1993
	Draft of paper to appear in AI AND LAW, with J. Norman

	RATIONALES AND ARGUMENT MOVES




I.  Procedure and Rationale.

In disputation, claims are supported by arguments, which refer to
rules, cases, and evidence.  Sometimes, the rationales of rules and
the rationales for decisions in cases appear in disputation as well.

Rationales appear in procedural contexts such as debate, dialectical
inquiry, and legal argument.  In purely declarative contexts, wherein
logic usually is defined, the effect of rationales on inference is
more mysterious.

In many models of argument, arguments are produced by chaining rules
from a set of defeasible rules, L, and are grounded in a set of
undisputed premises, or evidence, E.  Case-based reasoning
supplements the set of rules by permitting rules to be formulated
from cases.  There is thus a set, C of cases, the effect of which is
to augment L, Rules(L, C) = LRulesFrom(C).

This is one framework in which to formalize legal and policy
reasoning, a framework inherited from the logicians, suitably altered
by researchers in philosophical logic and artificial intelligence.
There is considerable agreement on the way that cases augment rules,
as described in the Rissland- Ashley work [Rissland-Ashley87].

Declaratively (i.e., from a traditional logical point of view), the
interest is in the complete set of arguments that can be constructed
upon L, C, and E:  Args(L, C, E).  A conclusion must be warranted
with respect to the full complement of arguments:  if an effective
counterargument is possible, then an argument fails to warrant its
conclusion, whether anyone ever finds that counterargument.
Alchourron and Bulygin [Alchourron-Bulygin71], Soeteman [Soeteman89],
and Simari and Loui [Simari-Loui92] are examples of declarative
accounts of legal reasoning, though the former works do not
explicitly construct arguments.

Procedurally (i.e., computationally), parties to a dialogue consume
limited resources, producing a succession of sets Argsi(L, C, E),
corresponding to the various stages i=1, 2, ..., n of the dispute.
Warrant is defined with respect to a particular set of arguments at a
particular stage, Argsi(L, C, E).  The appropriate stage is
determined by a termination rule.  Sometimes it is known in advance;
sometimes it is a bound that is revealed when it is reached;
sometimes an i is appropriate merely because Argsi has a quiescence,
e.g., because one party can make no useful response.  The protocol
for inquiry may allow parties to introduce objects significant to the
dispute, other than arguments.  For example, challenges might be
allowed in the dialogue.   Rescher [Rescher77], Alexy [Alexy89], Loui
[Loui92], Vreeswijk [Vreeswijk93], and Gordon [Gordon93] are examples
of this kind of work; Skalak and Rissland [Skalak-Rissland91],
Pollock [Pollock92], Prakken [Prakken93], and can be interpreted as
this kind of work, too.

A rationale for a rule is a structure that contains relevant
information about the reason for the rule's adoption.  A rationale
for a case, similarly, is relevant additional information about the
decision reached.  Following Toulmin, one can refer to the rationale
as the "backing" of the "warrant," where Toulmin's warrants are
essentially the rules in L.  In the language of legal philosophy,
ratio decidendi and ratio legis are rationales.  Recent authors have
referred to "principle" or "purpose."  The essential question is what
are the appropriate forms of rationales and how they can be brought
to bear in argument.

There are many kinds of rationales; rules are adopted on various
grounds.  Defeasible rules can be adopted through game-theoretic or
inductive reasoning, on the whim of authority, or by arbitrary
convention.  A defeasible rule that is a policy, which might be a
rule in a legal domain, often balances competing interests.
Sometimes the particular balance struck is part of the grounds for
the rule's adoption.  Sometimes the rule strikes a balance in a
principled way, but as often it has the right politic or expedience.
Sometimes the grounds for adopting a policy are decision-theoretic.
Decisions in precedent-setting cases can be made on similar grounds.

The rationales for rules and cases considered here constitute a
subset of those that can be imagined.  They might generally be
classified as compilation rationales.  These rationales might be
described fully within the vocabulary of a system of argument.
Excluded, for instance, are decision-theoretic rationales, which
require the introduction of additional information representing
utilities.  The present aim is to discuss how dialectical moves force
reversion to the forms from which rules were compiled, and how the
the model might thereby be made more comprehensive, how the
repertoire of formally modeled moves might be increased.

Rationales resulting from compilation are compilation rationales.
The compilation rationales to be discussed are as follows.  For
rules:  adopt a rule because it compresses a line of reasoning
(compression, or c-rationale); adopt a rule because it specializes a
general principle (specialization, or s-rationale); adopt a rule
because it expresses a regularity that fits a set of cases (fit, or
f- rationale).  For cases: form an opinion despite competing factors
by resolving the competition (resolution, or r-rationale); form an
opinion because the set of arguments in the recorded disputation of
the case, which may be incomplete, warrants the opinion (disputation,
or d- rationale).

To attack a well-formed argument, with rationales unmentioned, there
are already a couple of alternatives.  Attack some subpart of the
argument or provide a separate argument for a contrary conclusion.
If the protocol allows meta-argument, attack the sufficiency of the
argument at the present point in the dialogue.  Attack the legitimacy
of the move at the point at which it occurs.  That is, show that it
does not meet the player's burdens, or provide reasons for claiming
that it does not defeat the argument that it is said to defeat, or
otherwise impugn its place or station.  There is yet another class of
moves:  moves that make use of rationales.

Attack a rule used in the argument by citing its rationale and
claiming that the rule's scope is exceeded in this application.  Or
attack a rule that derives from a case, a case-based argument, by
citing the rationale for the decision in the case and arguing that
the decision is flawed.  A new argument that should have been
considered has been discovered.  Or argue that the decision provides
no guidance in the current situation.  An argument that can now be
made, in the current situation, would have effectively countered the
argument that led to the decision in the case. Or argue that a rule
is a particular form of a more general rule, or a modern restatement
of an older rule, a derivation from broader principle, or a version
of a separate rule; then restate the rule in its original form; then
attack the new rule, the strength of which has now been altered under
considerations of lex specialis, lex posterior, or lex superior.

The purpose of this paper is to sketch a formal account of what data
would be required to make such moves, and how those moves affect the
state of a disputation.

II.  Informal Examples of Compilation Rationales.

First, consider each of the rationales in simple quasi-legal
examples.

1.  compression, or c-rationale:

As a defeasible rule, "vehicles used for private transportation are
not allowed in the park." Meanwhile, defeasibly, "vehicles are
normally for private transportation."  There is therefore the
two-step argument, for disallowing vehicles in the park.  Adopt the
policy, with the rationale of compression, that as a rule, "no
vehicles in the park."

To attack an argument using a rule with a c-rationale, restate the
argument in an uncompressed form.  The resulting uncompressed
argument will be more susceptible to attack.  Uncompressed arguments
present more points to counterattack.  They are also not as direct,
so they are more easily defeated in some syntactic accounts of defeat
among arguments.

Attack by arguing that emergency vehicles are not used for private
transportation.  This does not affect the argument using the
compressed rule, but it devastates the uncompressed argument.

Compression tends not to be fragile because rules are typically
compressed when the argument being compressed is resistant to
counterargument.  It would be folly to compress long arguments, for
instance, into one-step rules.  Arguments constructed thereupon would
always be challenged because so many challenges of the uncompressed
form will be possible.

2.  specialization, or s-rationale:

As a principle, "tranquil public spaces should be preserved."  "Parks
are tranquil public spaces." "Disallowing vehicles in a space is a
kind of preserving tranquillity."  There is currently an argument for
a particular park, defeasibly, that it is a public space, and
defeasibly, that it should be undisturbed.  There is currently no
argument that such a park should have vehicles disallowed from being
in it.  There may be other ways to preserve.  The problem is that so
far, the contrapositive of the third rule is missing:  "In order to
preserve a tranquil space, disallow vehicles."  But the principle is
entreating in such a way that a policy-maker might still adopt as a
rule, "no vehicles in the park."

Usually, such a rule is adopted in the presence of counterarguments.
For instance, "barring vehicles increases commuting effort."  In such
instances, the rationale for the rule is more advanced.  It is a
balance of competing interests, which might actually be an
f-rationale, d- rationale, or r-rationale.  The s-rationale here is
more naive.  One way to preserve is to disallow vehicles; one way of
meeting the demands of an imperative is to implement in a particular
way.  Disallowing vehicles implements a kind of preservation. This
kind of reasoning could be subtle.  Here, a simpler approach is
taken.  There are often hidden assumptions or background rules.  The
missing contraposition might be implicit:  "defeasibly, preservation
entails disallowing vehicles."

Attack, again, by restating the argument so that the rule in question
has its antecedent expressed more generally:  "insofar as public
spaces should be preserved, no vehicles allowed in public spaces."  A
counterargument based on a rule, "vehicles are allowed on public
roads in public spaces," will now suffice as a reply (assuming that
the vehicle in question can be argued to have been on a public
road).  Prior to citing the rationale, such a counterargument might
be ineffective because it is less specific:  it refers to public
spaces, not to parks.  Formally, this will be equivalent to attacks
on c-rationales, except that there is usually a dominant rule or
principle in the argument that is compressed.

Attack, too, by identifying a different way of meeting the demands of
the guiding rule, by suggesting a different implementation.  This
attack corresponds to attacking a rule adopted without full
consideration of counterarguments.  It will be formally equivalent to
attacks using r- or d- rationales.

Since principles can be implemented in numerous ways, rules based on
s-rationales are fragile.  They eventually will be challenged and
replaced with rules or cases with based on f-, d-, or r- rationales.

3.  fit, or f-rationale:

Adopt a rule because it expresses a regularity among cases.  Cases
can be actual or hypothetical, but there should be widespread
agreement over the way they are decided.

Rule-adoption based on f-rationale is related to theory-formation in
scientific reasoning.  As in scientific theory-formation, coherence
and simplicity are important.  Unlike scientific theory- formation,
errors of fit are not tolerable.  Though errors are not tolerated,
there is a way to eliminate errors of legal fit that is not available
to scientific theorizing.  Errors of legal fit can be eliminated
without altering the offending legal rule.  A more specific legal
rule that deals with exceptions can simply be added to the body of
rules.  This option is not possible for scientific theory.

The policy "no vehicles in the park" might allegedly fit the cases:

(case1) disallowed:  a private automobile driving through the park;

(case2) disallowed:  an antique automobile parked in the park;

(case3) disallowed:  a golf cart driven into the park;

(case4) allowed:  a pedestrian strolling in the park.

An argument using a rule with f-rationale can be attacked by first
proposing a new rule that also successfully distinguishes the
recorded cases of allowed parking from cases of disallowed parking.
Then the attack continues by (a) noting that the new rule no longer
applies to the current fact situation (or at least, that the argument
that it applies has not been given), or by (b) noting that the
reformulated rule applies but is not as specific as originally
suggested.  In the latter situation, the argument is susceptible to
attack by counterarguments that would have been considered less
specific on the earlier formulation of the rule.  Once again, the
defeat relations among arguments can be altered by citing rationale.

Reformulating rules corresponds to arguing over which theory has the
best fit.  We are unwilling at the moment to postulate the conditions
under which a "policy theory" fits better than a competing policy
theory.  Philosophy of science, similarly, still cannot articulate
conditions precisely for one scientific theory fitting better than
another.  Thus, competing formulations of policies to fit cases
merely interfere with each other; neither can defeat the other until
coherence and simplicity and other criteria of fit have been
addressed.

An argument using a rule with an f-rationale may also be attacked by
adding or deleting cases.  For example, to attack the rationale of
this rule, add a case, such as

(case5) allowed:  a vehicle delivering a tree to be planted in the
park;

or delete a case e.g., claim that (case3) is incorrectly decided.  Or
propose a different regularity consistent with the cases: "vehicles,
excluding those performing essential park or public functions, are
not allowed in the park".

Since it is easy to theorize about cases with sets of defeasible
rules that allegedly express regularity, rules with f-rationale will
be robust only if the question of fit is addressed in detail.

4.  resolution, or r-rationale:

Suppose the case of the hurried government official who detours his
automobile through the park raised two arguments that interfered with
each other without either defeating the other.  "No vehicles in the
park."  "Public officials on official business have use of public
spaces."  The decision to disallow such detours sets a precedent upon
which a variety of future arguments can be constructed.  The
rationale of the decision, of the precedent, is that it resolves the
competing factors: preservation of public space, versus availability
of public resources for government business.

To attack an argument relying on this precedent, cite the rationale.
Then claim that the current case introduces additional interests
which, when weighed, could alter the balance against the prior
decision.  For instance, suppose a subsequent case also introduces
the element of time.  In the current case, the official drove through
the park when the park was closed.  In the prior case, the time of
day was Saturday noon.  Now arguments based on time of day,
government business, and preservation of public spaces must be
weighed.

Without citing the rationale and attacking the grounds for the
precedent, an argument for allowing the new detour based on time of
day could still be made.  The argument based on time and the argument
based on vehicles in the park are of incomparable specificity.
Hence, their disagreement might force a resolution in this case.
Discount the old precedent and the new resolution must start anew,
weighing time of day and government business against the ban on
vehicles in the park.  Leave the rationale of prior decision
unmentioned, and the current case will compare time of day against an
established precedent based both on government business and the ban
on vehicles in the park.  The difference is subtle.

Because new cases almost invariably introduce significant new factors
unweighed in the earlier decision, precedents with r-rationales tend
to be fragile.  But as noted, the stakes are not high when an
r-rationale case is discounted by this kind of attack.

R-rationales are special kinds of d-rationales.  So there are other
attacks on r-rationales that are described as attacks on
d-rationales.

5.  disputation, or d-rationale:

Disputation that informs decision in a case can be easier than the
weighing of indeterminate factors.  A decision might simply be
mandated by superior argument, where the adjudicator played no major
role. Appeal to such a case in future argument is susceptible to
review of the recorded disputation of the case.  The arguments that
were persuasive in the prior case may not be persuasive in the
present case and its new context.

When the record of the disputation that led to decision can be
recalled, the decision has a d- rationale.  The use of such a
precedent depends on whether the result of disputation cannot be
significantly corrupted when the same arguments are applied again.
Sometimes there are new arguments that can be made that would change
the decision or the clarity of the decision.  A different attack on a
rule with d-rationale occurs when past disputation was incomplete.
Not all arguments that could have been advanced were advanced in the
prior disputation.

Suppose that in the case of an ambulance parked in the park while its
crew was off-duty, the parking was decided to be disallowed.  One
side argued that the ambulance was permitted to park because it was
an emergency vehicle.  The adjudicator held, on the other hand, that
despite being an emergency vehicle, parking was disallowed for
emergency vehicles that were not prepared to respond to an
emergency.  Suppose the arguments were of such a form that the case
could be decided on syntactic grounds.  Consider a subsequent case of
an off-duty ambulance that remained prepared to respond.  The
persuasiveness of the precedent depends on whether the decision's
rationale, a d-rationale, is exposed.  According to precedent,
"off-duty ambulances are not allowed in the park."  The opposition
successfully defeats this argument by recalling that an ability to
respond to emergency was crucial to the past decision.  Imagine that
the ambulance's ability to respond can be established in the present
case.  The precedent is no longer persuasive.

III.  Formal Requirements.

The behaviors of the various rationales are sufficiently different
that some complexity is required in order properly to model them.

The c- and s-rationales for rules, and the d-rationale, for cases,
are appropriately modeled by substituting less compact arguments (or
suites of arguments) for the original argument.  Disputation can then
continue after the unpacking.

The f-rationale and r-rationale require an entirely different
mechanism.  When arguments using rules or cases with these rationales
are attacked, the dispute is about the outcomes of other disputes.  A
mechanism for meta-argument is required, and the simplest adequate
devices are used here.

We present first the formalism for rationales that can be treated
wholly at the object level, then augment the formalism to handle the
meta-level disputes.  For a formal system to treat all five kinds of
compilation rationales, it would have to integrate the mechanisms for
unpacking and meta- argument.  In the interest of clarity, this is
not done here.

III.1.  Object-Level Disputation.

Formally, the record of a disputation includes a sequence of moves,
Mn = <m0, m1, ..., mn>.  Each move may consist of several things:  a
claim, an argument for the claim, perhaps an argument for the
sufficiency of the pair at this point in the disputation.

A simple protocol for dispute is a two-player immediate-response
dialectic (several alternate protocols are described in [Loui92]):

i.  there are two advocates, who are players, and an adjudicator who
has no moves;

ii.  moves alternate between players;

iii.  each move must alter current opinion, which is determinable
syntactically, and which is either pro, con, or none;

iv. all arguments must be well-formed:  i.e., members of Args(L, C,
E);

v.  arguments do not occur repeatedly in the record:  i.e., once an
argument is introduced, it need not and cannot be introduced again.

The internal structure of the argument, ai, in each move, mi, has
been the topic of most recent research on argument (e.g.,
[Sartor93b], [Prakken93], [Simari-Loui92], [Loui-Norman93a]).  An
argument is a structure, <{l1, l2,, ...}, h>, where each lj is in
Rules(L, C), and h is the main claim of the argument.  Other authors
discuss minimality and connectedness properties at length:  that is,
how the lj's and h relate to one another.

The sufficiency of the move depends crucially on the defeat relations
among arguments introduced in Mn.

As an example, the following dispute proceeds according to a
reasonable dialectical protocol:

1.  pro:  {e1 >-- h }, h; opinion:  pro
2.  con:  {e2 >-- b; b >-- not-h }, not-h; opinion:  none 
3.  pro:  { e1 & e2 >-- not-b}, not-b; opinion:  pro

establishing h.

III.1.1.  Preliminaries.

In procedural models, citing a rationale is a prelude to an attack.
It is a necessary part of what makes the subsequent argument relevant
and sufficient.  It alters the context so that the subsequent
argument is a legitimate move by the player.  A rationale, cited,
permits ai+1 to respond to ai.  Without citing the rationale, ai+1 is
not a legitimate successor of ai.

In declarative models, there are at least two ways to regard
rationales. Citing rationales may alter L or C, restating the
formulation of rules and cases to which a player is willing to
agree.  In this way, the appropriate basis for warrant is Args(L',
C', E) instead of Args(L, C, E).  The second way is to suppose that
the rationale, cited, changes the relations of defeat among the
arguments, defeat, the binary relation on Args(L, C, E) that is
defined by the underlying system of argument.  Contemporary systems
regard argument a1 as defeating argument a2 on syntactic criteria, or
according to an externally supplied ordering, extord(Args(L, C, E)).
The latter might arise from orderings on its constituents:
extord(L), extord(C), extord(E).  With rationales, the cited
rationales, R, becomes a new index in the determination of defeat.
What was the mapping:

	extord(L), extord(C), extord(E) --> extord(Args(L, C, E)) -->
	defeat;

becomes the mapping:

	extord(L), extord(C), extord(E), R --> extord(Args(L, C, E))
	--> defeat.

If R is static, then R is only important to those who study these
mappings.  This is why rationales do not have much importance in
declarative settings.  Taking R to be dynamic, as a sequence Ri, one
may as well return to a procedural model. We will just assume a
procedural model of argument.

Let R(l) and R(c) respectively be all citable rationales for a
defeasible rule, l in L, and a precedent- setting case, c in C.  The
form of a rationale depends on the kind of rationale, as elaborated
below.  Practically, the most difficult part of arguing with
rationales will be discovering and formulating the set R(l), for a
rule l, or R(c), for a case, c.  Even when an authoritative decision
is explained, and even when legislative deliberation is well
preserved, formal expression of rationales as R is problematic.  The
assumption here is the usual assumption among formalists:  just as
evidence, E, wording of rules, L, and documentation of cases, C, can
be expressed in formal language, so too can rationales, R.  To
address the problem more fully would be more ambitious than what is
usually attempted by formalists.

The intention is that R(l) will be a singleton set for most rules
(likewise for R(c)).  There could be multiple citable rationales, and
the difference could matter to the course of a particular dispute.
There could also be no citable rationale.

If R(c) or R(l) is not a singleton for the relevant case or rule,
then the parties can dispute the appropriate rationale.  Since we
suppose no information that would allow adjudication of such a
dispute, the simplest reasonable rule will be adopted.  If a
rationale is raised for a rule or case in an argument, and there is a
multiplicity of possible rationales, then it suffices that the player
who makes use of the original argument can make progress under one of
the many rationales.  For example, suppose pro has the burden to
establish h.  Pro produces an argument A for h, using rule l.  If l
has multiple rationales in R(l), let them be named rat1(l), rat2(l),
etc.; if they are of different types, name them c-rat1(l), d-rat2(l),
etc.  In the suggested protocol it suffices for pro if h can be
established after unpacking pro's choice of the permitted
rationales.

Call the aforementioned the User's Prerogative Assumption.  Since the
procedural rules that implement this assumption merely complicate the
presentation in an uninteresting way, we shall assume that all R(c)
and R(l) are always singletons for a rule l or case c; this is the
simplest way of making the assumption of user's prerogative.

III.1.2.  Structures.

For rules of the form "p is defeasible reason for q", rationales take
the following forms.

A c-rationale is typically an argument, with premises p and
conclusion q.  There may be a background, B, against which this
argument was made.  The intention in adopting the rule is that
usually B will be present in contexts in which the rule is applied.
A c-rationale may thus be an argument from p and B to q.  Such an
argument is as above, a 2-tuple:  c-rat(l) = <T, h>, of rules T and
conclusion h.  Roughly speaking, this argument would be in the set of
well-formed arguments Args(T, {}, {p}B).

An s-rationale is formally identical to a c-rationale except that the
argument takes a particular form.  In a c-rationale, several rules
are used in the argument, which is compressed.  T is not a singleton
set. An s-rationale uses a single guiding rule.  It uses
supplementary rules in L and/or B.

A d-rationale of a case c is a set of arguments, d-rat(c), that has a
certain structure.  These arguments are typically not from Args(L, C,
E) but are from a different set, Args(L', C', E').  The applicability
of the case to the current situation depends crucially on whether the
arguments in d- rat(c) are in both of these sets, not just in
Args(L', C', E').  For a d-rationale, d-rat(c) is a set of arguments
that warrants the decision of the case.


III.1.3.  Attacks

Let ArgRecn be the recognized arguments at a stage n in the sequence
of moves.  In a simple disputation where moves do not refer to
rationales and all arguments are well-formed members of Args(L, C,
E), ArgRecn is simply the union of all arguments introduced in all
moves, m1, ..., mn.  In disputations where well-formedness of an
argument can be called into question (which includes disputations
that allow rationale-based attacks on arguments), ArgRecn expands and
contracts as the disputation proceeds.

ArgRecn includes both defeated and undefeated arguments.  It is not
the "arguments in force" concept that Vreeswijk defines
[Vreeswijk93], which is useful in analyzing warranted conclusions.
It is preliminary to determining which arguments are in force.  An
argument that was introduced in the dialogue but has subsequently
been excluded from ArgRec cannot even be considered for its
properties of defeat relative to the other arguments.

ArgRec is defined inductively:  an argument in m0 is in ArgRec0. If
mi does not contain a statement of rationale, then for an argument ai
in mi, ArgReci contains ArgRec(i-1)ai.  If mi contains a statement of
a rationale, then this is either a rationale-based attack on prior
argument, or else a reinstatement of an argument that has suffered a
rationale-based attack.

A statement of a rationale in a move requires the naming of the
argument that is attacked or defended.  It also requires the naming
of the rule or case, the rationale of which is at issue.  Let @i
indicate that i is a move that uses a rationale.  For such a move,
let ai be the argument concerned, and let li or ci be the rule or
case, as appropriate, in question.  Let ri be the rationale, whether
it is a c-, s-, or d-rationale.  Let playeri be the player who moved
in move i.

Trivial well-formedness requires that the attacked argument has
occurred, that the rule occurs in the argument, and that the
rationale is recognized:

ai must be in ArgReck for some k < i (k need not be i-1 since the
defense against rationale-based attacks must be possible);

li or ci must be a part of ai;

ri must be in R(li), or R(ci).

ri and ai may have occurred together in a previous move, j < i, where
both @i and @j.  This seems to permit repetition of moves, but mi
still might not be the same as mj.  Repetition will be prevented by a
requirement that moves be effective.

The same rule or case can repeatedly be the target of rationale-based
attacks if it occurs in distinct arguments.  This is simpler than
calling all arguments based on a rule or case into question at once.
Call this the One-At-A-Time Protocol.  Also note that both players
might be relying on the same argument, ai.  Let the first player who
attacks a rule, l, in an argument, a, be attacker(l, a); the opposing
player is user(l, a); likewise for attacking rules extracted from
cases.

Consider that @i and that i is a first attack.  To be a first attack,
ai and whichever of li or ci is relevant, do not already occur for
some j < i.  Note attacker(li, ai) = playeri.

Apparently, the immediate effect of the attack is to remove ai from
ArgReci.  That is, apparently, ArgReci = ArgRec(i-1) -- {ai}.  But
the move might modify the form of the argument removing ai and
substituting a revised argument in its stead.  So apparently, ArgReci
= ArgRec(i-1) -- {ai}{argrev}, where argrev is a modified form of
ai.

For a c-rationale or s-rationale, which is an argument <T, h>, argrev
is just the argument that uses <T, h> as a subargument instead of the
rule, li, that is attacked.  So if <T0, h0> = ai, then argrev is the
argument in which a subargument has been substituted for the
compressed rule:  <T0T -- {li}, h0>.  This substitution will be
denoted:  subst(<T0, h0>, li, T) if indeed it is an argument
(satisfies minimality and consistency conditions).  Otherwise, the
statement of the rationale destroys ai and there is no revised
argument added in its place.

This completes the inductive definition of ArgReci.

Finally, having defined ArgReci in terms of mi and ArgRec(i-1), we
require the move mi to be effective: it must alter current opinion so
that playeri's position is improved.  When argrev is part of mi, mi
must sometimes contain a response to the revised argument as well.

For a d-rationale, ri is a set of arguments.  mi must contain a new
argument, attacki, which attacks argrev and changes the current
opinion, deci.  In a d-rationale, the decision of the case, dec(ci),
is warranted among the arguments recorded for the case, ri.  That is,
enough arguments were recorded to support the decision outright.  So
attacki must be such that ri{attacki}, taken as a set of arguments,
would not have warranted the old decision outright, dec(ci).

Responses to these simple kinds of rationale-based attacks are just
moves that augment ArgRec.

For example, for a d-rationale, all of the arguments recorded of the
past case have been entered into ArgRec.  Among them was an argument,
argw, that warranted the decision of the case.  Also included is the
opponent's argrev, which has somehow changed the status of argw.  To
respond substantively, simply give an argument that restores argw's
ability to support its conclusion again.  Or simply retreat from the
attacked precedent-based argument and provide a new, unrelated
argument to support the old decision.

III.1.4.  Simple Symbolic Examples.

Example.  A dialogue without a rationale.

1.  pro:  arg1 = <{ b >-- a }, b!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:  arg2 = <{ c >-- d, d & b >-- not-a}, c! b!  not-a>

ArgRec2 = { arg1, arg2 }; dec2 = none.

3.  pro:  arg3 = <{ c & e >-- not-d }, c! e!  not-d>

ArgRec3 = { arg1, arg2, arg3 }; dec3 = pro.

Here, arguments are 2-tuples (a set of rules paired with a
conclusion).  We have embellished the second argument.  Instead of
just giving the conclusion of the argument, we give the evidence on
which the argument rests (marked with an exclamation point) and write
"" to separate the conclusion.  Rules are given in their sentential
form, a >-- b instead of using the pair <a, b>, and quotes are
suppressed.  Note that we use "=" to give a name to a structure.
This is not to be confused with an assertion.

At move 4, it is con's turn to move and opinion favors pro:  arg3
defeats arg2, thus reinstating arg1.  If con cannot move at this
point, pro wins.

Example.  A c-rationale.

1.  pro:  arg1 = <{ b >-- a }, b!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.    c-rat1( b >-- a ) = <{ b >-- c, c >-- a}, b!  a>

2.2.    Attack < b >-- a, arg1 >

2.3.    arg2 = <{ b & d >-- not-c }, b! d!  not-c>

Con states a rationale for a rule, which presumably is the legitimate
member of R( b >-- a ).  Con must state the argument being attacked.
The effect is to replace the compressed argument with the
uncompressed, but this is still not a sufficient response for con.
So con provides arg2, an attack on the uncompressed argument, the
raison d'etre for stating the rule's rationale.  @2.  Note pro =
user(b>--a, arg1). con = attacker(b>--a, arg1).

ArgRec2 = { arg1rev, arg2 }; dec2 = none.

where

arg1rev = subst( arg1, b >-- a , c-rat1( b >-- a ) )

3.  pro:  arg3 = <{ b & d & e >-- c, c >-- a }, b! d! e!  a>

Pro provides a new argument for a, arg3, that is undefeated in
ArgRec3.  The new argument for c is specific enough to defeat arg2,
which would reinstate arg1, but arg1 has been flushed from the ArgRec
in favor of arg1rev.

ArgRec3 = ArgRec2{ arg3 }; dec3 = pro.

Example.  An s-rationale.

1.  pro:  arg1 = <{ b >-- a }, b!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.    s-rat1( b >-- a ) = <{ d >-- e}, b! (d v not-b)! (a v
not-e)!  a>

2.2.    Attack < b >-- a, arg1 >

2.3.    arg2 = <{ d & f >-- not-e }, d! f!  not-c>

ArgRec2 = { arg1rev, arg2 }; dec2 = none.

where

arg1rev = subst( arg1, b >-- a , s-rat1( b >-- a ) )

Here, arg2 defeats arg1rev because it is more specific.  But arg2
does not defeat arg1 on specificity.

3.  pro:  arg3 = < { d & f & g >-- e }, b! (d v not-b)! f! g! (a v
not-e)!  a >

ArgRec3 = ArgRec2{ arg3 }; dec3 = pro.

Notice how similar this example is to the example of a c-rationale
and recovery from a c-rationale- based attack.

Example.  A d-rationale.

1.  pro:  arg1 = <{ b & c ]-- a }, b! c!  a>

ArgRec1 = { arg1 }; dec1 = pro.

Here, ]-- is used instead of >-- to indicate that this rule is
extracted from a case.

2.  con:

2.1.    d-rat1( b & c ]-- a ) = { da1, da2, da3 }

where

da1 = <{ b >-- a }, b!  a>,

da2 = <{ c >-- d, d >-- not-a }, c!  not-a>

da3 = <{ b >-- f, f & c >-- not-d }, b! c!  not-d>

In d-rat1( b & c ]-- a ), the argument for not-d (da3) defeats the
argument for not-a (da2), thus reinstating the argument for a (da1).
Con attacks, now, by showing that the argument for not-d is defeated
in the present context, where more evidence is available.

2.2.    Attack < b & c ]-- a, arg1 >

2.3.    arg2 = <{ b & g >-- not-f }, b! g!  not-f>

ArgRec2 = { da1, da2, da3, arg2 }; dec2 = none.

3.  pro:  arg3 = <{ g & c >-- not-d }, g! c!  not-d>

ArgRec3 = ArgRec2{ arg3 }; dec3 = pro.

This move suffices for pro because arg3 now defeats da2, thus
reinstating da1.  Current opinion is for pro, to decide a, because
da1 is now in the ArgRec.  Pro is lucky; the same new condition, g,
that allows a distinction from the precedent also allows a new
argument that replaces essentially what was lost.

III.2.  Meta-Level Disputation.

For both the r-rationale and the f-rationale, disputation about
disputation is required.  This requires meta-claims, i.e., claims
about claims, and meta-arguments about meta-claims.  There are
serious semantic difficulties for the formalist who takes defeasible
reasoning to the meta-level.

Technically, the semantic ascent to the meta-language is usually
preferable to the demotion of the reason relation ">--" from a
2-place relation in the metalanguage to an iterated 2-connective in
the language.  As Quine asks, "How do you hope to establish semantic
connections between object level and meta-level?" [Quine90]  A
declarative approach to meta-disputation would indeed require serious
study.  A procedural approach would be one way to side-step the
difficulty.  Earlier writers who have reached this point, notably
Toulmin and Rescher, have ignored this technical problem.  Pollock,
meanwhile, can be viewed as a first step in the procedural approach.

Here, we assume that a system of declarative argument and
meta-argument exists.  The system determines a few things:  whether
meta-arguments are undefeated and supporting, hence, whether their
meta-claims warranted; whether the arguments that make use of the
meta-claims are undefeated and supporting, hence, whether their
object-level claims are warranted.  This assumption is made for two
reasons: (a) to define the envisioned procedural system would be a
separate study not crucial to the picture of rationales that is drawn
here; and (b) the use of meta- argument here provides requirements
for those who would attempt to define such a system.

III.2.1.  Preliminaries.

For an r-rationale, the crucial assertion is an assertion about the
relation among arguments, a meta- assertion.  Arguments that were
maximal, that is, undefeated, in the cited case should continue to be
maximal in the current case in order for the past decision to have
the proper influence.

For an f-rationale, two kinds of meta-assertion are crucial.  They
are that a case should have a certain decision, and that a rule fits
a set of cases.

There are a few kinds of attacks on rules with f-rationales that we
can model and a few that we cannot model.  Even for the few that we
do model, we must introduce negated assertions of a sentence being a
reason for another sentence, e.g. not(b >-- a).

An r-rationale is similar to a d-rationale.  It is at least a set of
recorded arguments from the prior dispute.  For an r-rationale of a
case c, r-rat(c) is a set of undefeated arguments that interfere with
each other.  It is this interfering set of arguments that the
decision of the case resolves.  r-rat(c) also contains the implicit
argument that when those arguments are maximal, interfering, and
unresolved, a certain decision is appropriate.  An assumption here
is that the maximality of a set of arguments is assertable without
dispute (or what is nearly the same, that maximality can be
determined easily).  If the defeat relations among arguments are
clear, then this assumption is reasonable.

An argument so far has been a set of defeasible rules from L, and a
conclusion derivable from those rules using the accepted
(incontrovertible) evidential claims.  Henceforth, the set of rules
can contain rules from L and meta-rules.  These meta-rules relate a
specific kind of meta-claim, that a certain set of arguments is
maximal or not, to a different kind of meta-claim, a defeasible
rule.  For example, instead of allowing just

a >-- b

we allow as well

maximal(S) >-- (a >-- b).

The first occurrence of ">--" above is a relation in the
meta-meta-language, and the second occurrence of ">--" is the
relation in the meta-language used throughout the preceding
sections.  Derivations are now allowed to make use of an argument's
rules and meta-rules (arguments may use both kinds of ">--").  The
mathematical demands on the theory of argument imposed here are
serious and not to be ignored.  Fortunately, implementations have
shown that progress can be made with systems defined in this way,
e.g., [Sartor93b], despite the mathematical and philosophical
conundrums.

Maximal(S) asserts of a set of arguments, S = {A1, A2, ..., An} that
each of those arguments contained in S can be made in the current
setting and is undefeated.  If S is such that maximal(S), then S must
be contained in Argsi(L, C, E).  The predicate, maximal, is thus
dependent on all of the indexes:  i, L, C, and E.  Since i is the
most important index here, write maximali(S) when it is important to
distinguish the stage at which maximality is claimed.

This is not the final formulation for r-rationales.  As HYPO makes
clear, a precedent can be used in the presence of additional
arguments pro.  If a case decides that argument A1 for h outweighs
argument A2 for not-h, then if A1, A2, and an additional argument for
h, A3, can be made in a new setting, the decision of the prior case
is still relevant.  The precedent can also be used in a context where
there are fewer arguments con than those that figured in the past
resolution.  Hence, it need not be required that exactly those
maximal arguments in the past case be maximal in the present case.

Instead, of the predicate maximali(S), suppose there are two
predicates:  minpro-maximali(S1) and maxcon-maximali(S2).  The
arguments in each of the sets S1 and S2 were weighed in the prior
decision, and arguments in S1 taken together were more persuasive
than those in S2.  If at stage i, at least the arguments in S1 are
maximal, and if no more than the arguments in S2 for con are maximal,
then there is defeasible reason for using the case (or more
precisely, the rule extracted from the case).  If the maximality of
the arguments in S1 cannot be maintained at stage i, then the
precedent cannot be used.  If there are additional arguments con,
which were not weighed previously, then the case is again
inapplicable.

A formal account of determining when an argument should be considered
additional pro or additional con is owed.  As in HYPO, this
determination is trivial if the decision of the case is h and all
arguments in S1 and S2 are for h and not-h, respectively.
Determining whether an argument is pro or con can be inductively
defined in an obvious way, and will not be done here.  There will be
arguments that support both pro and con arguments, and these most
naturally contribute to minpro-maximali and be excluded from
maxcon-maximali.

An f-rationale is a set of cases, not all of which might be from C.
Let HCC be the actual cases augmented by hypothetical cases.  HC are
cases that did not actually occur, but are cases upon which there is
agreement of the hypothetical decisions given the hypothetical
facts.  Assume that the assertion that a case and its decision are
agreeable to all parties is incontrovertible.  Write ok(case1) if
case1 is so agreeable.  Once again, we do not seek to model every
kind of dispute.  Here, we choose not to model disputes over whether
a case should have a certain outcome.  Some of these disputes could
be modeled easily, some would require a complicated recursion, and
some are not obviously subject to reason at all.

Instead of introducing a language in which cases are described,
suppose simply that there is a relation fit-s(l, c), which holds when
a defeasible rule fits a case c.  For example, the rule l1 = "if f1
and f2, then h" fits those cases wherein f1, f2, and h hold.  It also
fits those cases wherein h does not hold, but at least one of f1 or
f2 also does not hold.  The rule does not fit a case wherein f1, f2,
and not-h are all true.  This is fit simpliciter.  A more robust
concept of a defeasible rule's fit to a case takes account of
context.

In the context of a set of other defeasible rules, LCont, l might fit
a case c even if it does not fit simpliciter.  This is because LCont
may provide through more specific rules an explanation of why c does
not conform to l, why it is not the case that fit-s(l, c).  So a rule
may fit, robustus, fit-r(l, c, LCont) when fit-s(l, c) or when there
is a more specific rule , l', in LCont which does fit c.  The whole
apparatus of arguments which permits chaining of rules could be
applied here to explain why l does not fit c, simpliciter, but is
allowed not to fit by a superior chain of rules in LCont.  Under the
criteria of syntactic superiority advanced in [Simari-Loui92],
[Prakken93], and [Loui- Norman93a], no chain of rules in LCont will
be superior to l unless a single rule in LCont is superior to l.  But
under other systems, a recursion of disputation is possible here, and
woe be to the formalizer who seeks to model this recursion.

Arguments of fit based on a larger number of cases are considered
better arguments. Likewise, arguments of fit based on a larger
context are better arguments.  Fit is assumed  incontrovertible.

III.2.2.  Structures.

Formally, an r-rationale is a set of arguments that occurred in the
case, a true assertion that all of those arguments are maximal with
respect to one another (none is defeated), and a meta-reason that
connects the maximality of certain arguments to the rule putatively
extracted from the case.   The arguments are partitioned into minpro
and maxcon, as discussed above. Technically all that are required are
the two sets of arguments, S1 and S2, that occurred in the resolution
of the case.  The rest can be recovered from context. Making the
other parts explicit adds clarity.  r-rat(c) = <

1.  S = S1S2,

2.  minpro-maximal(S1), maxcon-maximal(S2),

3.  minpro-maximal(S1) & maxcon-maximal(S2) >-- l

>.

The claim of maximality must be true, and the arguments in S must be
properly relevant to c.  To define proper relevance, consider the
rule extracted from the case to be:  l = l1 >-- l2.  There must be an
argument in S for l2.  We do not insist that all arguments in S be
possible with just l1 as evidence.  Nor must there be some argument
in S that requires all of l1 to be made.  Much more weakly, l1 must
be relevant to S; it should contain no superfluous literals.

An f-rationale is a set of cases together with a claim that the rule
fits (robustus) that set of cases with respect to a context.  <HCC,
LCont> is the f-rationale for a rule l, if and only if for every c in
HCC, fit-r(l, c, LCont).  LCont must be a subset of L.

III.2.3.  Attacks.

To attack an argument using a rule with r-rationale, cite the
rationale and name the argument and rule attacked.  Then substitute a
revised argument into ArgReci that makes explicit the connection
between the maximal arguments resolved by the case and the rule
extracted therefrom.  The modified argument is just like the earlier
argument except that a meta-rule has been put in place of the
object-level rule.  The meta-rule makes explicit the origin of the
object-level rule.  This allows subsequent attack of the statement
that S is maximal.

To attack the statement minpro-maximal(S), provide a new argument or
set of arguments, S', that are arguments that can be made in the
current case.  Then claim not(minpro-maximal(S)) as a result of the
presumed system of determining defeat among arguments.  If S'
contains an argument that defeats an argument in S, for example, then
not every member of S will be maximal (some member will now be
defeated).  Similarly, to attack maxcon-maximal(S), provide a new
argument or set of arguments, S' that can be made in the current
case.  Then claim not(maxcon-maximal(S)) because S' contains a new
maximal argument con.

To attack an argument using an f-rationale, state the f-rationale,
then alter either the cases or the context with respect to which fit
is claimed.  We have assumed that claims of fit are incontrovertible,
since we are providing no theory of how this is determined.  Adding a
case that the rule does not fit is the usual attack.

III.2.4.  Simple Symbolic Examples.

Example.  An r-rationale with maxcon-maximal attacked.

1.  pro:  arg1 = <{ b & c ]-- a }, b! c!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.  r-rat1( b & c ]-- a ) =
	< {da1, da2}, minpro-max({da1}) & maxcon-max({da2}) ,
	minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) >
where da1 = <{ b >-- a }, b!  a>, da2 = <{ c >-- d, d >-- not-a },
c!  not-a>

2.2.  Attack < b & c ]-- a, arg1 >

2.3.  arg1rev = <
	{ minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) },
	b! c! minpro-max({da1}) & maxcon-max({da2})!  a >

2.4.  arg2 = <{ e >-- f, c & f >-- not-d }, e! c! f!  not-d }>

2.5.  not(maxcon-max({da2}))

ArgRec2 = { arg1rev, da1, da2, arg2 }; dec2 = none.

Note that among da1 and da2, neither is defeating.  The opinion in
this case is significant because it creates a preference that cannot
be found in extord(Args(L, {}, E)) or in defeat, that is, among the
syntactically determinable or externally supplied orderings among
arguments.  The adjudicator chose between competing arguments that
could not be decided purely on form.  Con revises pro's argument arg1
by producing arg1rev which exposes the meta-reasoning.  Then arg2 is
produced, which is an additional argument con, and is maximal.  So
2.5 is assertable, not(maxcon- max({da2})), which is one of the
requirements for using the precedent.

Example.  An r-rationale with minpro-maximal attacked.

1.  pro:  arg1 = <{ b & c ]-- a }, b! c!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.  r-rat1( b & c ]-- a ) =
	< {da1, da2}, minpro-max({da1}) & maxcon-max({da2}) ,
	minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) >
where da1 = <{ b >-- g, g >-- a }, b!  a>, da2 = <{ c >-- d, d >--
not-a }, c!  not-a>

2.2.  Attack < b & c ]-- a, arg1 >

2.3.  arg1rev = <
	{ minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) },
	b! c! minpro-max({da1}) & maxcon-max({da2})!  a >

2.4.  arg2 = <{ b & e >-- not-g }, b! e!  not-g }>

2.5.  not(minpro-max({da1}))

ArgRec2 = { arg1rev, da1, da2, arg2 }; dec2 = none.

Again, among da1 and da2, neither is defeating, so the opinion in
this case is significant.  Again, the adjudicator chose between
competing arguments that could not be decided purely on form.  Con
revises pro's argument arg1 by producing arg1rev which exposes the
meta-reasoning as before.  This time, arg2 is produced, which defeats
an essential part of the case, one of the minpro-maximal arguments
(in fact, the only minpro-maximal argument), da1.  So 2.5 is
assertable, not(minpro- max({da1})), which again is a requirements
for using the precedent.

Example.  An f-rationale attacked for fit and redeemed in larger
context.

1.  pro:  arg1 = <{ b >-- a }, b!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.  f-rat2( b >-- a ) = { Cases1, fit-r( b >-- a , Cases1, Context1
) } where Cases1 = { case1, case2 } case1 = < { b, d }, a > case2 = <
{ not-b }, not-a > Context1 = {}

2.2.  Attack < b >-- a, arg1 >

2.3.  arg1rev = <
	{ ok(Cases1) &  fit-r( b >-- a , Cases1, Context1 ) >-- (b
	>-- a) }, ok(Cases1)! fit-r( b >-- a , Cases1, Context1 )!
	b!  a >

2.4.  arg2 = <
	{ ok(Cases2) &  not-fit-r( b >-- a , Cases2, Context1 ) >--
	not(b >-- a) }, ok(Cases2)! fit-r( b >-- a , Cases2, Context1
	)!  not(b >-- a) > where Cases2 = { case1, case2, case3 }
case3 = < b, c, not-a >

ArgRec2 = { arg1rev, arg2 }; dec2 = none.

Con has added a case, case3, which the rule, b >-- a, does not fit in
Context1.  Pro responds by exhibiting a larger context which accounts
for the alleged deviation.

3.  pro:  arg3 = <
	{ ok(Cases2) &  fit-r( b >-- a , Cases1, Context2 ) >-- (b
	>-- a) },
	 ok(Cases2)! fit-r( b >-- a , Cases2, Context2 )! b!  a >
where Context2 = { b & c >-- not-a }

ArgRec3 = { arg1rev, arg2, arg3 }; dec3 = pro.

Example.  Deepening an r-rationale-based attack.

1.  pro:  arg1 = <{ b & c ]-- a }, b! c!  a>

ArgRec1 = { arg1 }; dec1 = pro.

2.  con:

2.1.  r-rat1( b & c ]-- a ) =
	< {da1, da2}, minpro-max({da1}) & maxcon-max({da2}) ,
	minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) >
where da1 = <{ b >-- g, g >-- a }, b!  a>, da2 = <{ c >-- d, d >--
not-a }, c!  not-a>

2.2.  Attack < b & c ]-- a, arg1 >

2.3.  arg1rev = <
	{ minpro-max({da1}) & maxcon-max({da2}) >-- ( b & c ]- a ) },
	b! c! minpro-max({da1}) & maxcon-max({da2})!  a >

2.4.  arg2 = <{ b & e >-- not-g }, b! e!  not-g }>

2.5.  not(minpro-max({da1}))

ArgRec2 = { arg1rev, da1, da2, arg2 }; dec2 = none.

This is as before:  arg2 is produced, which defeats an argument that
must be minpro-maximal.  Now pro responds by attacking arg2 and
ejecting it from ArgRec3.

3.  pro:

3.1.  arg3 = <{ b & e & f >-- g }, b! e! f!  g>

3.2.  minpro-max({da1})

ArgRec3 = { arg1rev, da1, da2, arg2, arg3 }; dec3 = pro.

Note that the argument pro in the prior case, da1, can be
strengthened in the current situation:  instead of supporting g with
merely b, support g with all of b & e & f.  This alone does not
suffice to establish a, however.  Pro needs to cite the case in which
b, a prima facie reason for a, was decided to be more important than
c, a prima facie reason for not-a.  Among the object-level arguments
in ArgRec3, { da1, da2, arg2, and arg3 }, a is not warranted.  The
important point is that da1 was judged more important than da2 in the
past, and arg3 prevents arg2 from disrupting the past's bearing on
the present.

IV.  Related Work and Conclusions.

A ratio decidendum is an essential part of a case.  To cite a case
without attention to the ratio is to make analogies on surface
similarities.  Casually determined similarities may not actually be
relevant to the past decision or its subsequent use.  Similar remarks
could be made about the application of rules without regard to the
principles on which the rules are based:  without regard for ratio
legis.

There may be some latitude in the use of cases.  In some protocols,
whoever cites a case must produce the rationale.  In other protocols,
it is the responsibility of the opposition to raise any problem
regarding rationale.  Here, the assumption is that ratio decidendi
need not always be given when a case is cited as part of an
argument.  The assumption is that the use of the case is
appropriate.  The benefits of such an assumption are like the
benefits of any protocol that permits simpler argument moves.  Unless
the use of the case or the use of the rule is disputed, the
assumption is that the use is appropriate.  The same is true for
rules.  What is important is a mechanism in the protocol for
permitting an objection to the use of a rule or case, when a party to
the dispute elects to do so.

Rationales, especially r-rationales and d-rationales, illuminate why
Ashley can make distinctions among cases [Ashley89].  In our work,
rules are extracted from cases.  In any rule derived in this way, the
sharing of important properties with the precedent is reason for
sharing the decision of the precedent.  Counterarguments are possible
only by finding reasons for the opposite decision.  Ashley and our
improved analysis of r-rationales permit more sophisticated
counterarguing.  The opposition can simply cite properties that the
present case does not share with the precedent.  This kind of
distinction becomes possible when the r-rationale or d-rationale of
the case is available for examination.

Berman and Hafner recently discussed the teleology of rules
[Berman-Hafner93].  The rationales of the rules they discuss are more
complicated than the kinds discussed here.  Their rationales involve
a fundamentally different kind of reasoning:  the reasoning about
compromises in policy-making.  The present work is less ambitious in
scope and more ambitious in formality.  It remains to be seen how
many rationales can be expressed as compilation rationales of the
five kinds explored here.  Future work mut surely be directed at
representing the most important rationales in a particular legal
domain.  We do not expect that the full range of principles discussed
for instance in Hart [Hart61], Dworkin [Dworkin85], or Peczenik
[Peczenik89] could be accommodated with compilation rationales.  The
rationales chosen for investigation here are just the ones most
amenable to treatment in the existing model of argument and
disputation.  Branting [Branting93] is a formal analysis of
rationales that does not rely on argument systems.

Prakken briefly discusses the possibility of modeling principle and
purpose [Prakken93].  He follows Gardner [Gardner87] by taking most
of the principle and purpose to be reflected in the matching of past
cases to present case:  i.e., in the extraction of rules from cases.
"In this way it is possible to account for the defeasibility of legal
rules caused by principle and purpose without having to complicate
the formal model too much."  Of course, the matching of cases must be
performed on the essential aspects of the case.  It was precisely the
delineation of the essential from the inessential that led us to
investigate explicit representation of rationales.  Ashley
[Ashley89], for example, assumes that only the important aspects of
cases are formalized in the first place.

Prakken, noting agreement with Berman and Hafner, notes that
reasoning with rationales will be unavoidably meta-level reasoning.
Applying the model will determine whether the added representational
power is worth the complication of the model to include
meta-reasoning.

Formality plays an important role in some of AI's interpretations of
legal reasoning.  Once the importance of rationales is allowed, the
questions arise:  what kinds of rationales?  represented in what
way?  introduced according to what protocol?  General studies of
argument, such as Toulmin's, have provided room for criticising the
backing of a rule, the grounds on which it was adopted.  But no prior
work known to us has attempted to present details of this knowledge,
their structures, and the processes in which they participate.  To
future automaters of rule-based and case-based legal reasoning, we
hope studies of this kind will be useful.

Acknowledgements.

We are grateful for the meta-arguing of Violetta Cavalli-Sforza;
also, to Kevin Ashley and Mark Mittelman for their comments, and the
opportunity to present this work at U. Pittsburgh LRDC.

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