Models of Legal Argumentation

Trevor Bench-CaponDepartment of Computer Science

The University of LiverpoolLiverpool

UK

Overview

• Argument and Proof• Arguments Based on Cases

– HYPO– CATO

• Arguments Based on Rules• Bodies of Arguments – Dung • Argument Schemes – Toulmin• Persuasion Using Purpose and Value

Argument and Proof

• Argument– John is old because he

is aged 82

– Arguments persuade, not compel

– Arguments leave things implicit. The hearer fills in the gaps and may be convinced

• Proof– John is aged 82– John is a man– All men aged

greater than 70 are old

– 82 > 70– Therefore, John is

old

Argument and Proof

– Arguments may contain open textured concepts

– The proof requires a threshold for old

– The hearer needs only to accept that 82 is above the threshold

• Proof– John is aged 82– John is a man– All men aged

greater than 70 are old

– 82 > 70– Therefore, John is

old

•Argument–John is old becausehe is aged 82

Argument and Proof

– Arguments may introduce new information

– Speaker may assume John is man, but hearer knows he is a tortoise

• Proof– John is aged 82– John is a man– All men aged

greater than 70 are old

– 82 > 70– Therefore, John is

old

•Argument–John is old becausehe is aged 82

Legal Argument

• Legal Argument displays these typical characteristics of argument:– Unstated background and

uncontested facts– Open texture and context dependent

interpretation– New information and considerations

Arguments are Defeasible

• A sound proof has to be accepted• But arguments are inherently and

inescapably defeasible– They may be accepted, or challenged

• Different audiences may respond differently, accepting for different reasons, or offering different challenges

– The challenge can be accepted and the argument withdrawn, or it can be rebutted

– Thus arguments are embedded in a dialectic context – and the audience is important

M cC artyE isener vs M cC om ber

P ro to typesand D efo rm ations

U ntit ledR iss land and F riedm an

B ank rupcyE xp lo res C oncep t D rift

B ankX XR iss land , S ka lak , F riedm an

B ank rupcyG enera tion o f A rgum ent

S P IR ER iss land and D an ie ls

H om e O ffice /B ank rupcyIn fo rm ation R e trieva l

C A B A R E TR iss land and S ka lak

H om e O ffice D educ tionA rgum ent M oves

U ntit ledA sh ley and B run inghaus

T rade S ec re ts LawA utom atic iden tif ica tion o f F ac to rs

C A T OA sh ley and A levenT rade S ec re ts Law

F ac to r H ie ra rchy

H Y P OR iss land and A sh leyT rade S ec re ts Law

D im ens ions / 3 -P ly A rgum ent

SMILE

Arguments Based on Cases

Amherst

Pittsburgh

Rutgers

IBPAshley and Bruninghaus

Trade Secrets LawOutcome Prediction

GREBEBranting

Industrial InjuriesSemantic Net Based

Wyoming

Arguments Based on Cases• This was a focus of AI and Law

from the beginning• I will focus on

– HYPO (Rissland and Ashley)– CATO (Ashley and Aleven)

• Both systems operate inUS Trade Secrets Law

HYPO

• Main Features– Three-Ply Argument Structure– Use of Dimensions to Represent and

Compare Cases

Three Ply Argument

• First Ply:– A case is cited by proponent

• Second Ply:– The citation is attacked by opponent

• By distinguishing the case• With a counter example

• Third Ply:– The attack is rebutted by proponent

• Distinguishing the counter examples

Three Ply Argument

• Provides a simple but effective way of organising the argument

• Is clearly adversarial in nature• Allows for both distinguishing and

counter examples• Can be considered as an argument

scheme

Dimensions

• A dimension is a feature of the case which may need to be considered– In Trade Secret Law e.g.

• Security Measures Adopted• Disclosures Subject to Restrictions• Competitive Advantage Gained

Dimensions

• Are associated with– Preconditions– A range– Facts which determine the position

within the range– A direction

Security Measures Adopted• Precondition

– The plaintiff adopted some security measures

• Range– From Minimal measures through some

physical measures to nondisclosure agreements

• Facts– List of security measures adopted

• Direction– Stronger measures favour the plaintiff

Disclosures Subject to Restriction• Precondition

– Some disclosures were restricted

• Range– 0-100% of disclosures restricted

• Facts– Percentage of disclosures restricted

• Direction– Plaintiff favoured by more restricted

disclosures

Competitive Advantage Gained• Precondition

– Defendant saved development cost

• Range– $10,000 - $10,000,000

• Facts– Plaintiff development time and cost– Defendant development time and cost

• Direction– Greater savings favour plaintiff

HYPO Trade Secret Example

π = plaintiff∆ = defendant

CASE16 Yokana (∆)

F7 Brought-Tools (π)

F10 Secrets-Disclosed-Outsiders (∆)

F16 Info-Reverse-Engineerable (∆)

CASE30 American Precision (π)

F7 Brought-Tools (π)

F16 Info-Reverse-Engineerable (∆)

F21 Knew-Info-Confidential (π)

CASE Mason (?)

F1 Disclosure-in-Negotiations (∆)

F6 Security-Measures (π)

F15 Unique-Product (π)

F16 Info-Reverse-Engineerable (∆)

F21 Knew-Info-Confidential (π)

Mason (?) AmericanPrecision (π)

F21 (π)

F6 (π)

F15 (π)

Yokana (∆)

F16 (∆)

CFS

F9 (π)F10 (∆)

F7 (π)

F18 (π)F19 (∆)

F1 (∆)

Comparing Cases

• On the basis of similarities between past cases and the current fact situation, HYPO forms a case lattice

Case Lattice

Typically

• The first level will contain both plaintiff and defendant cases

• These are available to be cited– KFC, American Precision or Digital

Development for plaintiff– Speciner, Carver or Speedry for defendant

• If no case is available at the first level, we would need to descend a level until we found a case supporting our side– If F1 absent, Midland Ross or Yokana for

defendant

First Ply (for Plaintiff)

• Where disclosure in negotiations, security measures, knew information confidential and unique product, plaintiff should win. Digital Development

• Note that pro-defendant factors are included here

Distinguishing

• Either additional pro-defendant factor in current case

• Or additional pro-plaintiff factor in cited case

• Thus we may distinguish Mason from Digital Development since the product was reverse engineerable in Mason but not Digital Development.

• Note that Unique Product does not distinguish Mason from KFC – it makes Mason better

Counter Example

• A case at the same level of the case lattice held for the other side

• E.g. Carver is CE to Digital Development

• Better a case with all the shared factors and more (“trumping CE”)

• E.g. American Precision if Midland Ross cited for the defendant

Third Ply - Rebuttal

• Distinguishes the counter examples

• E.g. Carver is distinguishable because security measures, knew information confidential and unique product in Mason, but not Carver

Argument, not a Decision

• Except for the trumping, more on point, counter example, we may choose which side should win

• We may reject the distinctions as unimportant

• We may follow the cited case or the counter example

CATO

• Also in US Trade Secrets Law• Also uses 3 ply argument• But• Uses factors not dimensions• Organises factors into a hierarchy,

allowing additional argument moves• Some additional rebutting moves

Factors

• No degree – factors either apply or do not apply

• The presence of a factor always favours either the plaintiff or the defendant– Security measures – plaintiff– No security measures – defendant– Outsider disclosures restricted – plaintiff– Competitive advantage - plaintiff

Factor Hierarchy

Info Trade Secret -p

Efforts to maintain Secrecy -p

Info valuable -p

SecurityMeasures p

No SecurityMeasures - d

Waiver ofConfidentiality - d

CompetitiveAdvantage -p

Emphasising and Downplaying Distinctions• Precedent: No security measures• Case 1: Waiver of Confidentiality• Case 2: Security Measures• Case 1 and Case 2 can both be distinguished

because no security measures is absent• Case 1 can downplay the distinction because there

is an alternative argument against efforts to maintain secrecy

• Case 2 can emphasise the distinction, because there is now no argument against efforts to maintain secrecy

Confidentiality

Argument Moves in CATO

·Analogising a case to a past case with a favourable outcome·Distinguishing a case with an unfavourable outcome;.·Downplaying the significance of a decision; ·Emphasising the significance of a distinction; ·Citing a favourable case to emphasise strengths; ·Citing a favourable case to argue that weaknesses are not fatal; ·Citing a more on point counterexample to a case cited by an opponent; ·Citing an as on point counter example to a case cited by an opponent.

Arguments Based on Cases• Cases are compared according to

common features– Features tend to be at a level of

abstraction above facts (issues)• Arguments mainly based of

differences between cases• And the significance of these

differences

Arguments Based on Rules

• In Law, rules often conflict– The person named in a will should inherit– A murderer should not inherit

• Conflicting rules provide an argument for and an argument against

• How do we resolve such arguments?

Types of Conflict

• Rules may conflict in several ways:– Contradictory conclusions

• If P then Q, If R then not Q

– Denial of premises• If P then Q, if R then not P

– Rule inapplicable• If P then Q, if R then not (if P then Q)

Resolution Through General Principles• Prefer most specific rule

– Statutes are often written as general rule and exceptions

• Prefer most recent rule– A recent case is preferred to an old one

• Prefer most authoritative rule– Supreme court better than lower courts

• These principles can conflict• No general ordering seems possible

Weighing Reasons

• We can see the antecedents as reasons for the conclusion

• Some reasons may be stronger than others

• We should prefer the stronger reasons to the weaker reasons

Explicit Rule Priorities

• We can simply state which of a pair of conflicting rules has priority over the other

• Note: such priorities may themselves be the subject of debate

Dialogical Justification

P Q

R ¬ Q

S ¬ R

T ¬ (S ¬ R)

U ¬ T

Proponent wins

Proponent wins

Proponent wins

Opponent wins

Opponent wins

Reconstruction of HYPOPrakken and Sartor • Cases are represented as 3

implications: (i) if pro-plaintiff factors then plaintiff (ii) if pro-defendant factors then defendant (iii) (i) < (ii) if defendant won, else (ii) < (i)– May be broadened by omitting factors– May be distinguished– Are deployed in a dialogue game

HYPO Trade Secret Example

π = plaintiff∆ = defendant

CASE16 Yokana (∆)

F7 Brought-Tools (π)

F10 Secrets-Disclosed-Outsiders (∆)

F16 Info-Reverse-Engineerable (∆)

CASE30 American Precision (π)

F7 Brought-Tools (π)

F16 Info-Reverse-Engineerable (∆)

F21 Knew-Info-Confidential (π)

CASE Mason (?)

F1 Disclosure-in-Negotiations (∆)

F6 Security-Measures (π)

F15 Unique-Product (π)

F16 Info-Reverse-Engineerable (∆)

F21 Knew-Info-Confidential (π)

Mason (?) AmericanPrecision (π)

F21 (π)

F6 (π)

F15 (π)

Yokana (∆)

F16 (∆)

CFS

F9 (π)F10 (∆)

F7 (π)

F18 (π)F19 (∆)

F1 (∆)

Example

• Yokana gives 3 rules– R1: F7 P– R2: F16 & F10 D– R3: R2 > R1

• American Precision gives 3 rules– R4: F7 & F21 P– R5: F16 D– R6: R4 > R5

Rationales – Loui and Norman• This records the progress of the dispute

which may be important.– Consider a precedent which has F1 and F2

favouring plaintiff and F3 favouring the defendant and was won by plaintiff

– Given a new case with only F1 it is unclear that the plaintiff should win

– But suppose F2 was used to defeat F3: Now it can be seen that F1 can stand alone

Compare

R4: F1 P

R2: F3 D

R5: F2 not (F3 D)

R6: R5 > R2

Now we can confidently apply R4

R1: F1 & F2 PR2: F3 DR3: R1 > R2

Not clear that

R4: F1 P

We need a record of the dispute to decide which description is the right one

Argumentation Frameworks• We can often view a legal dispute

as a set of conflicting arguments• P.M. Dung has developed an

elegant way of looking at and reasoning about sets of conflicting arguments

Dung’s Argument Framework• Introduced in AIJ 1995• Arguments at their most abstract

– Only: which other arguments does an argument attack?

• Attacks always succeed– We cannot accept an argument and

its attacker

Definitions

An argumentation framework is a pair AF = <AR, attacks>

– Where AR is a set of arguments and attacks is a binary relation on AR, i.e. attacks AR AR.

An argument A AR is acceptable with respect to set of arguments S if:

(x)((xAR) &(attacks(x,A)) (y)(y S) & attacks(y,x).

A set S of arguments is conflict-free if (x) (y)( xS) & (y S) & attacks(x,y).

A conflict-free set of arguments S is admissible if (x)((xS) acceptable(x,S).

Preferred Extension

• A set of arguments S in an argumentation framework AF is a preferred extension if it is a maximal (with respect to set inclusion) admissible set of AR.

• Preferred Extensions are interesting because they represent maximal coherent positions, able to defend themselves against all attackers

• BUT: there may be multiple preferred extensions, and no way to choose between them

Odd Cycle

a

bc

We can’t acceptAnything here

Akin to Paradoxes

Preferred Extensionis the empty set

Even Cycle

a

b

c

d

We can acceptEither a and cOr b and d

Akin toDilemmas

TwoPreferred Extensions{a,c} and {b,d}

In general

• Every AF has a preferred extension– Which may be the empty set

• AFs do not have a unique preferred extension– Even cycles give rise to choices

• An argument may be in every preferred extension (sceptically acceptable)

• An argument may be in some preferred extensions (credulously acceptable)

• An argument may be in no preferred extension (indefensible)

Decision Problems and Complexity

ADM(H,S) Is S admissible P

PREF-EXT(H,S) Is S preferred Co-NP comp.

STAB-EXT(H,S) Is S stable P

HAS-STAB(H) Does H have a stable ext.

NP complete

CA(H,x) Is x accepted credulously

NP complete

SA(H,x) Is x accepted sceptically

2 complete

COHERENT(H) Is H coherent 2 complete

Proofs of these results can be found in a series ofpapers by Paul Dunne and myself.

Example Set of Cases

• Pierson: Plaintiff is hunting a fox on open land. Defendant kills the fox.

• Keeble: Plaintiff is a professional hunter. Lures ducks to his pond. Defendant scares the ducks away

• Young: Plaintiff is a professional fisherman. Spreads his nets. Defendant gets inside the nets and catches the fish.

Ghen vs Rich:

• Ghen harpooned a whale, lost it. Ellis found it, sold it to Rich, who processed it.

• Found for Ghen.– “the iron holds the whale”

• Whaling is governed by conventions which the court respects

Conti vs ASPCA

• Chester, a talking parrot used by ASPCA for educational purposes, escaped. Conti found it and kept it as a pet. ASPCA reclaimed it.

• Found for ASPCA• Chester was domesticated, and so

ferae nauturae did not apply

Burros Cases

• New Mexico vs Morton• Kleepe vs New Mexico

– Unbranded burros straying from state lands

– Showed that:• Branding established possession• Presence on land had to be more than

accidental straying

Representing Keeble

• A: Pursuer had a right to the animal• B: Pursuer not in possession• C: Owns the land (so owns the

animals)• D: Wild animals not confined• E: Efforts made to secure animals• F: Pursuer has right to pursue

livelihood unmolested

Keeble as AF

BF

A

C

D

E

Preferred extension is {A,C,E,F}

Two waysto win

Pierson as AF

• {A, B,E} as in Keeble• I, M: Pursuit is not enough• J: Hypothetical: the animal was taken• K: Hypothetical: animal was wounded• L: Hypothetical Certain control is enough• O: Reasonable prospect of capture• P : Reasonable prospect too uncertain• R: Reasonable prospect encourages desirable

activity• G: Not relevant: Interferer was trespassing• H: Not relevant: Pursuer was trespassing• Q: The land was open

Situationswhich would establish right

values

Excludessome pastcases

Pierson as AF

B

A

E

Preferred extensions are {B,I,M,P,Q} and {A,E,O,Q,R}

M (P)

L

KJ

IQ

H

G

O (R)

Two cycle

Young as AF

• Arguments in Pierson are all relevant– but now L is applicable and P is not

• F from Keeble is present• S: Defendant was in competition

with the plaintiff• T: The competition was unfair• U: Not for the court to rule on what

is unfair competition.

Young as AF(Trespass omitted)

B

A

E

Preferred extension is {B,L,S,U} Argument U breaks the 4 cycles

M (P)

L

KJ

I

O (R)F

TS

U

Ghen Versus Rich

• New Argument V: – The iron holds the whale is a

convention throughout the whaling industry

• Attacks U: establishes what is unfair competition is whaling

• Attacks B: Establishes what counts as possession in whaling

Ghen as AF(Trespass omitted)

B

A

E

Preferred extension is {A,E,F,K,T,V}

M (P)

L

KJ

I

O (R)F

TS

U

V

Conti and Burros Cases• Add some special cases

– W: Domestication sufficient– X: Unbranded animals go to the

owner of the land– Y: Branding sufficient– Z: Animals must live on the land:

straying on to someone’s land does not affect title

Effect on AF

BF

A

C

D

E

W

X

Y

Z

Argumentation Framework for Animals Cases

A

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

Analysis takenfromBench-Capon 2002Jurix 2002

Some cycles hereA

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

Argument Schemes

• In Dung’s framework anything can count as an argument, and anything can count as an attack

• Argument schemes suggest a form that arguments should have

• Argument schemes prescribe what will count as an attack

Modus Ponens as Argument Scheme• Form:

– If Antecedent then Consequent and– Antecedent: therefore– Consequent

• Attacks:– Consequent is not the case– Antecedent is not true– Consequent does not follow from

Antecedent

Compare: The three kinds of conflict for rule systems

Witness Testimony

• Form:– Witness 1 says that A and– Witness 1 is an a position to have observed

A; therefore– A

• Attacks:– Witness 2 says A is not the case– Witness 1 not in position to have observed A– Witness 1 is mistaken– Witness 1 is lying

Toulmin Argument Schema• One general Argument Schema

that has been much used in AI and Law derives from Stephen Toulmin.

• Introduces– Modal Qualification– Backing– Rebuttal

Toulmin’s Argument Scheme

Data Claim

Warrant

Backing

Rebuttal

Modal

Toulmin Example

John is82

John isold

Over 80Is old

DemographicData

John is aTortoise

Normally

Useful

• To identify different roles for premises:– Basic data– General Rules– Justification– Degree of support– Exceptions

• Used – in explanation, – to organise the presentation of an argument– as the basis of dialogue games

Systems Using Toulmin

• Toulmin’s schema (sometimes adapted) has been used by– Marshall (1989) – organisation of legal

argument– Lutomski (1989) – presentation of expert

testimony– Stoors (1991) – organisation of policy argument– Bench-Capon (1985) – explanation– Bench-Capon (1998) – dialogue game– Zeleznikow and Stranieri - explanation

Argument Schemes

• Potentially a very fruitful area of study– Especially particular schema (such as

witness testimony)

• As yet rather under researched

Disagreement and Persuasion• In the remainder of the talk I will look at

some of my current work• The starting point is why do people

disagree? And when they do, how do they persuade one another?

• I will look at – an extension to Dung’s framework, – an argument scheme for persuasive

argument

Perelman says:

• If men oppose each other concerning a decision to be taken, it is not because they commit some error of logic or calculation. They discuss apropos the applicable rule, the ends to be considered, the meaning to be given to values, the interpretation and characterisation of facts.

Taxation Debate

Raise taxes topromote equality

Lower taxes topromote enterprise

Brown sees force in both arguments – but what Brown does depends on (reveals?) whether Brown prefers equality or enterprise at a given time

To allow for rationaldisagreement• We must distinguish attack from

defeat• We can accept arguments which

are attacked, AND their attackers, provided the attacks fail

• Dung’s framework is too abstract to allow such talk – we need to be able to discuss value as well as conflict

Value-based Argumentation FrameworkA value-based argumentation framework (VAF) is a 5-tuple:VAF = <AR, attacks,V,val, P>

As for Standard AF Set of

values FunctionMapping

Elements of ARTo Elements of V

Set of PossibleAudiences

Audiences

• Following Perelman we want to use the notion of an audience

• Audiences will have different preferences between values

• We individuate audiences by their ordering on values

• There are as many audiences as there are value orderings

Audience Specific VAF

An audience specific VAF (AVAF) is a 5-tuple:AVAF = <AR, attacks,V,val, Valprefa>

As for Standard AF Set of

valuesFunctionMapping

Elements of ARTo Elements of V

Valprefa is the value preferences of audience a

Defeat in AVAF

An argument A AF defeatsa an argument B AF for audience a if and only if both

attacks(A,B) and not valprefa(val(B),val(A)).

Note: An argument is defeated by an attacker with the same value

Defeat is always relative to an audience If there is only one value in V we have a

standard argumentation framework

Definitions for AVAF

• An argument A AR is acceptable to audience a with respect to set of arguments S, if:

(x)((xAR & defeatsa(x,A)) (y)((y S) & defeatsa(y,x))).

• A set S of arguments is conflict-free for audience a if

(x) (y)(( xS & y S)

(attacks(x,y) valpref(val(y),val(x) valprefa))).

• A conflict-free set of arguments S is admissible for audience a if

(x)(xS acceptablea(x,S)).

Preferred Extension of an AVAF• A set of arguments S in an value-

based argumentation framework is a preferred extension for audience a if it is a maximal (with respect to set inclusion) admissible for audience a set of AR.

Objective Acceptance

• An argument is objectively acceptable if it is in the preferred extension for every audience

• An argument if subjectively acceptable if it is in the preferred extension for some audience

• An argument is indefensible if it is no preferred extension of any audience

Two Valued Three Cycle

a

bc

If blue > red, preferredextension is {a,b}

If red > blue, preferred extension is {b,c}

Note: b is in the preferred extension whateverthe value order

Two Valued Four CycleConnected Colours

a

b

c

d

If blue > red, preferred

extension is {a,c}

If red > blue, preferred

extension is {a,c}

Preferred extension is unique, AND independent

of value order

Some Technical Results on VAFS• If there are no cycles with a single value,

then there is a unique preferred extension– Efficient algorithm to find the preferred

extension

• Cycles can give rise to objective acceptance– Odd cycles with more than one value– Some configurations of even cycles

• Possibilities to prune lines of argument with repeating values

• Heuristics to select attacks

Note: what causes difficulties withoutvalues is a source ofObjective Acceptancewith them

Recall that there were Cycles in our Animals Cases

A

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

How does

considering

values help?

PiersonA

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

A: Pierson Had A RightTo the Animal

B: Pierson hadNo possession

E: Pierson was infull pursuit

I: Pursuit not Enough

O: Seizure notnecessary (wewant to encourage sociallyuseful activity)

M: we must insist onpossession for clear law

M and Oform a2-cycle:resolvedby Value

So A isSubjectivelyacceptable

Blue: Need clear law

Orange: Encourage useful activity

Keeble IA

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

Green: Protect property rights C: owns the land sopossesses the animals

D: Animals not confined

X: Unbrandedanimals belongto landowner.Not needed:Useless if bluegreater than greenUnnecessary else

Keeble IIA

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

Red: Promote economic activity F: Keeble was pursuinghis livelihood

YoungA

S

F CB

G H D

E I

J K L

M[P]

O[R]

Q

TU V

W

X

Y

Z

N

Purple: Restrictive view of role of courtsS: Defendant in CompetitionT: Competition wasUnfair

U: Not for theCourt to ruleon what is unfaircompetition

U breaksthe evencycleBTSEB

Without UB is defeatedby itsposition in the evencycle

Note: 4 cycleBTSEBTE objectivelyacceptable

Schema For Persuasive Argument• To consider individual arguments we

need to look inside the nodes to see what an argument looks like and how it can be attacked

• We have developed a general schema for persuasive argument in practical reasoning

• This schema can be applied to reasoning with legal cases

Form of Justification of An Action• It was right to do action A• In those circumstances R• To bring about these new

circumstances S• Which realised this goal G• Which promoted this value V

Schematically

R S G V A

Effect of anaction dependson the situation

The goal is the subsetof S that we wanted tobring about, the reason wedid A

The value is the purposefor which we wanted torealise the goal

We refer to a justification of this form as a position

Attacking A Position

• A position can be attacked in a variety of ways:– Denial of an element

• E.g. A will not produce S from R

– Contradiction of an element• E.g. G promotes W not V

– Alternatives• E.g. B will also produce S from R

– Side Effects• E.g. G demotes W as well as promoting V

We have identified 15 possible attacks – some with variants

Law As Practical Reasoning• We need to choose one of two actions

– Decide for the plaintiff– Decide for the defendant

• Circumstances are the case facts + a record of the decision

• Goals are subsets of the facts + a record of the decisions

• Values are behaviours to encourage and discourage

Note: we see the judgement as a choice of actionNot the identification of a property of the case

To Illustrate

F1 F2 F3 … Fn Pwins Dwins

F1 F2 F3 … Fn Pwins Dwins

1 0 0 1 0 0

1 0 0 1 1 0

Undecided Case

Deciding for P produces

Decided Case

F1 F2 F3 … Fn Pwins Dwins

0 1 1 0

Goal

Encourages potential plaintiffs to realise Fn and not F2

selection fromdecided case

In this Representation

• 7 of the 15 attacks are not possible• 2 pairs of attacks are identical

– Only two actions– Actions always achieve the same result– Goals straightforward consequences of

decided case– Distinct actions realise distinct goals

• One attack has two distinct variants• Thus we can look for seven distinct

forms of attack

Attacks and Argument Moves

• Two challenge the representation– Factors used to represent a case– Values associated with factors

• Four are variants of distinguishing a case

• One seems to be in neither HYPO nor CATO: disagreement as to which value is promoted in this context

Four Types of Distinction

• Precedent stronger: can be downplayed

• Current case weaker: can be downplayed

• Precedent stronger: can be emphasised

• Current case weaker: can be emphasised

A single movein HYPO

Two moves inCATO

Counter Examples

• A different position based on another precedent justifying the other action– Can be attacked in the same ways as the

original position

• A rebuttal of the choice of goal– Same factors as G, but different outcome– Can only be met by reformulating the goal– Like a trumping counter example in HYPO

Summary

• We have seen– How arguments differ from proof– Two systems for case based argument in AI

and Law– Arguments based on conflicting rules– Reasoning about sets of arguments– Argument schemes– How notions of value and purpose can be

used