Download - 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 lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
*ttackonconclusion
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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
5S*lo eredta es butproducti%itydecreased
*ttackonpremise6
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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
Prof1 Psays that6
Prof1 Phaspoliticalambitions
Peopleith
politicalambitionsare not
ob7ecti%e
Prof1 P isnotob7ecti%e
5S*lo eredta es butproducti%itydecreased
*ttackon
inference
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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
Prof1 Psays that6
Prof1 Phaspoliticalambitions
Peopleith
politicalambitionsare not
ob7ecti%e
Prof1 P isnotob7ecti%e
5S*lo eredta es butproducti%itydecreased
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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
Prof1 Psays that6
Prof1 Phaspoliticalambitions
Peopleith
politicalambitionsare not
ob7ecti%e
Prof1 P isnotob7ecti%e
Increasedine uality isgood
Increasedine ualitystimulatescompetiti
on
8ompetition isgood
5S*lo eredta es butproducti%itydecreased
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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
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
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
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
D
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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D
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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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
!1 *n argument is In iff all arguments that attack21 *n argument is Out iff some argument that attack
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-he preferred labellings
A B
C
D
A B
C
D
!1 *n argument is In iff all arguments that attack21 *n argument is Out iff some argument that attack
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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
S defends * if all attackers of *are attacked by a member of S
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
S defends * if all attackers of *are attacked by a member of S
S is admissible if it isconflict.free and defends all itsmembers
*dmissible#
S defends * if all defeaters of *
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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
*dmissible#
S defends * if all defeaters of *
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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
*dmissible#
S defends * if all defeaters of *
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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
*dmissible#
S defends * if all defeaters of *
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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
Preferred# S is preferred iit is ma imallyadmissible
S defends * if all defeaters of *
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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
Preferred# S is preferred iit is ma imallyadmissible
S defends * if all defeaters of *
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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
Preferred# S is preferred iit is ma imallyadmissible
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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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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
Prof1 Psays that6
Prof1 Phaspoliticalambitions
Peopleith
politicalambitionsare notob7ecti%e
Prof1 P isnotob7ecti%e
Increasedine uality isgood
Increasedine ualitystimulatescompetition
8ompetition isgood
5S*lo eredta es butproducti%itydecreased
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
* modelling in classicallogic
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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:<
* modelling in classicallogic
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 #
Default contrapositioni l i l
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in classicalargumentation
/en are usually not rapists/ J Q*b ⊃ QE
@ohn is a rapist ( E)*ssume hen possible that thingsare normal
Q*b
Default contrapositioni l i l
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in classicalargumentation
/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
Default contrapositioni l i l
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in classicalargumentation
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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"e should lo er ta es
3o erta esincreaseproducti%ity
Increasedproducti%ity isgood
"e should not lo er ta es
3o erta esincreaseine uality
Increasedine uality isbad
3o er ta esdo notincreaseproducti%ity
Prof1 Psays that6
Prof1 Phaspoliticalambitions
Peopleith
politicalambitionsare notob7ecti%e
Prof1 P isnotob7ecti%e
Increasedine uality isgood
Increasedine ualitystimulatescompetition
8ompetition isgood
5S*lo eredta es butproducti%itydecreased
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
@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! 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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! <
@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;
A1
A2
A3
B1
B2
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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! G
E; If you misbeha%e in the library, the librarian may remo
E! W E2 W E; so *2 W '2 W *; ( ith last link)
A1
A2
A3
B1
B2
-he defeat graphin *SPI8
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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! :
E; If you misbeha%e in the library, the librarian may remo
E! W E2 W E; so *2 W '2 W *; ( ith last link)
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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! =
@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; so *2 W '2 W *; ( ith last link)
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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!!
E; If you misbeha%e in the library, the librarian may remo
E! W E2 W E; so *2 W '2 W *; ( ith last link)
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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> 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 sincethis 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 conditionthat you donFt e change theinformation ith other policeofficers (offer)
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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 sincethis 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 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
Lno ledge bases Inference rules
P! since p
Paul ∪ +lga does not7ustify but they
could agree on
+! concede p,
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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 sceptical shechallenges e%erything for
hich she cannotconstruct a (defensibleor 7ustified) argument
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> ample !
Paul r
+lga s
Lno ledge bases Inference rules
P! since p
+! hy p#
p ⇒ r ⇒ p
s ⇒ ¬ r
Paul ∪ +lga does not7ustify but they
could agree on
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> ample !
Paul r
+lga s
Lno ledge bases Inference rules
P! since p
+! hy p#
P2 p since r
p ⇒ r ⇒ p
s ⇒ ¬ r
Paul ∪ +lga does not7ustify but they
could agree on
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> ample !
Paul r
+lga s
Lno ledge bases Inference rules
P! since p
+! hy p#
+2 ¬ r since s
P2 p since r
p ⇒ r ⇒ p
s ⇒ ¬ r
Paul ∪ +lga does not7ustify but they
could agree on
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> ample 2
Paulp
+lgap⊃ ¬ p
Lno ledge bases Inference rules
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
Lno ledge bases Inference rules
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
Lno ledge bases Inference rules
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
Lno ledge bases Inference rules
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
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
P Concede "hat endangers anin%estigation is not allo ed
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
P Concede "hat endangers anin%estigation is not allo ed
P > ception to E! since &ational impJ &ational importance ⇒ > ception to
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Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
P Concede "hat endangers anin%estigation is not allo ed
+ Why &ational importance#
P &ational importance since -erroris-errorist threat ⇒ &ational importan
P > ception to E! since &ational impJ &ational importance ⇒ > ception to
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
P Concede "hat endangers anin%estigation is not allo ed
+ Why &ational importance#
P &ational importance since -erroris-errorist threat ⇒ &ational importan
P > ception to E! since &ational impJ &ational importance ⇒ > ception to
+ Concede > ception to E!
Persuasion partformalised
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formalised+ Claim &ot allo ed to tell
P Why not allo ed to tell#
+ &ot allo ed to tell since telling endangers in%estigation J"hat endangers an in%estigation is not allo ed
P Concede "hat endangers anin%estigation is not allo ed
+ Why &ational importance#
P &ational importance since -erroris-errorist threat ⇒ &ational importan
P > ception to E! since &ational impJ &ational importance ⇒ > ception to
+ 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
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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 (;)*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