Argumentation in Artificial Intelligence

argumentation in artificial intelligence20 Years After Dung’s Work.

Federico Cerutti†

xxvi • vii • mmxv

† University of Aberdeen

P. BaroniU. Brescia

T. J. M. Bench-CaponU. Liverpool

C. CayrolIRIT

P. E. DunneU. Liverpool

M. GiacominU. Brescia

A. HunterUCL

H. LiU. Aberdeen

S. ModgilKCL

T. J. NormanU. Aberdeen

N. OrenU. Aberdeen

C. ReedU. Dundee

G. R. SimariU. Nacional der Sur

A. TonioloU. Aberdeen

M. VallatiU. Huddersfield

S. WoltranTU Wien

J. LeiteNew U. Lisbon

S. ParsonKCL

M. ThimmU. Koblenz

This tutorial was sponsored by the U.S. Army Research Laboratory and the U.K.Ministry of Defence, under Agreement Number W911NF-06-3-0001. The viewsand conclusions contained in this document are those of the author(s) andshould not be interpreted as representing the official policies, either expressedor implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K.Ministry of Defence or the U.K. Government. The U.S. and U.K. Governments areauthorized to reproduce and distribute reprints for Government purposesnotwithstanding any copyright notation hereon.

The tutor acknowledges the contribution of the Santander Universities Networkin supporting his travel

outline

∙ Introduction Why bother?

∙ Dung’s AF

Syntax, semantics, current state of research

∙ Argumentation Schemes

Arguments in human experience

∙ A Semantic-Web view of Argumentation

AIF, OVA+, and other tools

∙ Frameworks

Abstract, instantiated, probabilistic frameworks: kite-level view

∙ CISpaces

„One Ring to bring them all and in the darkness bind them”

∙ Algorithms and Implementations

…and how to choose among them

∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF Syntax, semantics, current state of research





∙ Frameworks


∙ CISpaces




∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF


∙ Argumentation Schemes Arguments in human experience



∙ Frameworks


∙ CISpaces




∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF




∙ A Semantic-Web view of Argumentation AIF, OVA+, and other tools

∙ Frameworks


∙ CISpaces




∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF






∙ Frameworks Abstract, instantiated, probabilistic frameworks: kite-level view

∙ CISpaces




∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF






∙ Frameworks


∙ CISpaces „One Ring to bring them all and in the darkness bind them”



∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF






∙ Frameworks


∙ CISpaces


∙ Algorithms and Implementations …and how to choose among them

∙ The frontier

outline

∙ Introduction

Why bother?

∙ Dung’s AF






∙ Frameworks


∙ CISpaces




∙ The frontier

what is missing

A lot

Dialogues

Argumentation and trust

Argumentation in multi-agent systems

Several approaches to represent arguments

Several extensions to Dung’s framework

Several frontier approaches

…

..why bother?

There is no milk in the shop and the milk you have is sour.

Beer Milk1 0

There is a coffee machine and fresh coffee in the cupboard.Beer makes you sick

Beer Milk Coffee?

0 0 1

There is fresh milk in your bag because you went to the shop earlier.The Principal is visiting later today, so you had better not alcohol

Beer Milk

0 1


There is a coffee machine and fresh coffee in the cupboard.Beer makes you sick

There is fresh milk in your bag because you went to the shop earlier.The Principal is visiting later today, so you had better not alcohol

Beer Milk Coffee?1 00 0 10 1

You should drink milk

You should drink beer


There is a coffee machine and fresh coffee in the cupboard.

Beer makes you sick

You should drink coffee

There is fresh milk in your bag because you went to the shop earlier.

The Principal is visiting later today, so you had better not

..dung’s argumentation framework

[Dun95]

Definition 1

A Dung argumentation framework AF is a pair

⟨A,→ ⟩

where A is a set of arguments, and→ is a binary relation on A i.e. →⊆ A×A.

A semantics is a way to identify sets of arguments (i.e. extensions)“surviving the conflict together”

(some) semantics properties

[BG07] [BCG11]


∙ Conflict-freeness (Def. 2)an attacking and an attacked argument can not stay together (∅ is c.f. by def.)

∙ Admissibility (Def. 5)

the extension should be able to defend itself, „fight fire with fire” (∅ is adm. by def.)

∙ Strong-Admissibility (Def. 7)

no self-defeating arguments (∅ is strong adm. by def.)

∙ Reinstatement (Def. 8)

if you defend some argument you should take it on board (∅ satisfies the principleonly if there are no unattacked arguments)

∙ I-Maximality (Def. 9)

no extension is a proper subset of another one

∙ Directionality (Def. 12)

a (set of) argument(s) is affected only by its ancestors in the attack relation


∙ Conflict-freeness (Def. 2)

an attacking and an attacked argument can not stay together (∅ is c.f. by def.)

∙ Admissibility (Def. 5)the extension should be able to defend itself, „fight fire with fire” (∅ is adm. by def.)














∙ Strong-Admissibility (Def. 7)no self-defeating arguments (∅ is strong adm. by def.)














∙ Reinstatement (Def. 8)if you defend some argument you should take it on board (∅ satisfies the principleonly if there are no unattacked arguments)














∙ I-Maximality (Def. 9)no extension is a proper subset of another one














∙ Directionality (Def. 12)a (set of) argument(s) is affected only by its ancestors in the attack relation





Beer makes you sick








Beer makes you sick




ba

c

d

fe

gh

complete extension (def. 15)

Admissibility and reinstatement

Set of conflict-free arguments s.t. each defended argument is included

b a

cd

f e

gh

{a, c,d, e, g},{a,b, c, e, g},{a, c, e, g}

grounded extension (def. 16)

Strong Admissibility

Minimum complete extension

b a

cd

f e

gh

{a, c, e, g}

preferred extension (def. 17)

Admissibility and maximality

Maximum complete extensions

b a

cd

f e

gh

{a, c,d, e, g},{a,b, c, e, g}

stable extension (def. 17)

„orror vacui:” the absence of odd-length cycles is a sufficient condition for existence ofstable extensions

Complete extensions attacking all the arguments outside

b a

cd

f e

gh

{a, c,d, e, g},{a,b, c, e, g}

complete labellings (def. 20)

Max. UNDEC ≡ Grounded

b a

cd

f e

gh

{a, c, e, g}


Max. IN ≡ Preferred

b a

cd

f e

gh

{a, c,d, e, g}


Max. IN ≡ Preferred

b a

cd

f e

gh

{a,b, c, e, g}


No UNDEC ≡ Stable

b a

cd

f e

gh

{a, c,d, e, g}


No UNDEC ≡ Stable

b a

cd

f e

gh

{a,b, c, e, g}

properties of semantics

CO GR PR STD-conflict-free Yes Yes Yes YesD-admissibility Yes Yes Yes YesD-strongly admissibility No Yes No NoD-reinstatement Yes Yes Yes YesD-I-maximality No Yes Yes YesD-directionality Yes Yes Yes No

complexity

[DW09]

complexity

σ = CO σ = GR σ = PR σ = STexistsσ trivial trivial trivial np-ccaσ np-c polynomial np-c np-csaσ polynomial polynomial Πp

2 -c conp-cverσ polynomial polynomial conp-c polynomialneσ np-c polynomial np-c np-c

an exercise

a

b c d

e

f

g

h

i

l

m

no

p

an exercise

a

b c d

e

f

g

h

i

l

m

no

p

ECO(∆) =

{a, c},{a, c, f},{a, c,m},{a, c, f,m},{a, c, f, l},{a, c, g,m}

an exercise

a

b c d

e

f

g

h

i

l

m

no

p

EGR(∆) =

{a, c}

an exercise

a

b c d

e

f

g

h

i

l

m

no

p

EPR(∆) =

{a, c, f,m},{a, c, f, l},{a, c, g,m}

an exercise

a

b c d

e

f

g

h

i

l

m

no

p

EST (∆) =

http://rull.dbai.tuwien.ac.at:8080/ASPARTIX/index.faces

http://rull.dbai.tuwien.ac.at:8080/ASPARTIX/index.faces

skepticisms and comparisons of sets of extensions

[BG09b]

skepticisms and comparisons of sets of extensions

..GR.

CO

.

PR

.

ST

⪯S⊕ relation

Comparing extensions individually:

E1 ⪯E∩+ E2 iff ∀E2 ∈ E2, ∃E1 ∈ E1: E1 ⊆ E2 and E1 ⪯E

∪+ E2 iff ∀E1 ∈ E1, ∃E2 ∈ E2: E1 ⊆ E2

signatures

[Dun+14]

signatures

The signature of a semantics is the collection of all possible sets of extensions an AF canpossess under a semantics (Def. 25).

S ⊆ 2A:

∙ ArgsS =∪

S∈S S;∙ PairsS = {⟨a,b⟩ | ∃S ∈ S s.t. {a,b} ⊆ S}.

• • • • •

S = { { a,d, e },{ b, c, e },{ a,b } }

ArgsS = {a,b, c,d, e} PairsS = {⟨a,b⟩, ⟨a,d⟩, ⟨a, e⟩, ⟨b, c⟩, ⟨b, e⟩, ⟨c, e⟩, ⟨d, e⟩}

signatures

∙ Incomparable (Def. 26): A ⊆ B iff A = B„Maximal”

∙ Tight (Def. 27): if S ∪ {a} ∈ S then ∃b ∈ S s.t. ⟨a,b⟩ ∈ PairsS

if an argument does not occur in some extension there must be a reason for that(typically a conflict)

∙ Adm-Closed (Def. 28): if ⟨a,b⟩ ∈ PairsS ∀a,b ∈ A ∪ B, A ∪ B ∈ S

„Admissibility”

Stable iff incomparable and tight

Preferred iff non-empty, incomparable and adm-closed

signatures

∙ Incomparable (Def. 26): A ⊆ B iff A = B

„Maximal”

∙ Tight (Def. 27): if S ∪ {a} ∈ S then ∃b ∈ S s.t. ⟨a,b⟩ ∈ PairsSif an argument does not occur in some extension there must be a reason for that(typically a conflict)

∙ Adm-Closed (Def. 28): if ⟨a,b⟩ ∈ PairsS ∀a,b ∈ A ∪ B, A ∪ B ∈ S

„Admissibility”



signatures

∙ Incomparable (Def. 26): A ⊆ B iff A = B

„Maximal”

∙ Tight (Def. 27): if S ∪ {a} ∈ S then ∃b ∈ S s.t. ⟨a,b⟩ ∈ PairsS

if an argument does not occur in some extension there must be a reason for that(typically a conflict)

∙ Adm-Closed (Def. 28): if ⟨a,b⟩ ∈ PairsS ∀a,b ∈ A ∪ B, A ∪ B ∈ S„Admissibility”



signatures

S = { { a,d, e },{ b, c, e },{ a,b } }

incomparable and adm-closed (⟨a,b⟩ ∈ PairsS ∀a,b ∈ A ∪ B, A ∪ B ∈ S)

a

b

c

d

f e

signatures

S = { { a,d, e },{ b, c, e },{ a,b } }

incomparable and adm-closed (⟨a,b⟩ ∈ PairsS ∀a,b ∈ A ∪ B, A ∪ B ∈ S)

a

b

c

d

f e

exercise

S = { { a,d, e },{ b, c, e },{ a,b,d } }

Does an AF ∆ having EPR(∆) = S exist?

No

PairsS = {⟨a,b⟩, ⟨a,d⟩, ⟨a, e⟩, ⟨b, c⟩, ⟨b, e⟩, ⟨c, e⟩, ⟨d, e⟩, ⟨b,d⟩}

b,d ∈ { a,d, e } ∪ { a,b,d }but { a,d, e } ∪ { a,b,d } = { a,b,d, e } /∈ S

exercise

S = { { a,d, e },{ b, c, e },{ a,b,d } }

Does an AF ∆ having EPR(∆) = S exist?

No

PairsS = {⟨a,b⟩, ⟨a,d⟩, ⟨a, e⟩, ⟨b, c⟩, ⟨b, e⟩, ⟨c, e⟩, ⟨d, e⟩, ⟨b,d⟩}

b,d ∈ { a,d, e } ∪ { a,b,d }but { a,d, e } ∪ { a,b,d } = { a,b,d, e } /∈ S

decomposability

[Bar+14]

decomposability

AF1

AF2AF3

Is it possible to consider a (partial) argumentation framework as a black-box and focusonly on the input/output interface?

decomposability

A semantics is:

∙ Fully decomposable (Def. 35):∙ any combination of “local” labellings gives rise to a global labelling;∙ any global labelling arises from a set of “local” labellings

∙ Top-Down decomposable (Def. 36):combining “local” labellings you get all global labellings, possibly more

∙ Bottom-Up decomposable (Def. 37):combining “local” labellings you get only global labellings, possibly less

CO ST GR PRFull decomposability Yes Yes No No

Top-down decomposability Yes Yes Yes YesBottom-up decomposability Yes Yes No No

decomposability

A semantics is:






decomposability

A semantics is:






decomposability

A semantics is:






..argumentation schemes

what is an argument?

The Argument Clinic

https://youtu.be/kQFKtI6gn9Y?t=75

what is an argument?

Argumentation is a verbal,social, and rational activity aimedat convincing a reasonable critic ofthe acceptability of a standpoint byputting forward a constellation ofpropositions justifying or refutingthe proposition expressed in thestandpoint.

Some elements of dialogue in the handout, but theywill not be considered here.

[WRM08]

practical inference: an example of argumentation scheme

Premises:Goal Premise Bringing about Sn is my goalMeans Premise In order to bring about Sn, I need to bring about SiConclusions:

Therefore, I need to bring about Si.

Critical questions:Other-Means Q. Are there alternative possible actions to bring about Si that

could also lead to the goal?Best-Means Q. Is Si the best (or most favourable) of the alternatives?Other-Goals Q. Do I have goals other than Si whose achievement is prefer-

able and that should have priority?Possibility Q. Is it possible to bring about Si in the given circumstances?Side Effects Q. Would bringing about Si have known bad consequences that

ought to be taken into account?

practical inference: an example of argumentation scheme

Premises:Goal Premise Bringing about Sn is my goalMeans Premise In order to bring about Sn, I need to bring about SiConclusions:

Therefore, I need to bring about Si.

Critical questions:Other-Means Q. Are there alternative possible actions to bring about Si that

could also lead to the goal?Best-Means Q. Is Si the best (or most favourable) of the alternatives?Other-Goals Q. Do I have goals other than Si whose achievement is prefer-

able and that should have priority?Possibility Q. Is it possible to bring about Si in the given circumstances?Side Effects Q. Would bringing about Si have known bad consequences that

ought to be taken into account?

an example

GoalBringing about being rich is my goal I want to be rich

Means/PlanIn order to bring about being rich I needto bring about having a job

To be rich I need a job

ActionTherefore I need to bring about having ajob

Therefore I have to searchfor a job.

an example

http://ova.arg-tech.org/

with

http://homepages.abdn.ac.uk/f.cerutti/pages/research/tutorialijcai2015/rich.html

http://ova.arg-tech.org/



..a semantic-web view of argumentation

[Rah+11]

Node Graph(argumentnetwork)

has-a

InformationNode

(I-Node)

is-a

Scheme NodeS-Node

has-a

Edge

is-a

Rule of inferenceapplication node

(RA-Node)

Conflict applicationnode (CA-Node)

Preferenceapplication node

(PA-Node)

Derived conceptapplication node (e.g.

defeat)

is-a

...

ContextScheme

Conflictscheme

contained-in

Rule of inferencescheme

Logical inference scheme

Presumptiveinference scheme ...

is-a

Logical conflictscheme

is-a

...

Preferencescheme

Logical preferencescheme

is-a

...Presumptivepreference scheme

is-a

uses uses uses

AIF-OWL

http://homepages.abdn.ac.uk/f.cerutti/pages/research/tutorialijcai2015/protege.mp4

[Bex+13]

On-line analysis of Moral Maze

https://www.youtube.com/watch?v=KVDgH-g8_gU

http://www.arg-tech.org/AIFdb/argview/4879http://toast.arg-tech.org/

http://www.arg-tech.org/AIFdb/argview/4879

http://toast.arg-tech.org/

..abstract argumentation frameworks

Value Based AF

Extended AF AFRA

Bipolar AF

value based argumentation framework

[BA09]

value based argumentation framework

..a2LC, FC

.. a3LC, FH

..

a1LC

a1 Hal should not take insulin, thusallowing Carla to be alive (value ofLife for Carla LC);

a2 Hal should take insulin andcompensate Carla, thus both ofthem stay alive (value of Life forCarla, and the Freedom — of usingmoney — for Carla FC);

a3 Hal should take insulin and thatCarla should buy insulin, thusboth of them stay alive (value ofLife for Carla, and the Freedom —of using money — for Hal FH).

Value Based AF

Extended AF AFRA

Bipolar AF

extended argumentation framework

[Mod09]

extended argumentation framework

a1 “Today will be dry in London sincethe BBC forecast sunshine”;

a2 “Today will be wet in London sinceCNN forecast rain”;

a3 “But the BBC are more trustworthythan CNN”;

a4 “However, statistically CNN aremore accurate forecasters thanthe BBC”;

a5 “Basing a comparison on statisticsis more rigorous and rational thanbasing a comparison on yourinstincts about their relativetrustworthiness”.

Value Based AF

Extended AF AFRA

Bipolar AF

afra: argumentation framework with recursive attacks

[Bar+11]

afra: argumentation framework with recursive attacks

a1 There is a last minute offer forGstaad: therefore I should go toGstaad;

a2 There is a last minute offer forCuba: therefore I should go toCuba;

a3 I do like to ski;

a4 The weather report informs that inGstaad there were no snowfallssince one month: therefore it isnot possible to ski in Gstaad;

a5 It is anyway possible to ski inGstaad, thanks to a good amountof artificial snow.

Value Based AF

Extended AF AFRA

Bipolar AF

bipolar argumentation framework

[CL05]

bipolar argumentation framework

..a3. a2. a1.

a4

a1 in favour of m, with premises{s, f, (s ∧ f) → m};

a2 in favour of ¬s, with premises{w,w → ¬s};

a3 in favour of ¬w, with premises{b,b → ¬w};

a4 in favour of f, with premises{l, l → f}

m Mary (who is small) is the killerf the killer is females the killer is smallw a witness says that the killer is tallb the witness is short-sightedl the killer has long hair and wear

lipstick

..structured argumentation frameworks

DeLP ABA

ASPIC+

DeductiveArgumentation

Logic for ClinicalKnowledge

delp: defeasible logic programming

[SL92] [GS14]


Π non-defeasible knowledge ⟨Π,∆⟩ ∆ defeasible knowledge

facts i.e. atomic informationstrict rules Lo ←− L1, . . . , Ln defeasible rules Lo −< L1, . . . , Ln

Def. 40

Let H be a ground literal: ⟨A,H⟩ is an argument structure if:

∙ there exists a defeasible derivation* for H from ⟨Π,A⟩;∙ there are no defeasible derivations from ⟨Π,A⟩ of contradictory literals;∙ and there is no proper subset A′ ⊂ A such that A′ satisfies (1) and (2).

*A defeasible derivation for Q from ⟨Π,∆⟩, is L1, L2, . . . , Ln = Q s.t.: (i) Li is a fact; or (ii) ∃Ri ∈ ⟨Π,∆⟩ withhead Li and body B1, . . . ,Bk, and every literal of the body is an element Lj of the sequence with j < i.


Def. 41

⟨B, S⟩ is a counter-argument for ⟨A,H⟩ at literal P, if there exists a sub-argument ⟨C,P⟩ of⟨A,H⟩ such that P and S disagree, that is, there exist two contradictory literals that have astrict derivation from Π ∪ {S,P}. The literal P is referred as the counter-argument pointand ⟨C,P⟩ as the disagreement sub-argument.

Def. 42

Let ⟨B, S⟩ be a counter-argument for ⟨A,H⟩ at point P, and ⟨C,P⟩ the disagreementsub-argument.

If ⟨B, S⟩ ≻* ⟨C,P⟩, then ⟨B, S⟩ is a proper defeater for ⟨A,H⟩.

If ⟨B, S⟩ ⊁ ⟨C,P⟩ and ⟨C,P⟩ ⊁ ⟨B, S⟩, then ⟨B, S⟩ is a blocking defeater for ⟨A,H⟩.

⟨B, S⟩ is a defeater for ⟨A,H⟩ if ⟨B, S⟩ is either a proper or blocking defeater for ⟨A,H⟩.

*≻ is an argument comparison criterion.

delp: defeasible logic programmingΠ1 ∆1

cloudydry_seasonwavesvacation¬working←− vacation

surf −< nice, spare_timenice −< wavesspare_time −< ¬busy¬busy −< ¬working¬nice −< rainrain −< cloudy¬rain −< dry_season

A0 =

surf −< nice, spare_timenice −< wavesspare_time −< ¬busy¬busy −< ¬working

A1 = {¬nice −< rain; rain −< cloudy}

A2 = {nice −< waves}

A3 = {rain −< cloudy}

A4 = {¬rain −< dry_season}


Π1

cloudydry_seasonwavesvacation¬working←− vacation

A0 =

surf −< nice, spare_timenice −< wavesspare_time −< ¬busy¬busy −< ¬working

A1 = {¬nice −< rain; rain −< cloudy}

A2 = {nice −< waves}

A3 = {rain −< cloudy}

A4 = {¬rain −< dry_season}

DeLP ABA

ASPIC+



assumption based argumentation framework

[Bon+97] [Ton14]


⟨L,R,A, ⟩L R A ⊆ L : A 7→ L

language set of rules assumptions contrariness

Def. 45

An argument for the claim σ ∈ L supported by A ⊆ A (A ⊢ σ) is a deduction for σsupported by A (and some R ⊆ R).*

Def. 46

An argument A1 ⊢ σ1 attacks an argument A2 ⊢ σ2 iff σ1 is the contrary of one of theassumptions in A2.

*A (finite) tree with nodes labelled by sentences in L or by τ /∈ L, the root labelled by σ , leaves either τor sentences in A, non-leaves σ′ with, as children, the elements of the body of some rule in R with head σ′ .


R = { innocent(X)←− notGuilty(X);killer(oj)←− DNAshows(oj),DNAshows(X) ⊃ killer(X);DNAshows(X) ⊃ killer(X)←− DNAfromReliableEvidence(X);evidenceUnreliable(X)←− collected(X, Y), racist(Y);DNAshows(oj)←−;collected(oj,mary)←−;racist(mary)←− }

A = { notGuilty(oj);DNAfromReliableEvidence(oj) }

notGuilty(oj) = killer(oj),

DNAfromReliableEvidence(oj) = evidenceUnreliale(oj).


DeLP ABA

ASPIC+



aspic+

[Pra10] [MP13] [MP14]

aspic+

Def. 47

An argumentation system is as tuple AS = ⟨L,R, ν⟩ where:

∙ : L 7→ 2L: a contrariness function s.t. if φ ∈ ψ and:∙ ψ /∈ φ, then φ is a contrary of ψ;∙ ψ ∈ φ, then φ is a contradictory of ψ (φ = –ψ);

∙ R = Rd ∪Rs: strict (Rs) and defeasible (Rd) inference rules s.t. Rd ∩Rs = ∅;∙ ν : Rd 7→ L, is a partial function.*

P ⊆ L is consistent iff ∄φ,ψ ∈ P s.t. φ ∈ ψ, otherwise is inconsistent.

A knowledge base in an AS is Kn ∪ Kp = K ⊆ L; {Kn,Kp} is a partition of K; Kn containsaxioms that cannot be attacked; Kp contains ordinary premises that can be attacked.

An argumentation theory is a pair AT = ⟨AS,K⟩.

*Informally, ν(r) is a wff in L which says that the defeasible rule r is applicable.

aspic+

Def. 48

An argument a on the basis of a AT = ⟨AS,K⟩, AS = ⟨L,R, ν⟩ is:

1. φ if φ ∈ K with: Prem(a) = {φ}; Conc(a) = φ; Sub(a) = {φ};Rules(a) = DefRules(a) = ∅; TopRule(a) = undefined.

2. a1, . . . , an −→ / =⇒ ψ if a1, . . . , an, with n ≥ 0, are arguments such that there exists astrict/defeasible rule r = Conc(a1), . . . ,Conc(an) −→ / =⇒ ψ ∈ Rs/Rd.Prem(a) = ∪n

i=1 Prem(ai); Conc(a) = ψ;Sub(a) = ∪n

i=1 Sub(ai) ∪ {a};Rules(a) = ∪n

i=1 Rules(ai) ∪ {r};DefRules(a) = {d | d ∈ Rules(a) ∩Rd};TopRule(a) = r

a is strict if DefRules(a) = ∅, otherwise defeasible; firm if Prem(a) ⊆ Kn, otherwiseplausible.

aspic+

Def. 49

Given a and b arguments, a defeats b iff a undercuts, successfully rebuts or successfullyundermines b, where:

∙ a undercuts b (on b′) iff Conc(a) /∈ ν(r) for some b′ ∈ Sub(b) s.t.r = TopRule(b′) ∈ Rd;

∙ a successfully rebuts b (on b′) iff Conc(a) /∈ φ for some b′ ∈ Sub(b) of the formb′′1 , . . . ,b′′

n =⇒ –φ, and a ⊀ b′;∙ a successfully undermines b (on φ) iff Conc(a) /∈ φ, and φ ∈ Prem(b) ∩ Kp, anda ⊀ φ.

Def. 50

AF is the abstract argumentation framework defined by AT = ⟨AS,K⟩ if A is the smallestset of all finite arguments constructed from K; and→ is the defeat relation on A.

aspic+

Rationality postulates

P1: direct consistency iff{Conc(a) | a ∈ S} isconsistent;

P2: indirect consistency iffCl({Conc(a) | a ∈ S}) isconsistent;

P3: closure iff {Conc(a) | a ∈ S} =Cl({Conc(a) | a ∈ S});

P4: sub-argument closure iff∀a ∈ S, Sub(a) ⊆ S.

∙ close under transposition

If φ1, . . . , φn −→ ψ ∈ Rs , then ∀i = 1 . . . n,φ1, . . . , φi−1,¬ψ,φi+1, . . . , φn =⇒ ¬φi ∈ Rs .

∙ Cl(Kn) is consistent;∙ the argument ordering ⪯ is reasonable, namely:

∙ ∀a,b, if a is strict and firm, and b is plausible ordefeasible, then a ≺ b;

∙ ∀a,b, if b is strict and firm, then b ⊀ a;∙ ∀a, a′,b such that a′ is a strict continuation of{a}, if a ⊀ b then a′ ⊀ b, and if b ⊀ a, thenb ⊀ a′;

∙ given a finite set of arguments {a1, . . . , an}, leta+\i be some strict continuation of{a1, . . . , ai−1, ai+1, . . . , an}. Then it is not the casethat ∀i, a+\i ≺ ai.

aspic+

Kp = { Snores;Professor }

Rd = { Snores =⇒d1 Misbehaves;Misbehaves =⇒d2 AccessDenied;Professor =⇒d3 AccessAllowed }

AccesAllowed = −AccessDenied

Snores <′ Professor;d1 < d2;d1 < d3;d3 < d2.

aspic+

aspic+

http://toast.arg-tech.org/4214

http://toast.arg-tech.org/4214

DeLP ABA

ASPIC+



deductive argumentation

[BH01] [GH11] [BH14]


Def. 53

A deductive argument is an ordered pair ⟨Φ, α⟩ where Φ ⊢i α. Φ is the support, orpremises, or assumptions of the argument, and α is the claim, or conclusion, of theargument.

consistency constraint when Φ is consistent (not essential, cf. paraconsistent logic).

minimality constraint when there is no Ψ ⊂ Φ such that Ψ ⊢ α

Def. 56

If ⟨Φ, α⟩ and ⟨Ψ, β⟩ are arguments, then

∙ ⟨Φ, α⟩ rebuts ⟨Ψ, β⟩ iff α ⊢ ¬β∙ ⟨Φ, α⟩ undercuts ⟨Ψ, β⟩ iff α ⊢ ¬ ∧Ψ


Def. 55

A classical logic argument from a set of formulae ∆ is a pair ⟨Φ, α⟩ such that

Φ ⊆ ∆ Φ ⊢ ⊥ Φ ⊢ α there is no Φ′ ⊂ Φ such that Φ′ ⊢ α.

Def. 57

Let a and b be two classical arguments. We define the following types of classical attack.a is a direct undercut of b if ¬Claim(a) ∈ Support(b)

a is a classical defeater of b if Claim(a) ⊢ ¬∧

Support(b)

a is a classical direct defeater of b if ∃ϕ ∈ Support(b) s.t. Claim(a) ⊢ ¬ϕ

a is a classical undercut of b if ∃Ψ ⊆ Support(b) s.t. Claim(a) ≡ ¬∧

Ψ

a is a classical direct undercut of b if ∃ϕ ∈ Support(b) s.t. Claim(a) ≡ ¬ϕ

a is a classical canonical undercut of b if Claim(a) ≡ ¬∧

Support(b).

a is a classical rebuttal of b if Claim(a) ≡ ¬Claim(b).

a is a classical defeating rebuttal of b if Claim(a) ⊢ ¬Claim(b).


..

bp(high)

ok(diuretic)

bp(high) ∧ ok(diuretic)→ give(diuretic)

¬ok(diuretic) ∨ ¬ok(betablocker)

give(diuretic) ∧ ¬ok(betablocker)

.

bp(high)

ok(betablocker)

bp(high) ∧ ok(betablocker)→ give(betablocker)

¬ok(diuretic) ∨ ¬ok(betablocker)

give(betablocker) ∧ ¬ok(diuretic)

.

symptom(emphysema),

symptom(emphysema)→ ¬ok(betablocker)

¬ok(betablocker)

...

DeLP ABA

ASPIC+



a logic for clinical knowledge

[HW12] [Wil+15]


Def. 58

Given treatments τ1 and τ2, X ⊆ evidence, there are three kinds of inductive argument:

1. ⟨X, τ1 > τ2⟩: evidence in X supports the claim that treatment τ1 is superior to τ2.2. ⟨X, τ1 ∼ τ2⟩: evidence in X supports the claim that treatment τ1 is equivalent to τ23. ⟨X, τ1 < τ2⟩: evidence in X supports the claim that treatment τ1 is inferior to τ2.

Def. 59

If the claim of argument ai is ϵi and the claim of argument aj is ϵj then ai conflicts with ajwhenever:

1. ϵi = τ1 > τ2, and ( ϵj = τ1 ∼ τ2 or ϵj = τ1 < τ2 ).2. ϵi = τ1 ∼ τ2, and ( ϵj = τ1 > τ2 or ϵj = τ1 < τ2 ).3. ϵi = τ1 < τ2, and ( ϵj = τ1 > τ2 or ϵj = τ1 ∼ τ2 ).


Def. 60

For any pair of arguments ai and aj, and a preference relation R, ai attacks aj with respectto R iff ai conflicts with aj and it is not the case that aj is strictly preferred to ai accordingto R.

A domain-specific benefit preference relation is defined in [HW12]

Def. 61 (Meta arguments)

For a ∈ Arg(evidence), if there is an e ∈ support(a) such that:

∙ e is not statistically significant, and e is not a side-effect, then this is an attacker:⟨Not statistically significant⟩;

∙ e is a non-randomised and non-blind trial, then this is an attacker:⟨Non-randomized & non-blind trials⟩;

∙ e is a meta-analysis that concerns a narrow patient group, then this is an attacker:⟨Meta-analysis for a narrow patient group⟩.


ID Left Right Indicator Risk ratio Outcome pe1 CP* NT† Pregnancy 0.05 superior 0.01e2 CP NT Ovarian cancer 0.99 superior 0.07e3 CP NT Breast cancer 1.04 inferior 0.01e4 CP NT DVT 1.02 inferior 0.05

N.B.: Fictional data.

*Contraceptive pill.†No Treatment.


..

⟨{e1}, CP > NT⟩

.

⟨{e2}, CP > NT⟩

. ⟨{e1, e2}, CP > NT⟩.

⟨{e3}, CP < NT⟩

.

⟨{e4}, CP < NT⟩

. ⟨{e3, e4}, CP < NT⟩.⟨Notstatistically

significant⟩

ID Left Right Indicator Risk ratio Outcome pe1 CP NT Pregnancy 0.05 superior 0.01e2 CP NT Ovarian cancer 0.99 superior 0.07e3 CP NT Breast cancer 1.04 inferior 0.01e4 CP NT DVT 1.02 inferior 0.05

..probabilistic argumentation frameworks

epistemic approach

[Thi12] [Hun13]

epistemic approach

[HT14] [BGV14]

epistemic approach

An epistemic probability distribution* for an argumentation framework ∆ = ⟨A,→ ⟩ is:

P : A → [0, 1]

Def. 65

For an argumentation framework AF = ⟨A,→⟩ and a probability assignment P, theepistemic extension is

{a ∈ A | P(a) > 0.5}

*In the tutorial a way to compute it for arguments based on classical deduction.

epistemic approach

COH: P is coherent if for every a,b ∈ A, if a attacks b then P(a) ≤ 1− P(b).

SFOU: P is semi-founded if P(a) ≥ 0.5 for every unattacked a ∈ A.

FOU: P is founded if P(a) = 1 for every unattacked a ∈ A.

SOPT: P is semi-optimistic if P(a) ≥ 1−∑

b∈a− P(b) for every a ∈ A with at least one attacker.

OPT: P is optimistic if P(a) ≥ 1−∑

b∈a− P(b) for every a ∈ A.

JUS: P is justifiableif P is coherent and optimistic.

TER: P is ternary if P(a) ∈ {0, 0.5, 1} for every a ∈ A.

RAT: P is rational if for every a,b ∈ A, if a attacks b then P(a) > 0.5 implies P(b) ≤ 0.5.

NEU: P is neutral if P(a) = 0.5 for every a ∈ A.

INV: P is involutary if for every a,b ∈ A, if a attacks b, then P(a) = 1− P(b).

Let the event “a is accepted” be denoted as a, and let be Eac(S) = {a|a ∈ S}. Then P is weaklyp-justifiable iff ∀a ∈ A, ∀b ∈ a−, P(a) ≤ 1− P(b).

epistemic approach

Def. 67

Restriction on complete* probability function P Classical semanticsNo restriction complete extensions

No arguments a such that P(a) = 0.5 stableMaximal no. of a such that P(a) = 1 preferredMaximal no. of a such that P(a) = 0 preferredMaximal no. of a such that P(a) = 0.5 groundedMinimal no. of a such that P(a) = 1 groundedMinimal no. of a such that P(a) = 0 groundedMinimal no. of a such that P(a) = 0.5 semi-stable

*Coherent, founded, and ternary. http://arxiv.org/abs/1405.3376

http://arxiv.org/abs/1405.3376

structural approach

[Hun14]

structural approach

P : {∆′ ⊑ ∆} 7→ [0, 1]

Subframework Probability∆1 a ↔ b 0.09∆2 a 0.81∆3 b 0.01∆4 0.09

PGR({a,b}) = = 0.00PGR({a}) = P(∆2) = 0.81PGR({b}) = P(∆3) = 0.01PGR({}) = P(∆1) + P(∆4) = 0.18

a computational framework

[Li15]

a computational framework

Convert to

ASPIC+ ArgumentationSystem

•Logical Language•Inference Rules•Contrariness Function•......

StructuredArgumentation

Framework(SAF)

DAF

DAFEAF

ExtendedEvidential

Framework(EEAF)

ProbabilisticExtendedEvidential

Framework

Convert to

Convert to

ExtendedEvidential

Framework(EEAF)

Model

ProbabilisticExtendedEvidential

Framework

Associate

Probabilities

Convert toPrEAF

Associate

Probabilities

Sem

anticsP

reserved

PrAF

Associate

Probabilities

..cispaces

[Ton+15]

CISpaces

http://alicice.com/PermBox/cisp.mp4

What is the cause of the illness?

Analyst Joe

?

Illness among peopleLivestock illnessPossible

Connection

CONTAMINATED WATER SUPPLY

Is this information credible?

Are there alternative explanations?

Is there evidence for the contamination of the water supply?

Analysts must reason with different types of evidence

research foci

Attributes of the problem domain

∙ Intelligence analysis is critical for making well-informed decisions∙ Large amount of conflicting incomplete information∙ Reasoning with different types of evidence

Research Question

How to develop agents to support to reasoning with different types of evidence in acombined approach throughout the process of analysis?

intelligence analysis

Def. 73

The application of individual and collective cognitive methods to evaluate, integrate,interpret information about situations and events to provide warning for potentialthreats or identify opportunities.

External Data

Sources

Presentation

Searchand Filter

Schematize

Build Case

Tell Story

Reevaluate

Search for support

Search for evidence

Search for information

FORAGING LOOP

SENSE-MAKING LOOP

Stru

ctur

e

Effort

inf

Shoebox

Ev

Ev

EvEv Ev

EvEv

Ev

Ev

Ev

Ev

Evidence File

Hyp1 Hyp2

Hypotheses

Pirolli & Card Model

Effective if:TIMELYTARGETEDand TRUSTED

collaboration among analysts

Team of Analysts: More effective, Prevent Bias, Different Expertise and Resources

Challenges atdifferent stagesof analysis

Schematize Build Case

Search for support

Search for evidence

Shoebox Evidence File

Hyp1 Hyp2

Hypotheses

Share data and analysis

Integrate and annotate

Assess credibility

inf

inf

inf

Gather information Identify Plausible Hypotheses

Mitigate Cognitive Biases

cispaces agent support

Interface

Communication layer

ToolBoxWorkBoxInfoBox ReqBox

ChatBox

Sensemaking Agent

Crowd-sourcingAgent

ProvenanceAgent

analyst

CISpaces Interface: Working space and access to agent support

Sensemaking Agent: Support collaborative analysis of argumentsCrowd-sourcing Agent: Enable participation of large groups of contributorsProvenance Agent: Assess the credibility of information

Interface

Communication layer


ChatBox

Sensemaking Agent

Crowd-sourcingAgent

ProvenanceAgent

analyst

ProvenanceAgent

Sensemaking Agent

sensemaking agent (smag) - analysis construction

∙ Annotation of Pro links;∙ Suggests CQs (Con links) to prevent cognitive biases.

Causal – Distribution of Activities

∙ Typically, if C occurs, then Ewill occur

∙ In this case, C occurs⇒ Therefore, in this case E will

occur

Association – Element Connections∙ An activity occurs, and an entity may beinvolved

∙ To perform the activity some property His required

∙ The entity fits the property H⇒ Therefore, the entity is associated with

the activity

smag analysis construction (cont.)

E is an expert in D

E asserts A in D

A is trueLab Expert on

water toxins and chemicals asserts

There is a bacteria contaminating the

water supply

Water supply in Kish is

contaminated Pro

Expert Opinion Cause to effectIdentification...

V

Analyst annotates pro links andnodes → match to an argumentscheme.

E is an expert in DLab Expert on


There is a bacteria contaminating the

water supply

Water supply in Kish is

contaminated

Expert OpinionE asserts A in D

A is true∙ E is an expert in domain D containing A,

∙ E asserts that A is true,

⇒ Therefore, A may plausibly be true.

E is an expert in DLab Expert on


CQ1: Is E an expert in D?CQ2: Is E reliable?V

ConCQ2

The expert is not reliable

Analyst select CQs. CISpaces showsa negative answer to a CQ to preventcognitive biases.

smag hypotheses identification

controversial standpoints as extensions

1. Transforming the current workbox view into an argumentation framework

q0,q1=>q2

PREMISE PREMISE

q0q1

q2

q3

q4

q1,q3=>q4

Contradictory statements:

q2-q4

CAUSE TO EFFECT

ASPIC+ argumentation framework:Premises: q0, q1, q3Rules: q0, q1 ⇒ q2; q1, q3 ⇒ q4 ;Negation: q2 − q4Arguments:A0 : q0 , A1 : q1 , A2 : q3A4 : A0, A1 ⇒ q2

A5 : A0, A2 ⇒ q4

2. ASPIC+/Dung’s AF implementation identifies the sets of acceptable arguments:

smag hypotheses identification (cont.)

3. CISpaces shows what conclusions can be supported∙ Labelled according to extensions computed

∙ Arguments shared through the Argument Interchange Format (AIF)

Unidentified illness affects

the local livestock in

Kish

Non-waterborne

bacteria were engineered and released in the water supply

Illness among young and elderly

people in Kish caused by bacteria

Toxic Bacteria

contaminate the local water system in Kish

NGO Lab reports

examined the contamination

NON-waterborne

bacteria contaminate the

water supply

There are bacteria in the water supply

Waterborne bacteria

contaminate the water

supply

V

V

V

V

V Waterborne bacteria have formed by a

sewage leakage in the water

supply pipes

V

Interface

Communication layer


ChatBox

Sensemaking Agent

Crowd-sourcingAgent

ProvenanceAgent

analyst

ProvenanceAgent

Crowd-sourcingAgent

crowdsourcing agent

1. Critical questions trigger the need for further information on a topic2. Analyst call the crowdsourcing agent (CWSAg)3. CWSAg distributes the query to a large group of contributors4. CWSAg aggregates the results and shows statistics to the analyst

cwsag results import

Q0-AnswerClear (Con)

Q1-Answer21.1 (Pro)

Q0-AGAINSTWater Contaminated

Q1-FORWater Contaminated

CONTRADICTORY

Interface

Communication layer


ChatBox

Sensemaking Agent

Crowd-sourcingAgent

ProvenanceAgent

analyst

ProvenanceAgent

ProvenanceAgent

N

S E

W

image info ij

observation

Observer Messenger Informer

message

info ik

Gangheading South

GangCrossing

North Border

N

S E

W

Surveillance

BORDER L1-L2

Image Processing

Analyst Joe

BORDER L1-L2

GP(ij)

GP(ik)

argument from provenance

- Given a provenance chain GP(ij) of ij, information ij:- (Where?) was derived from an entity A- (Who?) was associated with actor AG- (What?) was generated by activity P1- (How?) was informed by activity P2- (Why?) was generated to satisfy goal X- (When?) was generated at time T- (Which?) was generated by using some entities A1,…, AN- where A, AG, P1, …belong to GP(ij)

- the stated elements of GP(ij) infer that information ij is true,⇒ Therefore, information ij may plausibly be taken to be true.

CQA1: Is ij consistent with other information?

CQA2: Is ij supported by evidence?

CQA3: Does GP(ij) contain other elements that lead us not to believe ij?

CQA4: Are there provenance elements that should have been included for believing ij?

argument for provenance preference

- Given information ij and ik,- and their known parts of the provenance chains GP(ij) and GP(ik),- if there exists a criterion Ctr such that GP(ij)≪Ctr GP(ik), then ij ≪ ik- a criterion Ctr′ leads to assert that GP(ij)≪Ctr′ GP(ik)⇒ Therefore, ik should be preferred to ij.

Trustworthiness Reliability Timeliness Shortest path

CQB1: Does a different criterion Ctr1 , such that GP(ij)≫Ctr1 GP(ik) lead ij ≪ ik not being valid?

CQB2: Is there any exception to criterion Ctr such that even if a provenance chain GP(ik) is preferred toGP(ij), information ik is not preferred to information ij?

CQB3: Is there any other reason for believing that the preference ij ≪ ik is not valid?

pvag provenance analysis & import

IMPORT ANALYSISPrimary Source Pattern

Provenance Explanation

US Patrol Report

Extract

Used wasGeneratedBy

US Team Patrol

wasAssociatedWith

wasDerivedFromINFO:

Livestock illness

prov: time 2015-04-27T02:27:40Z

Farm Daily Report

Prepare

Used wasGeneratedBy

KishFarmer

wasAssociatedWith

wasDerivedFrom

type PrimarySource

Annotate

wasGeneratedBy

wasAssociatedWith

Livestock Pictures

Used

Livestock Information

IMPORT OF PREFERENCES?

theories/technologies integrated

∙ Argument representation:∙ Argument Schemes and Critical questions (domain specific)∙ „Bipolar-like” graph for user consumption∙ AIF (extension for provenance)∙ ASPIC(+)∙ Arguments based on preferences (partially under development)

∙ Theoretical framework for acceptability status:∙ AF∙ PrAF (case study for [Li15])∙ AFRA for preference handling (under development)

∙ Computational machinery: jArgSemSAT

..algorithms and implementations

[Cha+15]

ad-hoc procedures

ArgTools

[NAD14]

ad-hoc procedures

csp-based approach

ConArg

[BS12]

csp-based approach

A Constraint Satisfaction Problem (CSP) P is a triple P = ⟨X,D, C⟩ such that:

∙ X = ⟨x1, . . . , xn⟩ is a tuple of variables;∙ D = ⟨D1, . . . ,Dn⟩ a tuple of domains such that ∀i, xi ∈ Di;∙ C = ⟨C1, . . . , Ct⟩ is a tuple of constraints, where ∀j, Cj = ⟨RSj , Sj⟩,Sj ⊆ {xi|xi is a variable}, RSj ⊆ SDj × SDj where SDj = {Di|Di is adomain, and xi ∈ Sj}.

A solution to the CSP P is A = ⟨a1, . . . , an⟩ where ∀i, ai ∈ Di and ∀j,RSj holds on theprojection of A onto the scope Sj. If the set of solutions is empty, the CSP is unsatisfiable.

csp-based approach

Given an AF:

1. create a variable for each argument whose domain is always {0, 1} — ∀ai ∈ A, ∃xi ∈ Xsuch that Di = {0, 1};

2. describe constraints associated to different definitions of Dung’s argumentationframework: e.g.

{a1, a2} ⊆ A is D-conflict-free iff ¬(x1 = 1 ∧ x2 = 1);3. solve the CSP problem.

asp-based approach

ASPARTIX-D / ASPARTIX-V / DIAMOND

[EGW10] [Dvo+11]

asp-based approach

πST = { in(X)← not out(X), arg(X);out(X)← not in(X), arg(X);← in(X), in(Y), defeat(X, Y);defeated(X)← in(Y),defeat(Y, X);← out(X),not defeated(X)}.

Tests for subset-maximality exploit the metasp optimisation frontend for theASP-package gringo/claspD.

sat-based approaches

Cegartix

[Dvo+12]

ArgSemSAT/jArgSemSAT/LabSATSolver

[Cer+14b]


[Dvo+12]

∧a→b

(¬xa ∨ ¬xb)∧

∧b→c

¬xc ∨ ∨a→b

xa


[Cer+14b]

If a1 is not attacked, Lab(a1) = in

C1Lab(a1) = in⇔ ∀a2 ∈ a−1 Lab(a2) = outLab(a1) = out⇔ ∃a2 ∈ a−1 : Lab(a2) = in

Lab(a1) = undec⇔ ∀a2 ∈ a−1 Lab(a2) = in ∧ ∃a3 ∈ a−1 :

Lab(a3) = undec


[Cer+14b]

∧i∈{1,...,k}

((Ii ∨ Oi ∨ Ui) ∧ (¬Ii ∨ ¬Oi)∧(¬Ii ∨ ¬Ui) ∧ (¬Oi ∨ ¬Ui)

)∧

∧{i|ϕ(i)−=∅}

(Ii ∧ ¬Oi ∧ ¬Ui) ∧∧

{i|ϕ(i)−=∅}

Ii ∨

∨{j|ϕ(j)→ϕ(i)}

(¬Oj)

∧

∧{i|ϕ(i)−=∅}

∧{j|ϕ(j)→ϕ(i)}

¬Ii ∨ Oj

∧∧

{i|ϕ(i)−=∅}

∧{j|ϕ(j)→ϕ(i)}

¬Ij ∨ Oi

∧

∧{i|ϕ(i)−=∅}

¬Oi ∨

∨{j|ϕ(j)→ϕ(i)}

Ij

∧

∧{i|ϕ(i)−=∅}

∧{k|ϕ(k)→ϕ(i)}

Ui ∨ ¬Uk ∨

∨{j|ϕ(j)→ϕ(i)}

Ij

∧

∧{i|ϕ(i)−=∅}

∧{j|ϕ(j)→ϕ(i)}

(¬Ui ∨ ¬Ij)

∧

¬Ui ∨

∨{j|ϕ(j)→ϕ(i)}

Uj


[Cer+14b]


Ca1Lab(a1) = in⇔ ∀a2 ∈ a−1 Lab(a2) = outLab(a1) = out⇔ ∃a2 ∈ a−1 : Lab(a2) = in


[Cer+14b]


Cb1

Lab(a1) = out⇔ ∃a2 ∈ a−1 : Lab(a2) = inLab(a1) = undec⇔ ∀a2 ∈ a−1 Lab(a2) = in ∧ ∃a3 ∈ a−1 :

Lab(a3) = undec


[Cer+14b]


Cc1Lab(a1) = in⇔ ∀a2 ∈ a−1 Lab(a2) = out

Lab(a1) = undec⇔ ∀a2 ∈ a−1 Lab(a2) = in ∧ ∃a3 ∈ a−1 :

Lab(a3) = undec


[Cer+14b]


C2Lab(a1) = in⇒ ∀a2 ∈ a−1 Lab(a2) = outLab(a1) = out⇒ ∃a2 ∈ a−1 : Lab(a2) = in

Lab(a1) = undec⇒ ∀a2 ∈ a−1 Lab(a2) = in ∧ ∃a3 ∈ a−1 :

Lab(a3) = undec


[Cer+14b]


C3Lab(a1) = in⇐ ∀a2 ∈ a−1 Lab(a2) = outLab(a1) = out⇐ ∃a2 ∈ a−1 : Lab(a2) = in

Lab(a1) = undec⇐ ∀a2 ∈ a−1 Lab(a2) = in ∧ ∃a3 ∈ a−1 :

Lab(a3) = undec


[Cer+14b]

50

60

70

80

90

100

50 100 150 200IP

Cn

orm

alis

edto

10

0

Number of arguments

IPC normalised to 100 with respect to the number of arguments

C1

Ca1

Cb1

Cc1

C2

C3

iccma 2015

The First International Competition on Computational Models of Argumentation

http://argumentationcompetition.org/

Results announced yesterday

http://argumentationcompetition.org/

iccma 2015

iccma 2015

iccma 2015

a parallel algorithm

[BGG05] [Cer+14a] [Cer+15]




a b

e f

c d g h


a b

e f

c d g h


a b

e f

c d g h

Level 1 Level 2


a b

e f

c d g h

Level 1 Level 2

⟨{a, c, e}, {b,d, f}, {}⟩,⟨{a, c, f}, {b,d, e}, {}⟩,⟨{a,d, e}, {b, c, f}, {}⟩,⟨{a,d, f}, {b, c, e}, {}⟩


a b

e f

c d g h

Level 1 Level 2

Moving to the the last level,

B1: no argument in S3 is attacked from “outside” for Lab ∈{⟨{a, c, e}, {b,d, f}, {}⟩,⟨{a, c, f}, {b,d, e}, {}⟩

}

B2: g is attacked by d Lab ∈{⟨{a,d, e}, {b, c, f}, {}⟩,⟨{a,d, f}, {b, c, e}, {}⟩

}

Cases B1 and B2 are computed in parallel.


a b

e f

c d g h

Level 1 Level 2

⟨{a, c, e, g}, {b,d, f,h}, {}⟩,⟨{a, c, e,h}, {b,d, f, g}, {}⟩,⟨{a, c, f, g}, {b,d, e,h}, {}⟩,⟨{a, c, f,h}, {b,d, e, g}, {}⟩,⟨{a,d, e,h}, {b, c, f, g}, {}⟩,⟨{a,d, f,h}, {b, c, e, g}, {}⟩

We need to be smart

Holger H. Hoos, Invited Keynote Talk at ECAI2014

[VCG14] [CGV14]

features from an argumentation graph

Directed Graph (26 features)

Structure:

# vertices ( |A| )# edges ( | → | )# vertices / #edges ( |A|/| → | )# edges / #vertices ( | → |/|A| )densityaverage

Degree: stdevattackers max

min#averagestdevmax

SCCs:

min

Structure:

# self-def# unattackedflow hierarchyEulerianaperiodic

CPU-time: …

Undirected Graph (24 features)

Structure:

# edges# vertices / #edges# edges / #verticesdensity

Degree:

averagestdevmaxmin

SCCs:

#averagestdevmaxmin

Structure: Transitivity

3-cycles:

#averagestdevmaxmin

CPU-time: …

how hard is to get the features?

Direct Graph Features (DG) Undirect Graph Features (UG)Class CPU-Time # feat Class CPU-Time # feat

Mean stdDev Mean stDevGraph Size 0.001 0.009 5 Graph Size 0.001 0.003 4Degree 0.003 0.009 4 Degree 0.002 0.004 4SCC 0.046 0.036 5 Components 0.011 0.009 5Structure 2.304 2.868 5 Structure 0.799 0.684 1

Triangles 0.787 0.671 5

Average CPU-time, stdev, needed for extracting the features of a given class.

protocol: some numbers

∙ |SCCS∆| in 1 : 100;∙ |A| in 10 : 5, 000;∙ | → | in 25 : 270, 000 (Erdös-Rényi, p uniformly distributed) ;∙ Overall 10, 000 AFs.

∙ Cutoff time of 900 seconds (value also for crashed, timed-out or ran out of memory).

∙ EPMs both for Regression (Random forests) and Classification (M5-Rules) using WEKA;∙ Evaluation using a 10-fold cross-validation approach on a uniform randompermutation of instances.

result 1: best features for prediction

Solver B1 B2 B3AspartixM number of arguments density of directed graph size of max. SCCPrefSAT density of directed graph number of SCCs aperiodicityNAD-Alg density of directed graph CPU-time for density CPU-time for EulerianSSCp density of directed graph number of SCCs size of the max SCC

Determined by a greedy forward search based on the Correlation-based FeatureSelection (CFS) attribute evaluator.

AF structure SCCs CPU-time for feature extraction

result 2: predicting (log)runtime

RSME of Regression (Lower is better)B1 B2 B3 DG UG SCC All

AspartixM 0.66 0.49 0.49 0.48 0.49 0.52 0.48PrefSAT 1.39 0.93 0.93 0.89 0.92 0.94 0.89NAD-Alg 1.48 1.47 1.47 0.77 0.57 1.61 0.55SSCp 1.36 0.80 0.78 0.75 0.75 0.79 0.74

√√√√∑ni=1

(log10( ti )− log10( yi )

)2

n

AF structure SCCs CPU-time for feature extraction Undirect Graph

result 3: best features for classification

C-B1 C-B2 C-B3number of arguments density of directed graph min attackers

Determined by a greedy forward search based on the Correlation-based FeatureSelection (CFS) attribute evaluator.

AF structure Attackers

result 4: classification, i.e. selecting the best solver for a given af

Classification (Higher is better)|A| density min attackers DG UG SCC All

Accuracy 48.5% 70.1% 69.9% 78.9% 79.0% 55.3% 79.5%Prec. AspartixM 35.0% 64.6% 63.7% 74.5% 74.9% 42.2% 76.1%Prec. PrefSAT 53.7% 67.8% 68.1% 79.6% 80.5% 60.4% 80.1%Prec. NAD-Alg 26.5% 69.2% 69.0% 81.7% 85.1% 35.3% 86.0%Prec. SSCp 54.3% 73.0% 72.7% 76.6% 76.8% 57.8% 77.2%

AF structure Attackers Undirect Graph SCCs

result 5: algorithm selection

Metric: Fastest(max. 1007)

AspartixM 106NAD-Alg 170PrefSAT 278SSCp 453EPMs Regression 755EPMs Classification 788

Metric: IPC*(max. 1007)

NAD-Alg 210.1AspartixM 288.3PrefSAT 546.7SSCp 662.4EPMs Regression 887.7EPMs Classification 928.1

*Scale of (log)relative performance

..the frontier

belief revision and argumentation

[FKS09] [FGS13]

belief revision and argumentation

Potential cross-fertilisation

Argumentation in Belief Revision

∙ Justification-based truth maintenancesystem

∙ Assumption-based truth maintenancesystem

Some conceptual differences:in revision, external beliefs are

compared with internal beliefs and,after a selection process, somesentences are discarded, otherones are accepted. [FKS09]

Belief Revision in Argumentation

∙ Changing by adding or deleting anargument.

∙ Changing by adding or deleting a set ofarguments.

∙ Changing the attack (and/or defeat)relation among arguments.

∙ Changing the status of beliefs (asconclusions of arguments).

∙ Changing the type of an argument (fromstrict to defeasible, or vice versa).

abstract dialectical framework

[Bre+13]

abstract dialectical framework

Dependency Graph + Acceptance Conditions

argumentation and social networks

[LM11] [ET13]


a:The Wonder-Phone is the best new generation phone.+20 -20

b: No, the Magic-Phone is the best new generation phone.+ 20 - 20

c: here is a [link] to a review of the Magic-Phone giving poor scores due to bad battery performance+60 -10.

d: author of c is ignorant, since subsequent reviews noted that only one of the first editions had such problems: [links].+10 -40

e: d is wrong. I found out c) knows about that but withheld the information. Here's a [link] to another thread proving it!+40 -10


a:The Wonder-Phone is the best new generation phone.+20 -20 b: No, the Magic-Phone is the

best new generation phone.+ 20 - 20





a:The Wonder-Phone is the best new generation phone.+20 -20

b: No, the Magic-Phone is the best new generation phone.+ 20 - 20





http://www.quaestio-it.com/

http://www.quaestio-it.com/

argument mining

[CV12] [Bud+14]

argument mining

http://www-sop.inria.fr/NoDE/

http://corpora.aifdb.org/

http://www-sop.inria.fr/NoDE/

http://corpora.aifdb.org/

natural language interfaces

[CTO14] [Cam+14]


a1 : σA ⇒ γ

a2 : σB ⇒ ¬γa3 : ⇒ a1 ≺ a2

First Scenarioa1: Alice suggests to move in together with Janea2: Stacy suggests otherwise because Jane might have a hidden agendaa3: Stacy is your best friend

a1 a2 don’t know% agreement 12.5 68.8 18.8

• • • • •

Second Scenarioa1: TV1 suggests that tomorrow will raina2: TV2 suggests that tomorrow will be cloudy but will not raina3: TV2 is generally more accurate than TV1

a1 a2 don’t know% agreement 5.0 50.0 45.0


Scrutable Autonomous Systems (in particular from 7’ 30”)

http://www.scrutable-systems.org/resources/demonstrator_features.mov

..conclusion

Hal’s Argument

https://youtu.be/HwBmPiOmEGQ?t=43

..credits

credits

Template

adapted from mtheme https://github.com/matze/mtheme

https://github.com/matze/mtheme

Argumentation in Artificial Intelligence

Science

trust argumentation

lot dialogues argumentation

frontier approaches

probabilistic frameworks

af syntax

fresh milk

sick beer milk coffee

fresh coffee