formal models of argumentation

8/16/2019 Formal models of argumentation

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Introduction to formalmodels of argumentation

Henry PrakkenDundee (Scotland)

September 4 th , 2 !4


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"hat is argumentation#$i%ing reasons to supportclaims that are open to doubtDefending these claimsagainst attack&' Inference dialogue


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"hy study argumentation#In linguistics

*rgumentation is a form of language use

In *rtificial Intelligence+ur applications ha%e humans in the loop"e ant to model rational reasoning but ith standardsof rationality that are attainable by humans*rgumentation is natural for humans

-rade.off bet een rationality and naturalness

In /ulti.*gent Systems*rgumentation is a form of communication


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-oday formal models of

argumentation*bstract argumentation*rgumentation as inference0rame orks for structuredargumentation

Deducti%e %s1 defeasible inferences*rgument schemes

*rgumentation as dialogue


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"e should lo er ta es

3o erta esincreaseproducti%ity

Increasedproducti%ity isgood


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"e should not lo er ta es

3o erta esincreaseine uality

Increasedine uality isbad

*ttackonconclusion


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3o er ta esdo notincreaseproducti%ity

5S*lo eredta es butproducti%itydecreased

*ttackonpremise6


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Prof1 Psays that6

Prof1 Phaspoliticalambitions

Peopleith

politicalambitionsare not

ob7ecti%e

Prof1 P isnotob7ecti%e


*ttackon

inference


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Prof1 Psays that6


Peopleith


ob7ecti%e




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Prof1 Psays that6


Peopleith


ob7ecti%e


Increasedine uality isgood

Increasedine ualitystimulatescompetiti

on

8ompetition isgood



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A B

C D E

P1/1 Dung, +n the acceptability of arguments and its

fundamental role in nonmonotonic reasoning, logicprogramming, and n9person games1


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A B

C D E

!1 *n argument is In iff all arguments that attac21 *n argument is Out iff some argument that atta$rounded semantics minimises InlabellingPreferred semantics maximises InlabellingStable semantics labels all nodes


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A B

C

Stable semantics labels all nodes

$rounded semantics minimises InlabellingPreferred semantics maximises Inlabelling

!1 *n argument is In iff all arguments that attac21 *n argument is Out iff some argument that atta


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A B

C





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A B

C





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A B

C





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A B

C

D





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D

A B

C





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Difference bet eengrounded

and preferred labellings

A B

C

D

!1 *n argument is In iff all arguments that attack21 *n argument is Out iff some argument that attack

* ? /erkel is $erman since she has a $erman nam' ? /erkel is 'elgian since she is often seen i

8 ? /erkel is a fan of +ran7e since she ears a (unless she is $erman or 'elgian)D ? /erkel is not a fan of +ran7e since she loo someone ho does not like football

($eneralisations are left implicit)


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-he grounded labelling

A B

C

D



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-he preferred labellings

A B

C

D

A B

C

D



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@ustification status ofarguments

* is 7ustified if * is In in alllabellings

* is o%erruled if * is Out in alllabellings* is defensible other ise

* t t t i


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*rgument status ingrounded and preferred

semantics

A B

C

D

A B

C

D

A B

C

D

$rounded semanticsall arguments defensible

Preferred semantics* and ' defensible

8 o%erruledD 7ustified


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3abellings ande tensions

$i%en an argumentation frame ork AF ? Args,attack

S ⊆ Args is astableApreferredAgrounded argumente tension iff S ? In for somestableApreferredAgroundedlabelling


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$rounded e tension

A is acceptable rt S (or S defends A ) ifall attackers of A are attacked by S

S attacks A if an argument in S attacks A

3et AF be an abstract argumentationframe ork

F 0 AF ? ∅F i+1 AF ? B A ∈ Args C A is acceptable rt F i AF

F ∞ AF ? ∪ ∞i=0 ( F i+1 AF )If no argument has an infinite number ofattackers, then F ∞ AF is the groundede tension of *0 (other ise it is included)


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S d f d * if ll k f *


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A B

C D E

S defends * if all attackers of *are attacked by a member of S

F 1 ? B*F 2 ? B*,D

S d f d * if ll k f *


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A B

C D E


F 1 ? B*F 2 ? B*,D

F 3 ? F 2

S d f d * if ll d f t f *


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A B

C D E

S defends * if all defeaters of *are attacked by a member of S

S is admissible if it isconflict.free and defends all itsmembers

$rounded


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Stable e tensions

Dung (!==


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Preferred e tensionsDung (!==


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A B

C D E



*dmissible#

S defends * if all defeaters of *


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A B

C D E



*dmissible#



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A B

C D E



*dmissible#



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A B

C D E



*dmissible#



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A B

C D E



Preferred# S is preferred iit is ma imallyadmissible



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A B

C D E






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A B

C D E

S defends if all defeaters of are attacked by a member of S




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Proof theory for

abstract argumentation*rgument games bet een proponent P and opponent O

Proponent starts ith an argument-hen each party replies ith asuitable attacker* inning criterion

>1g1 the other player cannot mo%e

*cceptability status corresponds toe istence of a inning strategy1


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Strategies* strategy for player p is a partial game tree

>%ery branch is a game (se uence of allo able mo%es)-he tree only branches after mo%es by p

-he children of p

Fs mo%es are all the legal mo%es bythe other player

4;

P: A

O: B

P: D

O: C

O: F O: G

P: E

P: H


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Strategies* strategy for player p is inning iff

p ins all games in the strategy3et S be an argument game A is S.pro%able iff P has a inning strategyin an S.game that begins ith A

44


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-he $.game for grounded

semantics* sound and complete game

>ach mo%e must reply to the pre%iousmo%eProponent cannot repeat his mo%esProponent mo%es strict attackers,opponent mo%es attackers* player ins iff the other player

cannot mo%e

Proposition: A is in the groundede tension iff * is $.pro%able

4<


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*n attack graphA

B

C

D

E

F

4G


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* game treeP: A

A

B

C

D

E

F m !e

4:


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* game treeP: A

A

B

C

D

E

F

O: F

m !e

4


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* game treeP: A

A

B

C

D

E

F

O: F

P: E

m !e

4=


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* game treeP: A

O: B

A

B

C

D

E

F

O: F

P: E

m !e

<


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* game treeP: A

O: B

P: C

A

B

C

D

E

F

O: F

P: E

m !e


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* game treeP: A

O: B

P: C

O: D

A

B

C

D

E

F

O: F

P: E

m !e


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* game treeP: A

O: B

P: C P: E

O: D

A

B

C

D

E

F

O: F

P: E

m !e


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> ercise


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Eesearch on abstract

argumentation&e semantics*lgorithms

0inding labellings (e tensions)$ames

8omple ityDynamics (adding or deleting arguments or attacks)*ddition of ne elements to *0s

abstract support relationspreferences

Eeasons to be scepticalS1 /odgil J H1 Prakken, Eesolutions in structured*rgumentation1 In Pr cee"ings f #O$$A 2012 1H1 Prakken, Some reflections on t o current trends in formalargumentation1 In Festsc%rift f r $arek Serg t , Springer2 !21 H1 Prakken, +n support relations in abstract argumentation asabstractions of inferential relations1 In Pr cee"ings AI201'


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*rguing about attack

relationsStandards for determining defeatrelations are often

Domain.specificDefeasible and conflicting

So determining these standards isargumentation K

Eecently /odgil (*I@ 2 =) hase tended DungFs abstract approach*rguments can also attack attackrelations


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C

T

B

odgil 2 =

"ill it rain in

8alcutta#

''8saysrain 8&&

sayssun

-rust ''8 more than 8&&


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C

T

B

S

odgil 2 =

"ill it rain in

8alcutta#

''8saysrain 8&&

sayssun

-rust ''8 more than 8&&

Stats say 8&& better than ''8


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A B

C D E

A B


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Prof1 Psays that6


Peopleith

politicalambitionsare notob7ecti%e



Increasedine ualitystimulatescompetition

8ompetition isgood


C

E

D


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G4

-he ultimate status of

conclusions of arguments*rguments

* is 7ustified if * is In in all labellings* is o%erruled if * is Out in all labellings* is defensible other ise

8onclusionsφ is 7ustified if φ is the conclusion of some 7ustifiedargumentφ is defensible if φ is not 7ustified and φ is theconclusion of some defensible argumentφ is o%erruled if φ is not 7ustified or defensible andthere e ists an o%erruled argument for φ

@ustification is nonmonotonic K8n o%er 3 is monotonic iff for all p ∈ 3, S,SF ⊆ 3 Ifp ∈ 8n(S) and S ⊆ SF then p ∈ 8n(SF)

- o accounts of


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G<

o accounts ofthe fallibility

of argumentsPlausible Eeasoning all fallibilitylocated in the premises

*ssumption.based argumentation (Lo alski,

Dung, -oni,68lassical argumentation (8ayrol, 'esnard,Hunter, 6)

Defeasible reasoning all fallibilitylocated in the inferences

Pollock, 3oui, Mrees i7k, Prakken J Sartor,De3P, 6*SPI8 combines these accounts


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N&onmonotonicO %1

NDefeasibleO&onmonotonicity is a propertyof conse uence notions

Defeasibility is a property ofinference rules

*n inference rule is defeasible ifthere are situations in hich itsconclusion does not ha%e to beaccepted e%en though all itspremises must be accepted1

Eationality postulates


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Eationality postulatesfor structuredargumentation

> tensions should be closedunder subarguments-heir conclusion sets shouldbe

8onsistent8losed under deducti%einference

/1 8aminada J 31 *mgoud, +n the e%aluation of argumentation formalisms1Artificial Intelligence !:! (2 :) 2 G.;!

-he base logicF


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gapproach

(Hunter, 8+//* 2 ! )

*dopt a single base logicDefine arguments asconse uence in the adoptedbase logic-hen the structure ofarguments is gi%en by thebase logic


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8lassical argumentation('esnard, Hunter, 6)

*ssume a possibly inconsistent L' inthe language of classical logic

*rguments are classical proofs fromconsistent (and subset.minimal) subsetsof the L'Marious notions of attackPossibly add preferences to determine

hich attacks result in defeat>1g1 /odgil J Prakken, *[email protected] !;1*pproach recently abstracted to-arskian abstract logics

*mgoud J 'esnard (2 =.2 !;)


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8lassical argumentationformalised

$i%en 3 a propositional logical language and C.standard.logical conse uence o%er 3*n argument is a pair (S,p) such that

S ⊆ 3 and p ∈ 3S C. pS is consistent&o SF ⊂ S is such that SF C. p

Marious notions of attack, e1g1NDirect defeat O argument (S,p) attacks argument (SF,pF) iffp C. Q for some ∈ SF

NDirect undercut O argument (S,p) attacks argument (SF,pF)iff p ? Q for some ∈ SF+nly these t o attacks satisfy consistency, soclassical argumentation is only optimal forplausible reasoning

/odelling default


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:!

greasoning in classical

argumentation

Ruakers are usually pacifistEepublicans are usually not pacifist

&i on as a uaker and a republican


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:;

* modelling in classicallogic

Ruaker ⊃ PacifistEepublican ⊃ → QPacifist0acts Ruaker, Eepublican

Pacifist

Ruaker Ruaker ⊃ Pacifist

QPacifist

Eepublican Eepublican ⊃ QPacifis

Q(Ruaker ⊃ Pacifist)


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:4


Ruaker J Q*b! ⊃ PacifistEepublican J Q*b2 ⊃ → QPacifist0acts Ruaker, Eepublican*ssumptions Q*b!, Q*b2 ( attackable )

Pacifist

Ruaker Q*b!

QPacifist

Q*b2 EepublicanRuaker J Q*b!⊃ PacifistEepublican J Q*b2

⊃ QPacifist

*b!


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:<


Ruaker J Q*b! ⊃ PacifistEepublican J Q*b2 ⊃ → QPacifist0acts Ruaker, Eepublican*ssumptions Q*b!, Q*b2 ( attackable )

Pacifist

Ruaker Q*b!

QPacifist

Q*b2 EepublicanRuaker J Q*b!⊃ Pacifist

Eepublican J Q*b2⊃ QPacifist

*b!*b2

i %1 i l


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> tensions %1 ma imalconsistent subsets

"ith classical (and -arskian) argumentationpreferred and stable e tensions and ma imalconflict.free sets coincide ith ma imalconsistent subsets of the kno ledge base

8ayrol (!==


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Rs : R d:Ln ? Bp, L p ?


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:

t

r s

p

r, s → t ∈ E s

p, ⇒ r ∈ E d

r,s → tp, ⇒ r

Bs


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( ith t i


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( ith symmetricnegation)

0or any S ⊆ 3S is (directly) consistent iffS does not contain t oformulas φ and 9φ 16


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!

Eationality postulatesfor *SPI8

Subargument closure al ays satisfied8onsistency and strict closure

ithout preferences satisfied if

Es closed under transposition or closed undercontraposition andLn is indirectly consistent

ith preferences satisfied if in addition theargument ordering is reasonableF

Mersions of the eakest. and last link orderingare reasonable

So *SPI8 is good for both plausible anddefeasible reasoning


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- o uses of defeasible

rules0or domain.specific informationDefeasible generalisations, norms, 6

0or general patterns ofpresumpti%e reasoningPollockFs defeasible reasons

perception, memory, induction,

statistical syllogism, temporalpersistence

*rgument schemes

Domain.specific %s1f l


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;

pinference general

inference rulesd! 'ird ⇒ 0liess! Penguin → 'irdPenguin ∈ L

Ed ? B φ , φ ψ ⇒ ψ Es ? all %alid inference

rules of prop1 l1'ird 0lies ∈ LPenguin ⊃ 'ird ∈ LPenguin ∈ L

0lies

'ird

Penguin

0lies

'ird 'ird 0lies

Penguin Penguin ⊃ 'ird

Preferred e tensions dol i id i h


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4

not al ays coincide ithmcs

r! Ruaker ⇒ Pacifistr2 Eepublican ⇒ QPacifistS → p ∈ E s iff S C. p in Prop1 3 and S is finite

L Ruaker, Eepublican

Pacifist

Ruaker

¬ Pacifist

Eepublican

r! r2

PreferredAstablei d l


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<

e tensions do not al ayscoincide ith mcs

Pacifist

Ruaker

¬ Pacifist

EepublicanA1

A2

B1

B2

>! ? B*!,*2,'!,6

>2 ? B*!,'!,'2,6

PreferredAstablei d l


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G

e tensions do not al ayscoincide ith mcs

Pacifist

Ruaker

¬ Pacifist

EepublicanA1

A2

B1

B2

8onc(>!) ? -h(BRuaker, Eepublican, Pacifist )

8onc(>2) ? -h(BRuaker, Eepublican, QPacifist )

mcs(L) ? BBL ? BBRuaker, Eepublican


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8an defeasible reasoningb d d l ibl


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be reduced to plausiblereasoning#

-o classical argumentation#Problems ith contrapositi%einferences

-o assumption.based argumentation#Problems ith preferences

In both casesless comple metatheorybut more comple representations

Default contrapositioni l i l


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in classicalargumentation

/en are usually not rapists1

@ohn is a rapist*ssume hen possible that thingsare normal

"hat can e conclude about @ohnFsse #



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/en are usually not rapists/ J Q*b ⊃ QE

@ohn is a rapist ( E)*ssume hen possible that thingsare normal

Q*b



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/en are usually not rapists/ J Q*b ⊃ QE

@ohn is a rapist ( E)*ssume hen possible that thingsare normal

Q*b

-he first default implies thatrapists are usually not menE J Q*b ⊃ Q/

So @ohn is not a man



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Heterose ual adults are usuallynot married ?T

&on.married adults are usually notheterose ual

-his type of sensor usually doesnot gi%e false alarms ?T

0alse alarms are usually not gi%en bythis type of sensor

Statisticians callthese inferences N base

*ssumption.based


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argumentation (Dung,/ancarella J -oni 2 :)

* deducti%e system is a pair (3, E) here3 is a logical languageE is a set of rules ( φ ! , 111, φ n → φ ) o%er 3

*n assumption.based argumentation frame orkis a tuple (3, E, *, U) here

(3, E) is a deducti%e system* ⊆ 3, * V ∅, a set of assumptions&o rule has an assumption as conclusionU is a total mapping from Po (3) into 31 Ua isthe contrary of a1

*n argument S C. p is a deduction of p froma set S ⊆ *1*rgument S C. p attacks argument SF C.pFiff p ? U for some ∈ SF

Eeduction of *SPI8 defeasiblel *'* l (D J h


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rules to *'* rules (Dung J -hang,@*IE 2 !4)

*ssumptions3 consists of literals&o preferences&o rebuttals of undercutters

p ! , 6, p n ⇒

becomes

d i , p ! , 6, p n, notQ →

hered i ? n(p ! , 6, p n ⇒ )

d i ,notQ are assumptions ? Unot ? UQ Q ? U

!.!correspondence

bet een completee tensions of

*SPI8 and *'*

0 d f ibl t


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=<

0rom defeasible tostrict rules e ample

r! Ruaker ⇒ Pacifistr2 Eepublican ⇒ QPacifist

Pacifist

Ruaker

¬ Pacifist

Eepublican

r! r2


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8 *SPI8 f b d d


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8an *SPI8 preferences be reducedto *'* assumptions#

d! 'ird ⇒ 0liesd2 Penguin ⇒ Q0liesd! W d2

'ecomes

d! 'ird, notPenguin ⇒ 0lies

d2 Penguin ⇒ Q0lies

+nly orks in specialcases, e1g1 not ith

eakest.link ordering

" h ld l " h ld l

A B


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Prof1 Psays that6


Peopleith

politicalambitionsare notob7ecti%e



Increasedine ualitystimulatescompetition

8ompetition isgood


C

E

D


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A B

C D E


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A B

C D E

A’


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A B

C D E

A’

P1 P2 P3 P4

P8 P9P7P P!

Preferences in


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Preferences inabstract argumentationP*0s e tend ( args , attack ) to ( args,attack ,≤a)

≤a is an ordering on args

* "efeats ' iff * attacks ' and not * W '*pply DungFs theory to ( args,"efeat )

Implicitly assumes that*ll attacks are preference.dependent*ll attacks are independent from each other

*ssumptions not satisfied in general ?TProperties not inherited by all instantiationspossibly %iolation of rationality postulates

! 2

E! If you snore, you misbeha%eE2 If you snore hen nobody else is around, you donFt mis

f


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! ;

@ohn does notmisbeha%e in thelibrary

@ohn snores hennobody else is in

the library

@ohn misbeha%esin the library

@ohn snores inthe library

@ohn may be

remo%ed

E; If you misbeha%e in the library, the librarian may remo

E! W E2 W E;

E! E2

E;

E! If you snore, you misbeha%eE2 If you snore hen nobody else is around, you donFt mis

f b h h l b h l b


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! 4



the library



@ohn may be

remo%ed


E! W E2 W E;

E! E2

E;

E! W E2

E! If you snore, you misbeha%eE2 If you snore hen nobody else is around, you donFt misE If i b h % i h lib h lib i


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! <



the library



@ohn may be

remo%ed


E! W E2 W E;

E! E2

E;

A1

A2

A3

B1

B2



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! G


E! W E2 W E; so *2 W '2 W *; ( ith last link)

A1

A2

A3

B1

B2

-he defeat graphin *SPI8



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! :



A1

A2

A3

B1

B2

-he attack graphin P*0s


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E! If you snore, you misbeha%eE2 If you snore hen nobody else is around, you donFt misE If i b h % i th lib th lib i


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! =



the library


@ohn Snores inthe library

@ohn may be

remo%ed



E! E2

E;

E! If you snore, you misbeha%eE2 If you snore hen nobody else is around, you donFt misE; If o misbeha%e in the librar the librarian ma remo


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!!



A1

A2

A3

B1

B2

P*0s donFtrecogni e that '2Fs

attacks on*2 and *; are the

same

"ork outside the Dung


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ork outside the Dungparadigm

Defeasible 3ogic Programming(Simari et al1)

*rguments roughly as in *SPI8 but noDung semantics

8arneades ($ordon et al1)*rguments pro and con a claim

*bstract Dialectical 0rame orks('re ka J "oltran)6

*rgument(ation) schemes


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!!2

general form

'ut also critical uestions

Premise !,6 ,

Premise n-herefore (presumably), conclusi

*rgument schemes in


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!!;

rgument schemes in*SPI8

*rgument schemes are defeasibleinference rules

8ritical uestions are pointersto counterargumentsSome point to undermining attacksSome point to rebutting attacksSome point to undercutting attacks

Eeasoning ith default


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!!4

Eeasoning ith defaultgeneralisations

'ut defaults can ha%e e ceptions*nd there can be conflicting defaults

PIf P then normallyAusuallyAtypically RSo (presumably), R

. "hat e perts say is usually true

. People ith political ambitions are usually not ob7ecti%e

. People ith names typical from country 8 usually ha%e nati

. People ho flea from a crime scene hen the police arri%esnormally in%ol%ed in the crime

. 8hinese people usually donFt like coffee


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Perception

8ritical uestions*re the obser%erFs senses +L#*re the circumstances such thatreliable obser%ation of P isimpossible#6

P is obser%ed

-herefore (presumably), P


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!!G

Inducing generalisations

8ritical uestionsIs the si e of the sample large enough#

as the sample selection biased #

*lmost all obser%ed PFs ere RFs-herefore (presumably), If Pthen usually R

In !G of !: tests theballpoint shot ith this bo

caused this type of eye in7ury

* ballpoint shot ith thistype of bo ill usually causethis type of eye in7ury

> pert testimony


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!!:

p y("alton !==G)

8ritical uestions

Is > biased#Is P consistent ith hat other e perts say#Is P consistent ith kno n e%idence#

> is e pert on D> says that P

P is ithin D-herefore (presumably), P is the ca

Supporting and using


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Supporting and usinggeneralisations

MFs in7ury as caused bya fall

-his type of eyein7ury is usuallycaused by a fall

M has this type ofin7ury

> says that his typeof in7ury is usually

caused by a fall

> is an e perton this type of

in7ury

> perttestimony

scheme

Defeasiblemodus

ponens


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!!=

*rguments from conse uences

8ritical uestionsDoes * also ha%e bad (good)conse uences#*re there other ays to bring about $#111

*ction * causes $,$ is good (bad)-herefore (presumably), * should (not)

8ombining multiple goodAbad


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8ombining multiple goodAbadconse uences

*ction *results in 8!6

*ction *results in 8n8! is good68n is good-herefore,*ction * is

good

*ction *results in 8!6*ction *results in 8n8! is bad

68m is bad-herefore,*ction * is bad


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H1 Prakken, 0ormalising alegal opinion on alegislati%e proposal inthe *SPI8 frame ork1

"C3


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BC12 "C2

C1

"C1

"C13

C3

P2D#P

P1

"C123

"C12

"C23

"C3!1 *n argument is In iff all

arguments

re errelabelling !


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BC12 "C2

C1

"C1

"C13

C3

P2D#P

P1

"C123

"C12

"C23

argumentsthat defeat it are Out 1

21 *n argument is Out iff someargument that defeats it isIn 1

"C3!1 *n argument is In iff all

arguments

re errelabelling 2


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BC12 "C2

C1

"C1

"C13

C3

P2D#P

P1

"C123

"C12

"C23

argumentsthat defeat it are Out 1

21 *n argument is Out iff someargument that defeats it isIn 1


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Summary* formal metatheory of structuredargumentation is emerging'etter understanding needed ofphilosophical underpinnings and practical applicability

&ot all argumentation can be naturally reducedto plausible reasoning-he one base logicF approach is only suitablefor plausible reasoning

Important research issues*ggregation of argumentsEelation ith probability theory


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> ampleP -ell me all you kno about

recent trading in e plosi%ematerials ( re uest )

P hy donFt you ant to tell me#P hy arenFt you allo ed to tell

me#

P Xou may be right in general( concede ) but in this casethere is an e ception since this is a matter of nationalimportance

P since e ha%e heard about apossible terrorist attack

P +L, I agree ( offer accepted) 1

+ &o I onFt ( re7ect )

+ since I am not allo ed to tellyou

+ since sharing such information

could endanger an in%estigation

+ "hy is this a matter ofnational importance#

+ I concede that there is ane ception, so I retract that Iam not allo ed to tell you1 I

ill tell you on the condition that you donFt e change theinformation ith other policeofficers ( offer )


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recent trading in e plosi%ematerials (re uest)


me#

P Xou may be right in general(concede) but in this casethere is an e ception sincethis is a matter of nationalimportance


P +L, I agree (offer accepted)1

+ &o I onFt (re7ect)






ill tell you on the conditionthat you donFt e change theinformation ith other policeofficers (offer)


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recent trading in e plosi%ematerials (re uest)


me#

P Xou may be right in general(concede) but in this casethere is an e ception sincethis is a matter of nationalimportance


P +L, I agree (offer accepted)1

+ &o I onFt (re7ect)






ill tell you on the conditionthat you donFt e change theinformation ith other policeofficers (offer)

-ypes of dialogues


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("alton J Lrabbe) Dialogue Type Dialogue Goal Initial situation

Persuasi n resolution ofconflict

conflict ofopinion

-eg tiati n making a deal conflict ofinterest

.eli/erati n reaching a

decision

need for

actionInf rmati nseeking

e change ofinformation

personalignorance

I n uir gro th ofkno ledge

generalignorance

Dialogue systems(according to 8arlson


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( g!= ;)

Dialogue systems define the conditionsunder hich an utterance is appropriate*n utterance is appropriate if it promotesthe goal of the dialogue in hich it ismade

*ppropriateness defined not at speech actle%el but at dialogue le%el

Dialogue game approachProtocol should promote the goal of the dialogue

Dialogue game


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systems* communication language

"ell.formed utterances

Eules for hen an utterance isallo ed

Protocol

>ffect rules

-urntaking rules-ermination outcome rules

*gent designstrategies for selecting from the allo ed utteranc


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>ffect rulesSpecify commitments

N8laim pO and N8oncede pO commits to pNp since RO commits to p and RNEetract pO ends commitment to p111

8ommitments used for

Determining outcome>nforcing dialogical consistencyF111

Public semantics for


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dialogue protocolsPublic semantics can protocolcompliance be e ternally obser%ed #8ommitments are a participantFs publiclydeclared standpoints, so not the same asbeliefsK+nly commitments and dialogicalbeha%iour should count for mo%elegality

N8laim p is allo ed only if you belie%e pO %s1N8laim p is allo ed only if you are notcommitted to ¬ p and ha%e not challenged pO

/ore and less strict


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/ore and less strict

protocolsSingle.multi mo%e one or more mo%es perturn allo edSingle.multi.reply one or more replies

to the same mo%e allo edDeterministic no choice from legalmo%esDeterministic in communication language

no choice from speech act types+nly reply to mo%es from pre%ious turn#

Some properties that can


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be studied

8orrespondence ith playersFbeliefs

If union of beliefs implies p,canA ill agreement on p result#If players agree on p, doesunion of beliefs imply p#Disregarding %s1 assuming playerstrategies


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> ample !

Paul r

+lga s

p ⇒ r ⇒ p

s ⇒ ¬ r

Lno ledge bases Inference rules

P! since p

Paul ∪ +lga does not7ustify but they

could agree on

+lga is credulous sheconcedes e%erything

for hich she cannotconstruct a

(defensible or

7ustified)


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> ample !

Paul r

+lga s

p ⇒ r ⇒ p

s ⇒ ¬ r


P! since p


could agree on

+! concede p,


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> ample !

Paul r

+lga s

p ⇒ r ⇒ p

s ⇒ ¬ r


P! since p


could agree on

+lga is sceptical shechallenges e%erything for

hich she cannotconstruct a (defensibleor 7ustified) argument


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> ample !

Paul r

+lga s


P! since p

+! hy p#

p ⇒ r ⇒ p

s ⇒ ¬ r


could agree on


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> ample !

Paul r

+lga s


P! since p

+! hy p#

P2 p since r

p ⇒ r ⇒ p

s ⇒ ¬ r


could agree on


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> ample !

Paul r

+lga s


P! since p

+! hy p#

+2 ¬ r since s

P2 p since r

p ⇒ r ⇒ p

s ⇒ ¬ r


could agree on


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> ample 2

Paulp

+lgap⊃ ¬ p


P! claim p/odusponens

6

Paul ∪ +lga does not 7ustify pbut they ill agree on p if

players are conser%ati%e , that


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> ample 2

Paulp

+lgap⊃ ¬ p


P! claim p

+! concede p

/odusponens

6

Paul ∪ +lga does not 7ustify pbut they ill agree on p if

players are conser%ati%e , that


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l


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> ample 2

Paulp

+lgap⊃ ¬ p


P! claim p

+! hat about #

/odusponens

6

P2 claim

Possible solution (foropen.minded agents, ho

are prepared to

l


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> ample 2

Paulp

+lgap⊃ ¬ p


P! claim p

+! hat about #

/odusponens

6

P2 claim

+2 ¬ p since , ⊃ ¬ p Possible solution (foropen.minded agents, ho

are prepared to

Problem ho toensure rele%ance#

*utomated Support ofEegulated Data


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Eegulated Data

> change1 * /ulti.*gent Systems *pproach

PhD -hesis Pieter Di7kstra(2 !2)

0aculty of 3a5ni%ersity of $roningen

-he communication


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languageSp$$c% act Attack Surrenderre uest( ϕ) offer ( ϕF), re7ect( ϕ) .

offer( ϕ) offer( ϕF) ( ϕ V ϕF),re7ect( ϕ)

accept( ϕ)

re7ect( ϕ) offer( ϕF) ( ϕ V ϕF),hy.re7ect ( ϕ)

.

accept( ϕ) . .

hy.re7ect( ϕ) claim ( ϕF) .

claim( ϕ) hy( ϕ) concede( ϕ)

hy( ϕ) ϕ since S (an argument) retract( ϕ)

ϕ since S hy( ϕ) ( ϕ ∈ S)ϕF since SF (adefeater)

concede( ϕ)concede ϕF ( ϕF ∈ S)

concede( ϕ) . .

retract( ϕ) . .

den . .

h l


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-he protocolStart with a requestRepy to an earlier move of the other agentPick your replies from the table

Finish persuasion before resuming negotiationTurntaking :

In nego: after each moveIn pers: various rules possible

Termination :In nego: if offer is a ccepted or someone withdrawsIn pers: if main claim is r etracted or conceded

> ample dialogueformalised


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formalisedP Ee uest to tell

+ Ee7ect to tell

P "hy re7ect to tell#

>mbeddedpersuasion

111

+ +ffer to tell if no further e change

P *ccept after tell no further e change

Persuasion partformalised


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formalised+ Claim &ot allo ed to tell



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P Why not allo ed to tell#



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+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed



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P Concede "hat endangers anin%estigation is not allo ed



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P > ception to E! since &ational impJ &ational importance ⇒ > ception to


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+ Why &ational importance#

P &ational importance since -erroris-errorist threat ⇒ &ational importan




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+ Concede > ception to E!



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+ Concede > ception to E!

+ Retract &ot allo ed to te

8onclusion


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8onclusion*rgumentation has t o sides

Inferencesemanticsstrict %s defeasible inferences

preferencesDialogue

language protocolagent design

'oth sides can be formally andcomputationally modelled

'ut not in the same ay/etatheory of inference much more ad%ancedthan of dialogue

Eeading (!)


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Eeading (!)8ollections

-1@1/1 'ench.8apon J P1>1 Dunne (eds1), ArtificialIntelligence !:! (2 :), Special issue on *rgumentationin *rtificial IntelligenceI1 Eah an J $1E1 Simari (eds1), Argumentati n in

Artificial Intelligence 1 'erlin Springer 2 =1*1 Hunter (ed1), Argument an" # mputati n < (2 !4),special issue on -utorials on Structured *rgumentation

*bstract argumentationP1/1 Dung, +n the acceptability of arguments and itsfundamental role in nonmonotonic reasoning, logic

programming and n.person games1 Artificial Intelligence :: (!==


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Eeading (;)


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Eeading (;)*ssumption.based argumentation

*1 'ondarenko, P1/1 Dung, E1*1 Lo alski J 01 -oni, *n abstract,argumentation.theoretic approach to default reasoning,

Artificial Intelligence =; (!==:) G;.! !1P1/1 Dung, P1 /ancarella J 01 -oni, 8omputing ideal scepticalargumentation, Artificial Intelligence !:! (2 :) G42.G:41

DialogueS1 Parsons, /1 "ooldridge J 31 *mgoud, Properties andcomple ity of some formal inter.agent dialogues1 ) urnal f6 gic an" # mputati n !; (2 ;) ;4:.;:G1H1 Prakken, 8oherence and fle ibility in dialogue games forargumentation1 ) urnal f 6 gic an" # mputati n !< (2

formal models of argumentation

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