moves from the application of general
rules to specific facts to deduce an outcome. The premises require and
justify the conclusion. It is illogical to accept the general rule and
the specific instance but to deny the conclusion. [13]
However, the application of the general rule to the specific
instance is contingent on that instance being regarded as a member of the
general class defined in the rule. In terms of the above example, the 'q'
referred to in line (C) must be regarded as similar enough to the 'q' in
line (A) before deductive application of the rule can occur.
Inductive reasoning essentially operates as the reverse of deductive
reasoning. Here one starts with numerous observations and then tries to
relate them by creating a rule that can 'explain' each observation. For
example the following situations are observed :
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Outcome |
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X |
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X |
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X |
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Y |
(A)'If (A B C D E) then X'; and
(B)'If (M N O P E) then Y'.
The validity of such rules though remains contingent. [14]
Analogical reasoning, in contrast to deductive reasoning and inductive
reasoning, is not immediately concerned with the application of rules.
Here one simply says that a certain outcome should result because that
outcome has previously occurred in a similar case. This is a manifestation
of the formal principle of justice that similar situations should result
in similar outcomes. [15]
Analogical reasoning and inductive reasoning are extremely
closely related. [16]
One only considers that the outcome of two situations should
be similar because their facts are similar, by following the 'rule' that
'like case should be decided alike'. This can itself be seen as the corollary
of the more general belief that if two situations have the same outcome
then there must be a general rule that explains them. Thus in saying that
two similar factual situations must have similar outcomes we are really
saying that this would be the result from the application of a hypothetical
general rule that would contain both situations. [17]
Likewise, it is only possible to suppose that a general rule
can explain several situations if one regards those situations as similar
to each other.In this respect the mental processes in inductive and analogical
reasoning are very similar. In both cases general rules explaining factual
situations are assumed to exist; however, only in inductive reasoning does
one take the step of trying to explicitly state those rules. More fundamentally,
inductive reasoning and analogical reasoning are both inherently dependent
on the finding of similarity between situations.
(A) law is a series of well defined rules of universal application; and
(B) law is not rule based; legal outcomes are wholly dependent on the views of the parties, lawyers and the judge in a case. [19]
Of course, few if any jurisprudes adhere to these extreme versions of
either approach. [20]
While it would be fruitless to try and conclusively determine
the nature of law, it will be argued that law's true nature does not lie
at either of the extremes presented, and incorporates aspects of both positions.
Levi has given a useful breakdown of the process of legal reasoning,
which he sees occurring in three steps
(1) Similarity is seen between cases,
(2) The rule of law inherent in the first case is announced; and(3)
The rule of law is made applicable to the second case. [21]
While Levi's description of the legal reasoning process may not capture
all that is involved in legal reasoning it does reveal that perhaps the
key step in legal reasoning is the finding of similarity, or difference,
between cases and aspects of a case.
In this context MacCormick and Burton note that the finding of similarity
is dependent on the overall purposes that the legal system is trying to
achieve. [22]
The classification of facts for the purposes fitting them
into the major premise of a deduction and for the purposes of creating
analogies and inducing rules, occurs in a whole body of knowledge and theory
we use to make sense of the world. [23]
When deciding between competing fact classifications our evaluation
inherently involves considerations of the consequences of each classification
on our model of the world and in this sense similarities, dissimilarities,
classifications, and thus the meaning and scope of rules are made and not
found. [24]
[T]he scope of a rule of law, and therefore its meaning depends upon a determination of what facts will be considered similar to those present when the rule was first announced. [28]
Secondly, there is the closely related problem of deciding what meaning to give terms within a statute. For example, the Crimes Act (1958) (Vic.) states
s.91(1)A person shall be guilty of an offence, if when not at his place of abode, he has with him any article for use in the course of or in connexion with any burglary ...
While classifying an article as within s.91 of the Act may be easy in
some cases, this is not always so. What of a tool box ? All the items therein
could be used during a burglary yet all could have legitimate uses. Whether
an article is for use in the course of a burglary is a matter for debate.
This problem, of determining the meaning of individual phrases in rules,
is called the problem of 'open texture'. [29]
Resolving the problem of open texture is inherently dependent
on the use of analogy. [30]
Thus, even in this perhaps the most rule guided area of law,
where all the rules are collected and clearly expressed, the purely deductive
application of rules is not sufficient to solve all problems.Similar problems
arise when reasoning in the common law. It is often said that there are
common law 'rules'. However, in a strict sense this cannot be true. The
whole of the common law has been created on an individual case by case
basis. In a single case a judge can do no more than pronounce a decision
that applies to the facts of the case. It could be argued that the ratio
decidendi expresses the rule contained in a case. [31]
This rule will be binding on all subsequent cases that have
the same facts as the original case. However, the binding nature of the
ratio decidendi (and thus the scope of the rule) is severely limited
once it is appreciated that the ratio only applies to the strict
facts of the original case. It will only determine the outcome of another
case that has exactly the same facts, strictly, any change in the facts
results in a new situation the outcome of which is not determined by the
ratio decidendi. [32]
The belief that there are common law rules arises because
even though the ratio of one case may not be binding in a
later case, if the latter case has very similar facts to the original case
the ratio is nevertheless felt to be highly persuasive. [33]
Thus the second case is decided similarly to the first. As
this process continues, a large body of cases builds up, all of which have
similar facts and similar outcomes. Seeing this collection of cases it
is not unreasonable to assume that the original case laid down a general
rule which dictated the results in all the latter cases. [34]
In this way the common law appears to create rules that can
later be applied deductively. [35]
Even in such usage though, these common law rules experience
the same problems as statutory rules.
Case 1: A B C D,
Case 2: A B C E,
Case 3: A B C F,
Case 4: A B C G.
Further assume that Case 1 and Case 2 are regarded as analogous. From
this it can be implied that factors D and E are similar. Again, assume
that Case 1 and Case 3 are not regarded as analogous, implying that factors
D and F were not similar. How is Case 4 to be classified ? This depends
on whether factor G is regarded as more similar to factor D or more similar
to factor F.
A consequence of the importance of the finding of similarity to the
process of legal reasoning is that extreme versions of legal positivism
do not seem supportable. Since deductive reasoning is by itself insufficient
to explain legal reasoning, law must be composed of more than purely rules.
Nor however, can it be accepted that legal reasoning is totally subjective, [40]
legal rules provide a 'paradigm' which guides legal thought. [41]
This view of legal reasoning, as a process inherently dependent
on the finding of similarity between situations and on our world theories,
has consequences for the use of neural nets in legal expert systems. These
consequences will be explored in the following chapters.
(1) as and within inference engines [42]
in legal expert systems; and
(2) in legal information retrieval systems.
This chapter will discuss and explain each of these proposed uses. The following chapter will discuss some of the jurisprudential implications arising from these proposed uses.
Once trained, new cases can be presented to the neural net. In reaching
a verdict on a new case, the neural net classifies the case into one of
the general groups created during training. In so classifying a case, the
neural net appears to mimic analogical reasoning; similar cases result
in the same verdict.
Similar work has been performed by Bench-Capon who has created a neural
net based on a hypothetical statute. [55]
Bench-Capon's investigation is of further interest in that
it demonstrates that a neural net can successfully perform classifications
even when presented with a lot of 'noise' (inputs that are not relevant
to the classification). Thus, contrary to what other commentators have
said, [56]
neural nets have the potential to operate successfully even
when the factors affecting the classification are not known. [57]
In contrast to the above two approaches which essentially
try to model whole areas of law using neural nets, Walker et al (the 'VUA
team') 'simply' use neural nets within a more conventional case based reasoning
system. [58]
The VUA team have created PROLEXS, a 'hybrid' legal expert
system, which relies on more than one model of legal reasoning. Early versions
of the system operated by having a stored database of cases, each case
being stored as a set of 'conditions' each with an associated fixed weight,
along with a case threshold. [59]
When a case was to be applied analogically, the weights on
conditions present in the current fact situation were summed and then compared
to the case threshold of the past case to determine whether the current
situation was analogous to the stored case. [60]
In the first implementations of PROLEXS, the condition weights
and the threshold values had to be assigned by the domain expert. However,
the VUA team note that weight and threshold assignment is a difficult task
for a human domain expert. [61]
Consequently, the latest version of PROLEXS dispenses with
the case database within the case based reasoning sub-system. Instead,
a multi-layer neural net is trained using the conditions as the inputs
and the applicability or non-applicability of the open texture term as
the output to the neural net. [62]
The neural net learns the condition weights and case thresholds
during its training. This is essentially the same approach as taken by
Hobson and Slee, and Bench-Capon. It is claimed that this system can provide
more discerning weights than a human expert. [63]
[W]hen we attempt to model the legal reasoning process, we must use a device capable of emulating the parallel problem-solving process. To this end, normal digital computational devices are inadequate. [93]
It is claimed that neural networks will overcome this problem due to
the inherently parallel nature of their operation. [94]
If taken to its full extreme, Warner's view of the legal reasoning
process as inherently parallel has potentially fatal consequences for traditional
symbolic systems. However, apart from such vague and dubious observations
about the nature of legal reasoning the full implications of this idea
are not explored.
That the legal reasoning process is an inherently parallel process
is highly contentious. It seems acceptable to say, as Warner claims, that
when problems are solved the solution of 'unit problems' will impose a
state change on the problem domain rendering invalid all unit solutions previously achieved and changing the environment for all unit solutions yet to be achieved. [95]
However, this is not a description of a parallel process. This simply
notes that the answer to one question may change which questions are subsequently
asked. While this undoubtedly occurs in human reasoning, the contingent
nature of questions is quite easily represented in a tree diagram. [96]
Such tree diagrams form the basis of all rule based expert
systems. Systems such as PROLEXS [97]
display this 'parallel' problem solving capability by modifying
subsequently asked questions according to intermediate answers. This belief
that neural nets can solve all the problems that currently beset symbolic
legal expert systems is, perhaps unconsciously, echoed by Bench-Capon.
He has attempted to model what prima facie appears a rule based area of
law, with a neural net. [98]
If it is accepted that some legal reasoning occurs in 'parallel', it
still does not mean that all legal reasoning does. It is not in every legal
question that, as Levi would say, the application of the rule changes the
rule itself. Thus Warner's vision of the necessity of using neural nets
to model the supposedly parallel nature of the legal reasoning process
cannot be supported.
(1) they must understand the analogue meaning of words and
(2) they must understand moral decision making. [116]
According to Tito it is necessary to understand the analogue meaning
of words to determine whether something is within a general category. Similarly,
moral decisions must be made when determining at what level of generality
things are to be compared.
While Tito says she is not interested in whether computers can mimic
the results achieved by lawyers, but whether they can actually understand
analogical reasoning, [117]
her work does not consider the philosophical problems of what
constitutes intelligence and understanding in computers. [118]
Tito's work is still informative however, if viewed as a discussion
on the ability of computers to mimic the results achieved by lawyers.A
problem that faces all legal expert systems, including those that incorporate
neural nets, is that they only model legal concepts. It is unavoidable
that when an issue in the real world is to be considered by a computer,
it has to be circumscribed by a limited number of factors. This circumscription
will inevitably involve a loss of richness and the creation of a conceptual
bias [119]
in the computerised representation of the concept as compared
to the real world concept. In Tito's conception, the computer only has
a digital representation of concepts. Though this loss will be inversely
proportional to the complexity of and dependent on the composition of the
matrix used in the circumscription, if the input matrix does not accurately
reflect the real world concept then the conclusion drawn by the legal expert
system will not be accurate.It is as yet unclear whether the necessity
of understanding moral decision making for the finding of similarity is
a fundamental bar to computers performing analogical reasoning. Computers
may yet be implemented that do this, though what this entails is presently
unclear.
Similarity and neural nets.
In the quest to find similarity neural nets can conceivably be used
in several ways
(a) by comparing matrices of factors
(b) by determining weights to be given to factors that are used in
other systems.
(c) by identifying new factors that are common to members of a group
(d) by determining similarity in a less reductionist fashion than the
above.
For present purpose, approaches (a) and (b) are essentially the same.
Both rely on matrices of factors being presented to a neural net. Although
a neural net can classify patterns, deal with complex relationships and
subtle variations in factors, and so determine similarity by determining
how many attributes are shared, a key aspect of the finding of similarity
has already been performed by the designer. The designer of the system
has already made the all important decisions as to what limited factors
are to be considered relevant for a determination of similarity and further
at what level of generality they are to be compared.
In this scenario Tito's requirements mean that the computer can only
find similarity at the level of attribute matching, more subtle aspects
of similarity are outside the computer's scope. For this reason systems
such as PROLEXS that adopt the matrix approach will only ever have limited
ability to reason analogically.However, if a matrix can be chosen that
can accurately model a real world concept [120]
then that matrix can be implemented in a neural net. This
is a corollary of Kolmogorov's theorem. [121]
A key requirement in this approach is choosing the matrix
used to represent the concept, but what factors are to be included ? Neural
nets could also conceivably be used to identify new factors that are common
to a group. Bench-Capon shows how neural nets can find which factors are
significant amongst noise [122]
but claims that the significance of these factors cannot be
understood without independent knowledge of the domain. [123]
To say that the significance of such factors cannot be understood
without prior domain knowledge though is not to say that the newly identified
factors are not significant. According to some members of the critical
legal studies movement, the reasons given in cases are not the whole reasons
for the reaching of the results in those cases. [124]
If this view of law is correct then legal analysis and legal
expert systems based solely on those decisions will not accurately reflect
how and why cases are decided. Instead one should simply look at what actually
occurs. Thus when an analysis of a neural net highlights the importance
of an unsuspected factor this could be interpreted as telling us something
important about the underlying legal domain. Consequently, the use made
of noise is dependent on the jurisprudential theory that the system's developers
adopt; whether it is interpreted as a discovery about the law or is rejected
as a technical anomaly.The most promising approach to modelling similarities
is the less reductionist approach taken by SCALIR. [125]
Here similarity is not judged solely on the presence or absence
of specified factors, but also on the presence of sub-factor information.
Thus even though two input matrices may share few factors at the conceptual
level they can still be regarded as similar if they directly or indirectly
share common 'micro-features'. In this respect SCALIR contains a closer
approximation to employing the analogue meaning of words than do other
systems. However, before SCALIR type similarity determination can be implemented
in a legal expert system, rather than solely a document retrieval system,
the systems developers will have to choose how indirect a sharing of common
micro-features will amount to two objects being regarded as similar. This
is equivalent to choosing at what level of generality the two objects are
to be considered. Further, the approach adopted in SCALIR is still dependent
on the system's designers choosing what concepts are to be used to model
the legal domain. Thus within Tito's framework it is still not possible
to say the system implements moral decision making. However in incorporating
a closer approximation to the analogue meaning of words, the method to
determine similarity adopted in SCALIR is more subtle than those in other
neural net systems or that exist in symbolic reasoning systems.It cannot
be doubted then that neural nets can mimic the finding of similarity, though
on a restricted basis. However, the accuracy of the similarity found will
depend greatly on the composition of the matrix chosen by developers to
describe the legal concepts.
Open texture.
Two observations about the use of neural nets to resolve open texture
can now be made. Since the similarity found by neural nets is crude compared
to that achieved by humans there is much scope for real world decisions
to differ from those reached by neural nets; because unconsidered factors
will have been taken into account. [126]
Secondly, legal analogical reasoning is not simply the finding
of similarity between cases but involves manipulating the analogy found
to achieve a desired result. [127]
This is something that neural nets of themselves cannot perform.
Consequently, by themselves neural nets have a limited ability to perform
analogical reasoning. The ability of neural net systems to generalise input
patterns and to perform a flexible form of similarity determination however,
makes them strong candidates for use in a hybrid analogical reasoning system
Similarity cannot be thought of as an agent independent of the objects which are to be found similar; it may be said that it is more in the nature of a relation which the mind perceives after the fact. [128]
Since similarity does not exist independently of our perception of it,
creating this perception is of crucial importance. Unfortunately this presents
problems for neural nets. Presently neural nets take a series of inputs
and oracularly produce an output; it is left to the user of the system
to infer why similarity was found.
Creating such a perception involves two things, explaining why the
similarity was found and then justifying the finding. Several methods have
been proposed to get explanations and justifications from neural nets,
four of which are
(1) extract rules from the neural net; [129]
(2) present to the user those nodes (factors) that had a positive contributory
influence along with those that had a negative contributory influence on
the decision; [130]
(3) present the training set of the neural net to the user; [131]
and
(4) create a hybrid system where the output of the neural net is explained
ex post facto by other systems. [132]
The essential purpose of providing explanation and justification is
always to convince the human end user of the correctness of the result
achieved and in this respect the intended audience and use of the system
must always be remembered. [133]
Gallant has given a detailed analysis of how rules can be extracted
from neural nets, [134]
though as Bench-Capon notes, we cannot be sure of the correctness
of any rules derived from a neural net unless we have prior knowledge about
the domain itself. [135]
However, while rules may provide an explanation of a result
it is hard to regard them as a justification. If a domain expert was asked
'How did you reach that conclusion ?' a first answer might be 'It just
came to me'. Pressed further, the new response might be 'Factors X, Y and
Z were present and this points to that result'. A neural net can give a
similar explanation by saying 'Factors X, Y and Z were present and this
points to the result because they achieved that result in other cases'.
The expert (or neural net) might go further and formulate this last response
with a rule such as 'Whenever factors X, Y and Z are present, then this
result was achieved.' As an explanation this seems satisfactory, it was
because of experience that the expert and neural net gave that result.
A search for more detailed explanation from a neural net if even possible, [136]
seems unnecessary.Asking why the result is justified
is different. What amounts to sufficient justification for a decision depends
on the jurisprudential theory of law that one subscribes to. If one regards
as justified, a decision based solely on the fact that such a decision
was reached in past situations, then 'if ... then ...' rules as discussed
above may be accepted as both explanation and justification; they are simply
a short-hand way of saying this. However, if one's jurisprudential theory
requires a more detailed justification then it remains an open question
whether a neural net can justify its results. Detailed justification may
be possible using other systems; although a pre-requisite is the adoption
of a jurisprudential theory on what amounts to justification.Proposals
(b) and (c) for achieving explanations and justifications from neural nets
are slightly different. In both cases it is simply left to the user to
infer why the information presented justifies the result achieved.
The PROLEXS team state that these approaches have not proved satisfactory. [137]
Proposal (d), that of justifying the output of a neural net
ex post facto has not yet been reported as implemented though theoretical
work is underway. [138]
Thus it can be seen that neural nets have a limited ability
to justify their results. Whether this poses a serious problem to the use
of neural nets in law remains to be seen.
The neurons strive for equilibrium, and when the conditions of the equilibrium are translated into the terms of the case, the resulting solution cannot be totally unjust. [140]
The equating of justice with compromise is questionable. Firstly, the
two rules that were balanced may violate principles of formal justice,
or they might offend against moral principles in which case the resulting
compromise cannot be said to be just. More fundamentally, justice does
not necessarily equate with compromise. If justice is understood as meaning
'The result that a court of law would reach.' then equating justice with
compromise is unsupportable. Courts do not always achieve a result that
is a compromise of the presented claims. [141]
The point is not that compromise is never just or that what
a court of law would do is just, only that in equating justice with compromise,
a jurisprudential statement is being made that requires support. Thus attempting
to deal with conflicting rules through the use of compromise is not a necessarily
a desirable path. It depends on one's theory of justice. [142]
Used in the manner of Philipps, neural nets can only deal with contradiction
through compromise. [143]
Thagard's ECHO [144]
has the potential to overcome this difficulty as it does not
model conflict through compromise. However, ECHO has problems of its own, [145]
not least the complexity of its representations. Since Thagard
has not given detailed discussion of the legal use of ECHO the possibility
of using this system to model conflicting legal rules remains to be explored.
The judges and other legal actors are nodes of the network; the published case reports and statutes, teaching in the law schools, continuing education courses and learning on the job, and the informal and formal oral communications among the members of the legal community are the connections between nodes; the cases and statutes themselves are the patterns presented to and learned by the network. [161]
This is a descriptive theory of law [162]
that sits between positivist and critical theories of law. The law
is not the application of objective facts but nor is it merely the preferences
of individual judges. [163]
Instead no single actor or single rule determines the outcome of
a case; the outcome emerges from the interaction of the whole system. [164]
Similarly, under this theory rules and theories of law are to be
regarded only as approximations of the underlying law, much as a neural
net constructs a mathematical function to approximate the distinctions
present in its input data. [165]
While the practical implementation of such a neural net
is far beyond current capabilities, this is not Silverman's aim. According
to Silverman
At the most general level, our metaphor of law matters.... new metaphors of law can lead to an increased awareness of alternatives for the legal system. [166]
With a new metaphor the way we think about judges, law, society, and our role therein can radically change.
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John Hobson and David Slee, 'Indexing the Theft Act 1968 for Case Based Reasoning [CBR] and Artificial Neural Networks [ANNs]' in Proceedings of the Fourth National Conference on Law, Computers and Artificial Intelligence (1994) unnumbered additions.
Alan Hunt, 'The Big Fear: Law Confronts Postmodernism.' (1990) 35 McGill Law Journal 507.
Daniel Hunter, Alan Tyree and John Zeleznikow, 'There is less to this argument than meets the eye.' (1993) 4 Journal of Law and Information Science 46.
Jorgen Karpf, 'Inductive Modelling in Law: Example Based Expert Systems in Administrative Law' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 297.
Duncan Kennedy, 'Freedom and Constraint in Adjudication: A Critical Phenomenology' (1986) 36 Journal of Legal Education 518.
Raymond Kurzweil, The Age of Intelligent Machines (1990).
Kenneth Lambert and Mark Grunewald, 'Legal Theory and Case-Based Reasoners: The Importance of Context and the Process of Focusing.' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 191.
Edward Levi, An Introduction to Legal Reasoning (1948).Lloyd of Hampstead, Lloyd's Introduction to Jurisprudence (1985).
Neil MacCormick, Legal Reasoning and Legal Theory (1978).
V Mital and L Johnson, Advanced Information Systems for Lawyers (1992).
Robert Moles, 'Logic Programming - An Assessment of its potential for Artificial Intelligence Applications in Law' (1991) 2 Journal of Law and Information Science 137.
Robert Moles and Surendra Dayal, 'There is more to life than logic' (1993) 3 Journal of Law and Information Science 188.
James Murray, 'The Role of Analogy in Legal Reasoning' (1982) 29 University of California Law Review 833.
Lothar Philipps, 'Distribution of Damages in Car Accidents Through the Use of Neural Networks' (1991) 13 Cardozo Law Review 987.
Daniel Rose and Richard Belew, 'A connectionist and symbolic hybrid for improving legal research.' (1991) 35 International Journal of Man-Machine Studies 1.
Daniel Rose and Richard Belew, 'Legal Information Retrieval: A Hybrid Approach' in Proceedings of the Second International Conference on Artificial Intelligence and Law (1989) 138.
David Rumelhart, James McClelland and the PDP Research Group, Parallel Distributed Processing: Explorations in the Microstructure of Cognition (1986).
M Sergot, F Sadri, R Kowalski, F Kriwaczek, P Hammond and T Cory, 'The British Nationality Act as a Logic Program' (1986) 29 Communications of the ACM 370.
Alexander Silverman, Mind, Machine, and Metaphor: An Essay on Artificial Intelligence and Legal Reasoning (1993).
Joseph Singer, 'The Player and the Cards: Nihilism and Legal Theory' (1985) 94 The Yale Law Journal 1.
John Stick, 'Can Nihilism be Pragmatic ?' (1987) 100 Harvard Law Review 332.
Julius Stone, Legal System and Lawyer's Reasonings (1964).
Cass Sunstein, 'On Analogical Reasoning' (1993) 106 Harvard Law Review 741.
Richard Susskind, 'Expert Systems in Law: A Jurisprudential Approach to Artificial Intelligence and Legal Reasoning' (1986) 49 The Modern Law Review 168.
Paul Thagard, 'Connectionism and Legal Inference' (1991) 13 Cardozo Law Review 1001.
Paul Thagard, 'Explanatory coherence' (1989) 12 Behavioural and Brain Sciences 435.
Celeste Tito, 'Artificial Intelligence: Can Computers Understand Why Two Legal Cases Are Similar ?' (1987) 7 Computer/Law Journal 409.
Alan Tyree, Expert Systems in Law (1989).
G van Opdorp, R Walker, J Schrickx, C Groendijk and P van den Berg, 'Networks at Work: a connectionist approach to non-deductive legal reasoning' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 278.
R Walker, A Oskamp, J Schrickx, G Van Opdorp and P van den Berg, 'PROLEXS:
creating law and order in a heterogenous domain' 35 (1991) International
Journal of Man-Machines Studies 35.
David Warner, 'A Neural Network Based Law Machine: Initial Steps' (1992)
18 Rutgers Computer and Technology Law Journal 51.
David Warner, 'A Neural Network-based Law Machine: the problem of legitimacy.' (1993) 2(2) Law Computers & Artificial Intelligence 135.
David Warner, 'The Role of Neural Networks in the Law Machine Development' (1990) 16 Rutgers Computer and Technology Law Journal 129.
David Warner, 'Toward a Simple Law Machine' (1989) 29 Jurimetrics 451.
John Zeleznikow and Daniel Hunter, Building Intelligent Legal Information Systems - Representation and Reasoning in Law (1994).
John Zeleznikow and Daniel Hunter, 'Rationales for the Continued Development of Legal Expert Systems' (1992) 3 Journal of Law and Information Science 94.
John Zeleznikow, George Vossos and Daniel Hunter, 'The IKBALS Project: Multi-Modal Reasoning in Legal Knowledge Based Systems' (1993) 2 Artificial Intelligence and Law 169.
[Note 2] See John Zeleznikow and Daniel Hunter, Building Intelligent Legal Information Systems - Representation and Reasoning in Law (1994) ch 6 for an introduction to symbolic reasoning using rules and logic.
[Note 3] Kurzweil, above n 1.
[Note 4] A 'domain expert' is an expert in the domain in which the expert system is sought to be constructed. A knowledge engineer is someone who works with the domain expert to collect that experts knowledge and assemble it for use in the legal expert system: Kurzweil, above n 1.
[Note 5] Refer generally to Maureen Caudill and Charles Butler, Naturally Intelligent Systems (1990). For a detailed discussion of neural-net concepts and theory see David Rumelhart, James McClelland and the PDP Research Group, Parallel Distributed Processing: Explorations in the Microstructure of Cognition (1986). For a 'hands on' introduction the computer package of Maureen Caudill and Charles Butler, Understanding Neural Networks: Computer Explorations (1992) is useful.
[Note 6] Caudill and Butler, 'Naturally intelligent systems', above n 5, ch 1.
[Note
7] The classic example of
the problem of linear separability is the XOR problem: ibid 173-4. In the
graph below, it is not possible to draw a single straight line that separates
all the O's and all the X's, thus they are not linearly separable.
[Note 8] See the discussion of Kolmogorov's theorem: ibid 174-7.
[Note 9] 'Back-propagation' is a technique whereby the error made by a neural net in classifying a pattern can be progressively reduced, so that it reaches an 'acceptable' level: ibid ch 14.
[Note 10] Supervised learning is a procedure for training a neural net in which the neural net is presented with an input pattern and the output that is desired when that pattern is presented to the neural net. The neural net learns to associate the input pattern with the output pattern. The learning is 'supervised' because the creator of the neural net must present the two patterns to the network and also oversee that learning is occurring correctly. An obvious requirement of such training is that for every input pattern there must be a known output pattern; this is impossible in some environments, including some legal applications: ibid.
[Note 11] In this paper, 'lawyer' is used widely to refer to those who are involved in reasoning with and applying the law. Thus it would include judges, solicitors, barristers and legal academics, see Zeleznikow and Hunter, above n 2, ch 2.
[Note 12] Eg Paul Edwards (ed), The Encyclopedia of Philosophy (1967).
[Note 13] Neil MacCormick, Legal Reasoning and Legal Theory (1978) 21-4.
[Note 14] Martin Golding, Legal Reasoning (1984) 43-4. It is always possible that a factual situation will arise which has an outcome different to that previously observed, thus invalidating the rule founded on the earlier situations.
[Note 15] James Murray, 'The Role of Analogy in Legal Reasoning' (1982) 29 University of California Law Review 833, 849.
[Note 16] Golding, above n 14, 44 states that induction is simply another form of analogy. While they are closely related there is a difference between analogy and induction, outlined below.
[Note 17] MacCormick, above n 13, 163.
[Note 18] MacCormick, above n 13, 229.
[Note 19] MacCormick, above n 13; Zeleznikow and Hunter, above n 2, ch 4 pp 9-16. The first of these views is an extreme version of the legal positivism of H.L.A. Hart, The Concept of Law (1961). The second view is an extreme version of the arguments presented by the American legal realists and members of the critical legal studies and post modernist movements eg Margaret Davies, Asking the Law Question (1994); Alan Hunt, 'The Big Fear: Law Confronts Postmodernism.' (1990) 35 McGill Law Journal 507.
[Note 20] MacCormick, above n 13, 197. However, see Joseph Singer, 'The Player and the Cards: Nihilism and Legal Theory' (1985) 94 The Yale Law Journal 1 and the reply John Stick, 'Can Nihilism be Pragmatic ?' (1987) 100 Harvard Law Review 332.
[Note 21] Edward Levi, An Introduction to Legal Reasoning (1948) 1. Steven Burton, An Introduction to Law and Legal Reasoning (1985) 26-39 gives a similar taxonomy. Levi's view has been criticised by Murray, above n 15, 848-50; however for present purposes this criticism is not important.
[Note 22] MacCormick, above n 13, ch. 5 et seq; Burton, above n 21, 103.
[Note 23] MacCormick, above n 13, 103.
[Note 24] MacCormick, above n 13, ch. 5, ch. 7; Duncan Kennedy, 'Freedom and Constraint in Adjudication: A Critical Phenomenology' (1986) 36 Journal of Legal Education 518
[Note 25] MacCormick, above n 13, ch 2; Burton, above n 21; Julius Stone, Legal System and Lawyer's Reasonings (1964) chs 6,7; Cf Lloyd of Hampstead, Lloyd's Introduction to Jurisprudence (1985) 1139 footnote 95 for a list of authorities who deny deduction plays a role in legal reasoning.
[Note 26] MacCormick, above n 13, 19.
[Note 27] Burton, above n 21, 44-50; Stone, above n 25, 55-8.
[Note 28] Levi, above n 21, 2. Similarly Lloyd notes that it has 'long been accepted that a case only binds as to "like facts". But what are like facts ...' Lloyd, above n 25, 1116. While given as a discussion of 'rules' in the common law, this is equally applicable to statutory rules.
[Note 29] MacCormick, above n 13, 66.
[Note 30] MacCormick, above n 13; Levi, above n 21; Burton, above n 21.
[Note 31] Rupert Cross and J Harris, Precedent in English Law (1991).
[Note 32] MacCormick, above n 13, 219-24; Stone, above n 25, 267-74. Indeed Stone regards the multitude of ratios that exist in a decision as requiring extreme scepticism about the ability of computers ever to reason with cases, ibid 37-8; Cf Cross, above n 31.
[Note 33] This results from the need for reality and coherence in the legal system, MacCormick, above n 13, ch. 7.
[Note 34] MacCormick, above n 13, 216-8.
[Note 35] In truth though, common law rules only serve to hide the cases underlying the supposed rule and to mask the reaching of a decision by analogy. Burton, above n 21, 60; Levi, above n 21, 8-9.
[Note 36] Cross, above n 31, 191-2; Levi states that thinking of case-law reasoning as inductive is erroneous. However, he agrees that case law concepts can be created out of particular instances, since there is movement from the particular to the general: Levi, above n 21, 27.
[Note 37] MacCormick, above n 13, ch. 7.
[Note 38] MacCormick, above n 13; Levi, above n 21; Burton, above n 21; Stone, above n 25; Murray, above n 15; James Gordley, 'Legal Reasoning: An Introduction' (1984) 72 California Law Review 139; Cass Sunstein, 'On Analogical Reasoning' (1993) 106 Harvard Law Review 741.
[Note 39] Eg Stone, above n 25, 283.
[Note 40] Steven Burton, 'Reaffirming Legal Reasoning: The Challenge from the Left' (1986) 36 Journal of Legal Education 358; Cf Singer, above n 20 with Stick, above n 20.
[Note 41] K Hamilton, 'Prolegomenon to Myth and Fiction in Legal Reasoning, Common Law Adjudication and Critical Legal Studies' (1989) 35 The Wayne Law Review 1449.
[Note 42] An 'inference engine' is a part of an expert system that is 'a system for applying the rules [of the system's database] to the knowledge base to make decisions.': Kurzweil, above n 1, 293.
[Note 43] Stephen Gallant, Neural network learning and expert systems (1993) ch 14.
[Note 44] This definition is adapted from that provided in Zeleznikow and Hunter, above n 2, ch 5. The authors note that the actual task that a legal expert system will perform varies markedly according to its intended user.
[Note 45] Eg, Kenneth Lambert and Mark Grunewald, 'Legal Theory and Case-Based Reasoners: The Importance of Context and the Process of Focusing.' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 191.
[Note 46] Case based reasoners are expert systems that try to reason using a corpus of cases rather than explicit rules: Zeleznikow and Hunter, above n 2, ch 8.
[Note 47] John Zeleznikow, George Vossos and Daniel Hunter, 'The IKBALS Project: Multi-Modal Reasoning in Legal Knowledge Based Systems' (1993) 2 Artificial Intelligence and Law 169, 171-2.
[Note 48] For example, if the database contained the two rules 'As between two innocents he who caused the damage should pay' and 'No liability without fault' it is unclear how these rules are both to be applied in a no-fault accident. The resolution of this conflict must be resolved by reference to other tests.
[Note 49] Davies, above, n 19, ch 7 demonstrates how both Hart's concept of a 'rule of recognition' and Kelsen's concept of a 'grundnorm' would necessarily import 'extra-legal' assumptions into the legal system.
[Note 50] Refer to ch 2 for a discussion of this problem in symbolic reasoners.
[Note 51] David Warner, 'A Neural Network Based Law Machine: Initial Steps' (1992) 18 Rutgers Computer and Technology Law Journal 51, 51-4; David Warner, 'The Role of Neural Networks in the Law Machine Development' (1990) 16 Rutgers Computer and Technology Law Journal 129, 139.
[Note 52] All neural nets operate as some form of pattern classifier. They learn to associate certain general input patterns with certain general output patterns, see ch 2 of this paper.
[Note 53] John Hobson and David Slee, 'Indexing the Theft Act 1968 for Case Based Reasoning [CBR] and Artificial Neural Networks [ANNs]' in Proceedings of the Fourth National Conference on Law, Computers and Artificial Intelligence (1994) unnumbered additions.
[Note 54] Success in this respect must be understood to mean performing a classification, according to the index points chosen by the creators, which is the same as that which the creators would arrive at using those same index points.
[Note 55] Trevor Bench-Capon, 'Neural Networks and Open Texture' Proceedings of the Fourth International Conference on Artificial Intelligence and Law (1993) 292.
[Note 56] G van Opdorp, R Walker, J Schrickx, C Groendijk and P van den Berg, 'Networks at Work: a connectionist approach to non-deductive legal reasoning' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 278.
[Note 57] Bench-Capon, above n 55, 296 While the ability of a neural net to classify patterns even in the presence of noise is notable, as will be discussed in the next chapter, defining input as 'noise' is dependent on a pre-existing theory of the domain. This may be problematic.
[Note 58] R Walker, A Oskamp, J Schrickx, G Van Opdorp and P van den Berg, 'PROLEXS: creating law and order in a heterogenous domain' 35 (1991) International Journal of Man-Machines Studies 35; van Opdorp, above n 56.
[Note 59] Walker, above n 58, 55-6.
[Note 60] Ibid 56.
[Note 61] Ibid 56-7; van Opdorp, above n 56, 280-1.
[Note 62] van Opdorp, above n 56, 281-4.
[Note 63] Ibid 280-1.
[Note 64] Bench-Capon, above n 55, 297.
[Note 65] M Sergot, F Sadri, R Kowalski, F Kriwaczek, P Hammond and T Cory, 'The British Nationality Act as a Logic Program' (1986) 29 Communications of the ACM 370.
[Note 66] Refer to the debate conducted in the following articles Robert Moles, 'Logic Programming - An Assessment of its potential for Artificial Intelligence Applications in Law' (1991) 2 Journal of Law and Information Science 137; John Zeleznikow and Daniel Hunter, 'Rationales for the Continued Development of Legal Expert Systems' (1992) 3 Journal of Law and Information Science 94; Robert Moles and Surendra Dayal, 'There is more to life than logic' (1993) 3 Journal of Law and Information Science 188; Daniel Hunter, Alan Tyree and John Zeleznikow, 'There is less to this argument than meets the eye.' (1993) 4 Journal of Law and Information Science 46.
[Note 67] It is unclear what use Hobson and Slee intend for their 'index'. If it is truly meant to be used as an index of cases then their treatment of open textured issues is less questionable than if they intend it to be used within a legal expert system.
[Note 68] David Warner, 'The Role of Neural Networks in the Law Machine Development' (1990) 16 Rutgers Computer and Technology Law Journal 129, 135-38. The claim that neural nets can inherently model the process of legal reasoning will be critically discussed in the next chapter.
[Note 69] Lothar Philipps, 'Distribution of Damages in Car Accidents Through the Use of Neural Networks' (1991) 13 Cardozo Law Review 987.
[Note 70] Philipps, above n 69, 989-91, 999.
[Note 71] Paul Thagard, 'Explanatory coherence' (1989) 12 Behavioural and Brain Sciences 435; Paul Thagard, 'Connectionism and Legal Inference' (1991) 13 Cardozo Law Review 1001. On creating inference networks generally using neural nets, see Gallant, above n 43, chs 14, 15.
[Note 72] Though the system could logically be used to resolve conflicts between single rules.
[Note 73] ECHO requires competing hypothesis to be given to the system, along with evidence, details of how each hypothesis explains the evidence and details of how the propositions are contradicted by the evidence. ECHO then determines which hypothesis best coheres with the evidence Thagard, 'Explanatory coherence', above n 71.
[Note 74] Interestingly Stick, above n 20, 363 notes that many contemporary theories of law are based upon coherence theories of truth. Thagard's ECHO could be useful in investigating such theories.
[Note 75] Richard Susskind, 'Expert Systems in Law: A Jurisprudential Approach to Artificial Intelligence and Legal Reasoning' (1986) 49 The Modern Law Review 168, 184.
[Note 76] Robert Birmingham 'A Study After Cardozo: De Cicco v Schweizer, Noncooperative Games, and Neural Computing' (1992) 47 University of Miami Law Review 121 discusses this. A re-rationalisation of a case occurs when a later case rationalises the decision in an earlier case on grounds that are different from those stated in the judgement of the earlier case.
[Note 77] This will be discussed further in ch 5 of this paper.
[Note 78] For example Bench-Capon, above n 55; van Opdorp et al, above n 56; Gallant, above n 43. This will be critically discussed in the following chapter.
[Note 79] Laurent Bochereau, Daniele Bourcier and Paul Bourgine, 'Extracting Legal Knowledge by Means of a Multilayer Neural Network Application to Municipal Jurisprudence' in Proceedings of the Third International Conference on Artificial Intelligence and Law 288. Similar work has been undertaken by Bench-Capon, above n 55, 296. For a detailed discussion of the extraction of rules from neural nets generally, see Gallant, above n 43, ch 17.
[Note 80] Zeleznikow and Hunter, above n 2, ch 11, p 20.
[Note 81] This will be discussed in ch 5.
[Note 82] For a comprehensive discussion of legal information retrieval systems and methods and their associated limitations see Zeleznikow and Hunter, above n 2, ch 3.
[Note 83] For example, if a document is indexed on the term 'solicitor' then searching for 'lawyer' will not retrieve it, even though it may be relevant. While this problem can be reduced using a search on all synonyms this does not guarantee all relevant documents will be retrieved: ibid.
[Note 84] Daniel Rose and Richard Belew, 'Legal Information Retrieval: A Hybrid Approach' in Proceedings of the Second International Conference on Artificial Intelligence and Law (1989) 138; Daniel Rose and Richard Belew, 'A connectionist and symbolic hybrid for improving legal research.' (1991) 35 International Journal of Man-Machine Studies 1.
[Note 85] For a discussion of semantic networks and knowledge representation generally see Zeleznikow and Hunter, above n 2, ch 7.
[Note 86] Rose and Belew, 'Legal Information Retrieval', above n 84, 141.
[Note 87] Rose and Belew, 'A connectionist and symbolic hybrid', above n 84, 20-2.
[Note 88] Ibid 22.
[Note 89] Ibid 29-30.
[Note 90] Susskind, above n 75.
[Note 91] David Warner, 'Toward a Simple Law Machine' (1989) 29 Jurimetrics 451; David Warner, 'A Neural Network Based Law Machine: Initial Steps' (1992) 18 Rutgers Computer and Technology Law Journal 51; Warner, 'The role of neural networks', above n 68.
[Note 92] Warner, 'Toward a Simple Law Machine', above n 91, Part 5; Warner, 'The role of neural networks', above n 68, 131-2.
[Note 93] Warner, 'A neural network based law machine', above n 91, 53.
[Note 94] Ibid 53-4.
[Note 95] Warner, 'The role of neural networks', above n 68, 132.
[Note 96] See Zeleznikow and Hunter, above n 2, ch 6; Alan Tyree, Expert Systems in Law (1989) for a discussion of representing laws using logic and tree diagrams.
[Note 97] Walker et al, above n 58.
[Note 98] Bench-Capon, above n 55.
[Note 99] Warner, 'The role of neural networks', above n 68, 138-9.
[Note 100] Ibid 139.
[Note 101] Anne Gardner, An Artificial Intelligence Approach to Legal Reasoning (1987).
[Note 102] Warner, 'The role of neural networks', above n 68, 139.
[Note 103] Heuristics are 'rules of thumb' used by experts in a field Gardner, above n 101, 41-3.
[Note 104] Warner, 'The role of neural networks', above n 68, 139.
[Note 105] Ibid 139.
[Note 106] Kennedy, above n 24; Jorgen Karpf, 'Inductive Modelling in Law: Example Based Expert Systems in Administrative Law' in Proceedings of the Third International Conference on Artificial Intelligence and Law (1991) 297, 300 notes that only certain combinations of factors are legal combinations.
[Note 107] Eg Kennedy, above n 24.
[Note 108] Birmingham, above n 76, 132-4.
[Note 109] MacCormick, above n 13.
[Note 110] Susskind, above n 75, 183.
[Note 111] MacCormick, above n 13; Levi, above n 21; Burton, above n 21; Gordley, above n 38; Sunstein, above n 38; Murray, above n 15; Kevin Ashley, 'Toward a Computational Theory of Arguing with Precedent' in Proceedings of the Second International Conference on Artificial Intelligence and Law (1989). However, the finding of similarity between cases is a prerequisite to any subsequent manipulations of the analogy.
[Note 112] V Mital and L Johnson, Advanced Information Systems for Lawyers (1992), 257; Celeste Tito, 'Artificial Intelligence: Can Computers Understand Why Two Legal Cases Are Similar ?' (1987) 7 Computer/Law Journal 409, 411-2 agrees with Mital and Johnson. After noting the importance of similarity Burton, above n 21, 39 simply says the process is a mystery.
[Note 113] Mital and Johnson, above n 112, 257. The authors note that this has been criticised because it would mean that people would not be able to say why or in what aspects two cases are similar; which seems unrealistic.
[Note 114] Ibid.
[Note 115] Ibid.
[Note 116] Tito, above n 112. The need for a moral theory is echoed by MacCormick, above n 13, chs 5, 7 who argues that the finding of an analogy is dependent on our view of what purpose the legal system is trying to achieve. Sunstein, above n 38, 773-81 at footnote 116, also notes the need for a general theory with which to evaluate similarities and thinks this should cause scepticism about efforts to program computers to engage in analogical reasoning.
[Note 117] Tito, above n 112.
[Note 118] For a concise discussion on this issue see the debate between John Searle, and Paul Churchland and Patricia Churchland in 'Artificial Intelligence a Debate' (1990) 262(1) Scientific American 19. The discussion of neural nets is particularly interesting.
[Note 119] Karpf, above n 106, 299.
[Note 120] Accurately is here being taken to mean : model to a degree of richness that is sufficient to satisfy lawyers.
[Note 121] See ch 2 for discussion of this theorem.
[Note 122] Bench-Capon, above n 55.
[Note 123] Ibid 296-7.
[Note 124] Kennedy, above n 24.
[Note 125] Refer to ch 4 for a discussion of the operation of SCALIR.
[Note 126] Walker et al, above n 58, 63; Birmingham, above n 76,132-4.
[Note 127] Levi, above n 21; MacCormick, above n 13; Burton, above n 21; Gordley, above n 38; Sunstein, above n 38; Murray, above n 15; Ashley, above n 111.
[Note 128] Mital and Johnson, above n 112, 256.
[Note 129] Bochereau et al, above n 79; A modification of this approach is presented in David Warner, 'A Neural Network-based Law Machine: the problem of legitimacy.' (1993) 2(2) Law Computers & Artificial Intelligence 135, 141. The difference between the two approaches essentially concerns when the rules are to be generated. Bochereau sees neural nets as being used specifically to extract rules while Warner argues that rules will be extracted at run time in response to questioning. It is possible that the latter approach would provide more flexibility.
[Note 130] van Opdorp et al, above n 56, 285. Warner, 'A neural network based law machine: the problem of legitimacy', above n 129, 139. The difference between the two approaches is that in the latter the percentages of the input variables that can be attributed to the output variable is also determined.
[Note 131] van Opdorp et al, above n 56, 285
[Note 132] Ibid 285
[Note 133] Lambert and Grunewald, above n 45; Zeleznikow and Hunter, above n 2, ch 2.
[Note 134] Gallant, above n 43, ch 17.
[Note 135] Bench-Capon, above n 55, 296.
[Note 136] The search for complete explanations may be pointless as there are aspects of human action that humans cannot themselves explain: Daniel Dennett, Consciousness Explained (1991) 84-95 gives a good discussion of this.
[Note 137] van Opdorp, above n 56, 285.
[Note 138] See the discussion on the SPLIT-UP system in Zeleznikow and Hunter, above n 2, ch 11 p 20 and the associated references.
[Note 139] Zeleznikow and Hunter, above n 2, ch 11 p.20.
[Note 140] Philipps, above n 69, 999.
[Note 141] For example in R v Watson; Ex parte Armstrong (1976) CLR 249, the High Court was faced with conflicting lines of authority as to what amounted to judicial bias. In the result, one line of authority was totally rejected.
[Note 142] Mital and Johnson, above n 112, 259. However, Mital and Johnson indicate that a conflict between the interpretation of factors within a case may be solved by the use of compromise.
[Note 143] The practical implications of this will be discussed later.
[Note 144] Discussed in ch 4.
[Note 145] ECHO requires competing hypothesis to be entered into the neural net along with their supporting facts. How each hypothesis is supported by evidence and what evidence contradicts what hypothesis then has to be entered by the system designer. Such decisions can be highly subjective and it is unclear what implications these requirements could have on the use of ECHO in the legal domain.
[Note 146] Rose and Belew, 'A connectionist and symbolic hybrid', above n 84, 20-2.
[Note 147] Kennedy, above n 24.
[Note 148] Mital and Johnson, above n 112, 253.
[Note 149] Neural nets can be classified not only according to their learning rules and architectures, but also as distributed or localist networks. In distributed networks, of which adaptive filter networks are one type, only the nodes at the input and output levels represent real world concepts, hidden layers are simply there to aid in the mapping performed by the network. In localist models, each node of the network represents a real world concept.
[Note 150] Above n 118.
[Note 151] Apart from the discussion of the use of hypotheticals and compromise which follows, it should be noted that the study of neural nets is still a comparatively embryonic field. A multitude of network designs exist from which application developers can choose. Designs generally have numerous design parameters the values of which can be chosen more or less ad hoc. Both the type of network design used and the values of the parameters chosen, affect the behaviour of the neural net. How many hidden layers to include in the neural net and how many nodes to include in each of those layers, the learning rule and learning rate, the amount of noise present when the network is trained and even the order in which training examples are presented to the neural net can all affect the neural net's behaviour and the classifications it produces. Thus these factors can affect the way the neural net reasons with the information presented to it. However, the legal literature discussing neural nets does not discuss such issues; an exception being: Rose and Belew, above n 84.
[Note 152] Mital and Johnson, above n 112, 265.
[Note 153] van Opdorp et al, above n 56, 282-4.
[Note 154] Eg Karpf, above n 106; Hobson and Slee, above n 53; Walker et al, above n 58.
[Note 155] Hobson and Slee, above n 53, 12; Walker et al, above n 58, 57. In this context Bench-Capon, above n 55, also used hypotheticals to train his ANN, however this was dictated by the fact that his whole legal domain was hypothetical. This use of hypotheticals has been criticised Karpf, above n 106, 299.
[Note 156] van Opdorp, above n 56.
[Note 157] Bench-Capon, above n 55. Other researchers such as Hobson and Slee, above n 53, do not mention how their hypotheticals are generated.
[Note 158] Philipps, above n 69, 996.
[Note 159] Warner claims that this view is inherent in the works of Anthony D'Amato: Warner, 'The role of neural networks', above n 68, 138.
[Note 160] Alexander Silverman, Mind, Machine, and Metaphor: An Essay on Artificial Intelligence and Legal Reasoning (1993).
[Note 161] Ibid 80.
[Note 162] Ibid 81.
[Note 163] Ibid 80.
[Note 164] Ibid. An expanded version of this theory sees law not only as an interconnected network, but also as an interconnected network that 'resonates' with society; the law both influences and is influenced by the society in which it is constructed: ibid 84-6.
[Note 165] Ibid 81-3.
[Note 166] Ibid 94-5.