handout for the course abstract argumentation and interfaces to argumentative reasoning

Abstract Argumentation

and

Interfaces to ArgumentativeReasoning

Handouts

Federico Cerutti

September 2016

Contents

Contents 1

1 Dung’s AF 31.1 Principles for Extension-based Semantics: [BG07] . . . . . 3

1.2 Acceptability of Arguments [PV02; BG09a] . . . . . . . . . . 4

1.3 (Some) Semantics [Dun95] . . . . . . . . . . . . . . . . . . . . 5

1.4 Labelling-Based Semantics Representation [Cam06] . . . . 6

1.5 Skepticism Relationships [BG09b] . . . . . . . . . . . . . . . 9

1.6 Signatures [Dun+14] . . . . . . . . . . . . . . . . . . . . . . . 9

1.7 Decomposability and Transparancy [Bar+14] . . . . . . . . 12

1.8 Extension-based I/O Characterisation [GLW16] . . . . . . . 13

2 Implementations 142.1 Ad Hoc Procedures . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Constraint Satisfaction Programming . . . . . . . . . . . . . 14

2.3 Answer Set Programming . . . . . . . . . . . . . . . . . . . . 15

2.4 Propositional Satisfiability Problems . . . . . . . . . . . . . 15

2.5 Second-order Solver [BJT16] . . . . . . . . . . . . . . . . . . 23

2.6 Which One? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Ranking-Based Semantics 283.1 The Categoriser Semantics [BH01] . . . . . . . . . . . . . . . 28

3.2 Properties for Ranking-Based Semantics [Bon+16] . . . . . 28

4 Argumentation Schemes 334.1 An example: Walton et al. ’s Argumentation Schemes for

Practical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 AS and Dialogues . . . . . . . . . . . . . . . . . . . . . . . . . 34

5 Semantic Web Argumentation 385.1 AIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 AIF-OWL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6 CISpaces 436.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.2 Intelligence Analysis . . . . . . . . . . . . . . . . . . . . . . . 43

6.3 Reasoning with Evidence . . . . . . . . . . . . . . . . . . . . . 46

6.4 Arguments for Sensemaking . . . . . . . . . . . . . . . . . . 46

6.5 Arguments for Provenance . . . . . . . . . . . . . . . . . . . . 48

Cardiff University, 2016 Page 1

7 Natural Language Interfaces 507.1 Experiments with Humans: Scenarios [CTO14] . . . . . . . 50

7.2 Lessons From Argument Mining: [BR11] . . . . . . . . . . . 55

Bibliography 56


1 Dung’s ArgumentationFramework

Acknowledgement

This handout include material from a number of collaborators including

Pietro Baroni, Massimiliano Giacomin, Thomas Linsbichler, and Stefan5

Woltran.

Definition 1 ([Dun95]). 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 . ♠

An argumentation framework has an obvious representation as a di-10

rected graph where the nodes are arguments and the edges are drawn

from attacking to attacked arguments.

The set of attackers of an argument a1 will be denoted as a−1 , {a2 :

a2 → a1}, the set of arguments attacked by a1 will be denoted as a+1 , {a2 :

a1 → a2}. We also extend these notations to sets of arguments, i.e. given15

E ⊆A , E− , {a2 | ∃a1 ∈ E,a2 → a1} and E+ , {a2 | ∃a1 ∈ E,a1 → a2}.

With a little abuse of notation we define S → a ≡ ∃a ∈ S : a → b. Simi-

larly, b → S ≡∃a ∈ S : b → a.

Given Γ= ⟨A ,→⟩ and Γ′ = ⟨A ′,→′⟩, Γ∪Γ′ = ⟨A ∪A ′,→∪→′⟩.

1.1 Principles for Extension-based Semantics:20

[BG07]

Definition 2.+ Given an argumentation framework AF = ⟨A ,→⟩, a set

S ⊆ A is D-conflict-free, denoted as D-cf (S), if and only if @a,b ∈ S such

that a → b. A semantics σ satisfies the D-conflict-free principle if and only

if ∀AF,∀E ∈ Eσ(AF) E is D-conflict-free . ♠25

Definition 3. Given an argumentation framework AF = ⟨A ,→⟩, an ar-

gument a ∈ A is D-acceptable w.r.t. a set S ⊆ A if and only if ∀b ∈ A

b → a ⇒ S → b.

The function FAF : 2A 7→ 2A which, given a set S ⊆ A , returns the

set of the D-acceptable arguments w.r.t. S, is called the D-characteristic30

function of AF. ♠


Dung’s AF • Acceptability of Arguments [PV02; BG09a]

Definition 4. Given an argumentation framework AF = ⟨A ,→⟩, a set

S ⊆ A is D-admissible (S ∈ AS (AF)) if and only if D-cf (S) and ∀a ∈ Sa is D-acceptable w.r.t. S. The set of all the D-admissible sets of AF is

denoted as AS (AF). ♠

Dσ = {AF|Eσ(AF) 6= ;}5

Definition 5.+ A semantics σ satisfies the D-admissibility principle if and

only if ∀AF ∈Dσ Eσ(AF)⊆AS (AF), namely ∀E ∈ Eσ(AF) it holds that:

a ∈ E ⇒ (∀b ∈A ,b → a ⇒ E → b). ♠

Definition 6. Given an argumentation framework AF = ⟨A ,→⟩, a ∈A and S ⊆ A , we say that a is D-strongly-defended by S (denoted as

D-sd(a,S)) iff ∀b ∈A , b → a, ∃c ∈ S \{a} : c → b and D-sd(c,S \{a}). ♠

Definition 7.+ A semantics σ satisfies the D-strongly admissibility prin-ciple if and only if ∀AF ∈Dσ, ∀E ∈ Eσ(AF) it holds that

a ∈ E ⊃D-sd(a,E) ♠

Definition 8.+ A semantics σ satisfies the D-reinstatement principle if and

only if ∀AF ∈Dσ, ∀E ∈ Eσ(AF) it holds that:

(∀b ∈A ,b → a ⇒ E → b)⇒ a ∈ E. ♠

Definition 9.+ A set of extensions E is D-I-maximal if and only if ∀E1,E2 ∈E , if E1 ⊆ E2 then E1 = E2. A semantics σ satisfies the D-I-maximality10

principle if and only if ∀AF ∈Dσ Eσ(AF) is D-I-maximal. ♠

Definition 10. Given an argumentation framework AF = ⟨A ,→⟩, a non-

empty set S ⊆ A is D-unattacked if and only if 6 ∃a ∈ (A \ S) : a → S. The

set of D-unattacked sets of AF is denoted as US (AF). ♠

Definition 11. Let AF = ⟨A ,→⟩ be an argumentation framework. The15

restriction of AF to S ⊆A is the argumentation framework AF↓S = ⟨S,→∩(S×S)⟩. ♠

Definition 12.+ A semantics σ satisfies the D-directionality principle if

and only if ∀AF = ⟨A ,→⟩,∀S ∈US (AF),AE σ(AF,S)= Eσ(AF↓S), where

AE σ(AF,S), {(E∩S) | E ∈ Eσ(AF)}⊆ 2S . ♠20

1.2 Acceptability of Arguments [PV02; BG09a]

Definition 13. Given a semantics σ and an argumentation framework

⟨A ,→⟩, an argument AF ∈Dσ is:

• skeptically justified iff ∀E ∈ Eσ(AF), a ∈ S;

• credulously justified iff ∃E ∈ Eσ(AF), a ∈ S. ♠25


Dung’s AF • (Some) Semantics [Dun95]

Definition 14. Given a semantics σ and an argumentation framework

⟨A ,→⟩, an argument AF ∈Dσ is:

• justified iff it is skeptically justified;

• defensible iff it is credulously justified but not skeptically justified;

• overruled iff it is not credulously justified. ♠5

1.3 (Some) Semantics [Dun95]

Lemma 1 (Dung’s Fundamental Lemma, [Dun95, Lemma 10]). Given anargumentation framework AF = ⟨A ,→⟩, let S ⊆ A be a D-admissible setof arguments, and a,b be arguments which are acceptable with respect toS. Then:10

1. S′ = S∪ {a} is D-admissible; and

2. b is D-acceptable with respect to S′. ♣

Theorem 1 ([Dun95, Theorem 11]). Given an argumentation frameworkAF = ⟨A ,→⟩, the set of all D-admissible sets of ⟨A ,→⟩ form a completepartial order with respect to set inclusion. ♣15

Definition 15 (Complete Extension).+ Given an argumentation frame-

work AF = ⟨A ,→⟩, S ⊆A is a D-complete extension iff S is D-conflict-free

and S =FAF (S). C O denotes the complete semantics. ♠

Definition 16 (Grounded Extension).+ Given an argumentation frame-

work AF = ⟨A ,→⟩. The grounded extension of AF is the least complete20

extension of AF. GR denotes the grounded semantics. ♠

Definition 17 (Preferred Extension).+ Given an argumentation frame-

work AF = ⟨A ,→⟩. A preferred extension of AF is a maximal (w.r.t. set

inclusion) complete extension of AF. P R denotes the preferred seman-tics. ♠25

Definition 18. Given an argumentation framework AF = ⟨A ,→⟩ and

S ⊆A , S+ , {a ∈A | ∃b ∈ S ∧ b → a}. ♠

Definition 19 (Stable Extension).+ Given an argumentation framework

AF = ⟨A ,→⟩. S ⊆A is a stable extension of AF iff S is a preferred exten-

sion and S+ =A \ S. S T denotes the stable semantics. ♠30


Dung’s AF • Labelling-Based Semantics Representation[Cam06]

C O GR P R S T

D-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

Table 1.1: Satisfaction of general properties by argumentation semantics[BG07; BCG11]

S T

P R

C O GR

Figure 1.1: Relationships among argumentation semantics

1.4 Labelling-Based Semantics Representation[Cam06]

Definition 20. Let Γ = Γ be an argumentation framework. A labelling

L ab ∈ L(Γ) is a complete labelling of Γ iff it satisfies the following condi-

tions for any a1 ∈A :5

• L ab(a1)= in⇔∀a2 ∈ a−1 L ab(a2)= out;

• L ab(a1)= out⇔∃a2 ∈ a−1 : L ab(a2)= in. ♠

The grounded and preferred labelling can then be defined on the basis

of complete labellings.

Definition 21. Let Γ = Γ be an argumentation framework. A labelling10

L ab ∈L(Γ) is the grounded labelling of Γ if it is the complete labelling of Γ

minimizing the set of arguments labelled in, and it is a preferred labellingof Γ if it is a complete labelling of Γ maximizing the set of arguments

labelled in. ♠

In order to show the connection between extensions and labellings, let15

us recall the definition of the function Ext2Lab, returning the labelling

corresponding to a D-conflict-free set of arguments S.

Definition 22. Given an AF Γ= Γ and a D-conflict-free set S ⊆A , the cor-

responding labelling Ext2Lab(S) is defined as Ext2Lab(S)≡L ab, where

• L ab(a1)= in⇔ a1 ∈ S20

• L ab(a1)= out⇔∃ a2 ∈ S s.t. a2 → a1



σ=C O σ=GR σ=P R σ=S T

EXISTSσ trivial trivial trivial NP-cCAσ NP-c polynomial NP-c NP-cSAσ polynomial polynomial Π

p2 -c coNP-c

VERσ polynomial polynomial coNP-c polynomialNEσ NP-c polynomial NP-c NP-c

Table 1.2: Complexity of decision problems by argumentation semantics[DW09]

• L ab(a1)= undec⇔ a1 ∉ S∧@ a2 ∈ S s.t. a2 → a1 ♠

[Cam06] shows that there is a bijective correspondence between the

complete, grounded, preferred extensions and the complete, grounded,

preferred labellings, respectively.

Proposition 1. Given an an AF Γ= Γ, L ab is a complete (grounded, pre-5

ferred) labelling of Γ if and only if there is a complete (grounded, preferred)extension S of Γ such that L ab = Ext2Lab(S). ♣

The set of complete labellings of Γ is denoted as LC O (Γ), the set of

preferred labellings as LP R(Γ), while LGR(Γ) denotes the set including

the grounded labelling.10

Remark 1.+ To exercise yourself, try Arg Teach [DS14] at http://www-argteach.

doc.ic.ac.uk/


http://www-argteach.doc.ic.ac.uk/



Dung’s AF • Skepticism Relationships [BG09b]

GR

C O

P R

GR

C O

P RS T

Figure 1.2: ¹S⊕ relation for any argumentation framework (left) and forargumentation framework where stable extensions exist (right).

1.5 Skepticism Relationships [BG09b]

E1 ¹E E2 denotes that E1 is at least as skeptical as E2.

Definition 23. Let ¹E be a skepticism relation between sets of exten-

sions. The skepticism relation between argumentation semantics ¹S is

such that for any argumentation semantics σ1 and σ2, σ1 ¹S σ2 iff ∀AF ∈5

Dσ1 ∩Dσ2 , EAF (σ1)¹E EAF (σ2). ♠

Definition 24. Given two sets of extensions E1 and E2 of an argumenta-

tion framework AF:

• E1 ¹E∩+ E2 iff ∀E2 ∈ E2, ∃E1 ∈ E1: E1 ⊆ E2;

• E1 ¹E∪+ E2 iff ∀E1 ∈ E1, ∃E2 ∈ E2: E1 ⊆ E2. ♠10

Lemma 2. Given two argumentation semantics σ1 and σ2, if for anyargumentation framework AF EAF (σ1) ⊆ EAF (σ2), then σ1 ¹E

∩+ σ2 andσ1 ¹E

∪+ σ2 (σ1 ¹E⊕ σ2). ♣

1.6 Signatures [Dun+14]

Let A be a countably infinite domain of arguments, and15

AFA = {⟨A ,→⟩ | A ⊆A,→⊆A ×A }.

Definition 25. The signature Σσ of a semantics σ is defined as

Σσ = {σ(F) | F ∈ AFA}

(i.e. the collection of all possible sets of extensions an AF can possess

under a semantics). ♠20

Given S⊆ 2A, ArgsS =⋃S∈S S, PairsS = {⟨a,b⟩ | ∃S ∈S s.t. {a,b}⊆ S}. S

is called an extension-set if ArgsS is finite.

Definition 26. Let S⊆ 2A. S is incomparable if ∀S,S′ ∈S, S ⊆ S′ implies

S = S′. ♠


Dung’s AF • Signatures [Dun+14]

Definition 27. An extension-set S ⊆ 2A is tight if ∀S ∈ S and a ∈ ArgsS

it holds that if S ∪ {a} 6∈ S then there exists an b ∈ S such that ⟨a,b⟩ 6∈PairsS. ♠

Definition 28. S ⊆⊆ 2A is adm-closed if for each A,B ∈ S the following

holds: if ⟨a,b⟩ ∈PairsS for each a,b ∈ A∪B, then also A∪B ∈S. ♠5

Proposition 2. For each F ∈ AFA:

• S T (F) is incomparable and tight;

• P R(F) is non-empty, incomparable and adm-closed. ♣

Theorem 2. The signatures for S T and P R are:

• ΣS T = {S | S is incomparable and tight};10

• ΣP R = {S 6= ; | S is incomparable and adm-closed}. ♣


Dung’s AF • Signatures [Dun+14]

Consider

S= { { a,d, e },

{ b, c, e },

{ a,b,d } }


Dung’s AF • Decomposability and Transparancy [Bar+14]

1.7 Decomposability and Transparancy [Bar+14]

Definition 29. Given an argumentation framework AF = (A ,→),

a labelling-based semantics σ associates with AF a subset of L(AF), de-

noted as Lσ(AF). ♠

Definition 30. Given AF = (A ,→) and a set Args⊆A , the input of Args,5

denoted as Argsinp, is the set {B ∈A \Args | ∃A ∈Args, (B, A) ∈→}, the con-ditioning relation of Args, denoted as ArgsR , is defined as →∩(Argsinp×Args). ♠

Definition 31. An argumentation framework with input is a tuple

(AF,I ,LI ,RI ), including an argumentation framework AF = (A ,→), a10

set of arguments I such that I ∩A =;, a labelling LI ∈LI and a rela-

tion RI ⊆ I ×A . A local function assigns to any argumentation frame-

work with input a (possibly empty) set of labellings of AF, i.e.

F(AF,I ,LI ,RI ) ∈ 2L(AF). ♠

Definition 32. Given an argumentation framework with input15

(AF,I ,LI ,RI ), the standard argumentation framework w.r.t.

(AF,I ,LI ,RI ) is defined as AF ′ = (A ∪I ′,→ ∪R′I ), where I ′ = I ∪

{A′ | A ∈ out(LI )} and R′I = RI ∪ {(A′, A) | A ∈ out(LI )}∪ {(A, A) | A ∈

undec(LI )}. ♠

Definition 33. Given a semantics σ, the canonical local function of σ20

(also called local function of σ) is defined as Fσ(AF,I ,LI ,RI )= {Lab↓A |Lab ∈Lσ(AF ′)}, where AF = (A ,→) and AF ′ is the standard argumenta-

tion framework w.r.t. (AF,I ,LI ,RI ). ♠

Definition 34. A semantics σ is complete-compatible iff the following

conditions hold:25

1. For any argumentation framework AF = (A ,→), every labelling L ∈Lσ(AF) satisfies the following conditions:

• if A ∈A is initial, then L(A)= in

• if B ∈ A and there is an initial argument A which attacks B,

then L(B)= out30

• if C ∈ A is self-defeating, and there are no attackers of C be-

sides C itself, then L(C)= undec

2. for any set of arguments I and any labelling LI ∈ LI , the ar-

gumentation framework AF ′ = (I ′,→′), where I ′ = I ∪ {A′ | A ∈out(LI )} and →′= {(A′, A) | A ∈ out(LI )}∪ {(A, A) | A ∈ undec(LI )},35

admits a (unique) labelling, i.e. |Lσ(AF ′)| = 1. ♠


Dung’s AF • Extension-based I/O Characterisation[GLW16]

Definition 35. A semantics σ is fully decomposable (or simply decom-posable) iff there is a local function F such that for every argumenta-

tion framework AF = (A ,→) and every partition P = {P1, . . .Pn} of A ,

Lσ(AF) = U (P , AF,F) where U (P , AF,F) , {LP1 ∪ . . . ∪ LPn |LPi ∈ F(AF↓Pi ,Pi

inp, (⋃

j=1···n, j 6=i LP j )↓Piinp ,Pi

R)}. ♠5

Definition 36. A complete-compatible semantics σ is top-down decom-posable iff for any argumentation framework AF = (A ,→) and any parti-

tion P = {P1, . . .Pn} of A , it holds that Lσ(AF)⊆U (P , AF,Fσ). ♠

Definition 37. A complete-compatible semantics σ is bottom-up decom-posable iff for any argumentation framework AF = (A ,→) and any parti-10

tion P = {P1, . . .Pn} of A , it holds that Lσ(AF)⊇U (P , AF,Fσ). ♠

C O S T GR P R

Full decomposability Yes Yes No NoTop-down decomposability Yes Yes Yes YesBottom-up decomposability Yes Yes No No

Table 1.3: Decomposability properties of argumentation semantics.

1.8 Extension-based I/O Characterisation [GLW16]

Definition 38. Given input arguments I and output arguments O with

I ∩O = ;, an I/O-gadget is an AF F = (A,R) such that I,O ⊆ A and I−F =;. ♠15

Definition 39. Given an I/O-gadget F = (A,R) the injection of J ⊆ I to Fis the AF .(F, J)= (A∪ {z},R∪ {(z, i) | i ∈ (I \ J)}). ♠

Definition 40. An I/O-specification consists of two sets I,O ⊆ A and a

total function f : 2I 7→ 22O. ♠

Definition 41. The I/O-gadget F satisfies I/O-specification f under se-20

mantics σ iff ∀J ⊆ I : σ(.(F, J))|O = f(J). ♠

Theorem 3. An I/O-specification f is satisfiable under σ iffS T : >P R: ∀J ⊆ I : |f(J)| ≥ 1

C O : ∀J ⊆ I : |f(J)| ≥ 1∧⋂f(J) ∈ f(J)

GR: ∀J ⊆ I : |f(J)| = 1♣


2 Implementations

Acknowledgement


Massimiliano Giacomin, Mauro Vallati, and Stefan Woltran.

Comprehensive survey recently published in [Cha+15].5

2.1 Ad Hoc Procedures

NAD-Alg [NDA12; NAD14]

2.2 Constraint Satisfaction Programming

A Constraint Satisfaction Problem (CSP) P [BS12; RBW08] is a triple

P = ⟨X ,D,C⟩ such that:10

• X = ⟨x1, . . . , xn⟩ is a tuple of variables;

• D = ⟨D1, . . . ,Dn⟩ a tuple of domains such that ∀i, xi ∈ D i;

• C = ⟨C1, . . . ,Ct⟩ is a tuple of constraints, where ∀ j,C j = ⟨RS j ,S j⟩,S j ⊆ {xi|xi is a variable}, RS j ⊆ SD

j ×SDj where SD

j = {D i|D i is a

domain, and xi ∈ S j}.15

A solution to the CSP P is A = ⟨a1, . . . ,an⟩ where ∀i,ai ∈ D i and ∀ j,RS j

holds on the projection of A onto the scope S j. If the set of solutions is

empty, the CSP is unsatisfiable.


Implementations • Answer Set Programming

CONArg2 [BS12]

In [BS12], the authors propose a mapping from AFs to CSPs.

Given an AF Γ, they first create a variable for each argument whose

domain is always {0,1} — ∀ai ∈A ,∃xi ∈ X such that D i = {0,1}.

Subsequently, they describe constraints associated to different defi-5

nitions of Dung’s argumentation framework: for instance {a1,a2} ⊆ A is

D-conflict-free iff ¬(x1 = 1∧ x2 = 1).

2.3 Answer Set Programming

Answer Set Programming (ASP) [Fab13] is a declarative problem solving

paradigm. In ASP, representation is done using a rule-based language,10

while reasoning is performed using implementations of general-purpose

algorithms, referred to as ASP solvers.

AspartixM [EGW10; Dvo+11]

AspartixM [Dvo+11] expresses argumentation semantics in Answer Set

Programming (ASP): a single program is used to encode a particular ar-15

gumentation semantics, and the instance of an argumentation framework

is given as an input database. Tests for subset-maximality exploit the

metasp optimisation frontend for the ASP-package gringo/claspD.

Given an AF Γ, Aspartix encodes the requirements for a “semantics”

(e.g. the D-conflict-free requirements) in an ASP program whose database20

considers:

{arg(a) | a ∈A }∪ {defeat(a1,a2) | ⟨a1,a2⟩ ∈→}

The following program fragment is thus used to check the D-conflict-

freeness [Dvo+11]:

πc f = { in(X )← not out(X ),arg(X );

out(X )← not in(X ),arg(X );

← in(X ), in(Y ),defeat(X ,Y )}.

25

πS T = { 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 )}.

2.4 Propositional Satisfiability Problems

In the propositional satisfiability problem (SAT) the goal is to determine

whether a given Boolean formula is satisfiable. A variable assignment

that satisfies a formula is a solution.30


Implementations • Propositional Satisfiability Problems

In SAT, formulae are commonly expressed in Conjunctive Normal Form

(CNF). A formula in CNF is a conjunction of clauses, where clauses are

disjunctions of literals, and a literal is either positive (a variable) or neg-

ative (the negation of a variable). If at least one of the literals in a clause

is true, then the clause is satisfied, and if all clauses in the formula are5

satisfied then the formula is satisfied and a solution has been found.

PrefSAT [Cer+14b]

Requirements for complete labelling as a CNF [Cer+14b]: for each argu-

ment ai ∈ A , three propositional variables are considered: I i (which is

true iff L ab(ai) = in), Oi (which is true iff L ab(ai) = out), Ui (which is10

true iff L ab(ai)= undec). Given |A | = k and φ : {1, . . . ,k} 7→A .

∧i∈{1,...,k}

((I i ∨Oi ∨Ui)∧ (¬I i ∨¬Oi)∧(¬I i ∨¬Ui)∧ (¬Oi ∨¬Ui)

)(2.1)

∧{i|φ(i)−=;}

I i (2.2)

∧{i|φ(i)− 6=;}

(I i ∨

( ∨{ j|φ( j)→φ(i)}

(¬O j)

))(2.3)

∧{i|φ(i)− 6=;}

( ∧{ j|φ( j)→φ(i)}

¬I i ∨O j

)(2.4)15

∧{i|φ(i)− 6=;}

( ∧{ j|φ( j)→φ(i)}

¬I j ∨Oi

)(2.5)

∧{i|φ(i)− 6=;}

(¬Oi ∨

( ∨{ j|φ( j)→φ(i)}

I j

))(2.6)

∧{i|φ(i)− 6=;}

( ∧{k|φ(k)→φ(i)}

(Ui ∨¬Uk ∨

( ∨{ j|φ( j)→φ(i)}

I j

)))(2.7)

∧{i|φ(i)− 6=;}

(( ∧{ j|φ( j)→φ(i)}

(¬Ui ∨¬I j)

)∧

(¬Ui ∨

( ∨{ j|φ( j)→φ(i)}

U j

)))(2.8)

∨i∈{1,...k}

I i (2.9)20



As noticed in [Cer+14b], the conjunction of the above formulae is re-

dundant. However, the non-redundant CNFs are not equivalent from an

empirical evaluation [Cer+14b]: the overall performance is significantly

affected by the chosen configuration pair CNF encoding–SAT solver.



Algorithm 1 Enumerating the D-preferred extensions of an AFPrefSAT(Γ)

1: Input: Γ= Γ2: Output: Ep ⊆ 2A

3: Ep := ;4: cnf := ΠΓ

5: repeat6: cnf d f := cnf

7: pre f cand := ;8: repeat

9: lastcompf ound := SatS(cnf d f )

10: if lastcompf ound != ε then

11: pre f cand := lastcompf ound

12: for a1 ∈ I-ARGS(lastcompf ound) do

13: cnf d f := cnf d f ∧ Iφ−1(a1)

14: end for

15: remaining := F ALSE

16: for a1 ∈A \ I-ARGS(lastcompf ound) do

17: remaining := remaining∨ Iφ−1(a1)

18: end for

19: cnf d f := cnf d f ∧ remaining

20: end if

21: until (lastcompf ound != ε∧ I-ARGS(lastcompf ound) != A )

22: if pre f cand != ; then

23: Ep := Ep ∪ {I-ARGS(pre f cand)}

24: oppsolution := F ALSE

25: for a1 ∈A \ I-ARGS(pre f cand) do

26: oppsolution := oppsolution∨ Iφ−1(a1)

27: end for

28: cnf := cnf ∧ oppsolution

29: end if30: until (pre f cand != ;)

31: if Ep =; then32: Ep = {;}

33: end if34: return Ep



Parallel-SCCp [Cer+14a; Cer+15]

Based on the SCC-Recursiveness Schema [BGG05].

ab

ef

cd

gh



Algorithm 1 Computing D-preferred labellings of an AFP-PREF(Γ)

1: Input: Γ= Γ2: Output: Ep ∈ 2L(Γ)

3: return P-SCC-REC(Γ,A )

Algorithm 2 Greedy computation of base casesGREEDY(L,C)

1: Input: L = (L1, . . . ,Ln := {Sn1 , . . . ,Sn

h}),C ⊆A

2: Output: M = {. . . , (Si,Bi), . . .}3: M :=;4: for S ∈⋃n

i=1 Li do in parallel5: B := B-PR(Γ↓S ,S∩C)6: M = M∪ {(S,B)}7: end for8: return M

BOUNDCOND(Γ,Si,L ab) returns (O, I) where O = {a1 ∈ Si | ∃a2 ∈S ∩a−

1 : L ab(a2) = in} and I = {a1 ∈ Si | ∀ a2 ∈ S ∩a−1 ,L ab(a2) = out},

with S ≡ S1 ∪ . . .∪Si−1.



Algorithm 3 Determining the D-grounded labelling of an AF in a set CGROUNDED(Γ,C)

1: Input: Γ= Γ, C ⊆A

2: Output: (L ab,U) : U ⊆A ,L ab ∈LA \U3: L ab := ;4: U := A

5: repeat6: initial f ound := ⊥7: for a1 ∈ C do8: if {a2 ∈U | a2 → a1}=; then9: initial f ound := >

10: L ab := L ab∪ {(a1,in)}11: U := U \a1

12: C := C \a1

13: for a2 ∈ (U ∩a+1 ) do

14: L ab := L ab∪ {(a2,out)}15: U := U \a2

16: C := C \a2

17: end for18: end if19: end for20: until (initial f ound)21: return(L ab,U)



Algorithm 4 Computing D-preferred labellings of an AF in CP-SCC-REC(Γ,C)

1: Input: Γ= Γ, C ⊆A

2: Output: Ep ∈ 2L(Γ)

3: (L ab,U)=GROUNDED(Γ,C)

4: Ep := {L ab}

5: Γ=Γ↓U

6: L:= (L1 := {S11, . . . ,S1

k}, . . . ,Ln := {Sn1 , . . . ,Sn

h})

=SCCS-LIST(Γ)7: M := {. . . , (Si,Bi), . . .}=GREEDY(L,C)

8: for l ∈ {1, . . . ,n} do9: E l := {ES1

l := (), . . . ,ESkl := ()}

10: for S ∈ Ll do in parallel

11: for L ab ∈ Ep do in parallel

12: (O, I) := L-COND(Γ,S,Ll ,L ab)

13: if I =; then

14: ESl [L ab]={{(a1,out) | a1 ∈O} ∪ {(a1,undec) | a1 ∈ S \O}}

15: else

16: if I = S then

17: ESl [L ab]= B where (S,B) ∈ M

18: else

19: if O =; then

20: ESl [L ab]=B-PR(Γ↓S , I ∩C)

21: else

22: ESl [L ab]={{(a1,out) | a1 ∈O}}

23: ESl [L ab]= ES

l [L ab]⊗P-SCC-REC(Γ↓S\O, I ∩C)

24: end if

25: end if

26: end if

27: end for

28: end for

29: for S ∈ Ll do

30: E′p := ;

31: for L ab ∈ Ep do in parallel

32: E′p = E′

p ∪ ({L ab}⊗ESl [L ab])

33: end for

34: Ep := E′p

35: end for36: end for37: return Ep


Implementations • Second-order Solver [BJT16]

2.5 Second-order Solver [BJT16]

http://research.ics.aalto.fi/software/sat/sat-to-sat/so2grounder.

shtml

Given a representation of an argumentation framework such as:

• a(X ) holds iff X is an argument;5

• r(X ,Y ) holds iff X attacks Y ;

then:

• TCF = {@N, M | r(N, M) ∧ s(N) ∧ s(M).}

• TAD ={

∀N | att(N) ⇐⇒ ( a(N) ∧ ∃M | r(M, N) ∧ s(M) ).

∀N | def (N) ⇐⇒ ( a(N) ∧ ∀M | r(M, N)=⇒ att(M) ).

}

• TFP = {TAD . ∀N | s(N) ⇐⇒ def (N).}10

• TGR =

TFP .

@s′,att′,de f ′ :

TFP [s/s′,def /def ′,att/att′] ∧( ∀N | s′(N)=⇒ s(N) ) ∧( ∃N | s(N)∧¬s′(N) )

• TST = {TAD . ∀N | a(N)=⇒ ( s(N) ⇐⇒ ¬att(N) ).}

• TCO = {TFP . TCF .}

• TPR =

TCO.

@s′,att,′ ,def ′ :

TCO[s/s′,def /def ′,att/att′] ∧( ∀N | s(N)=⇒ s′(N) ) ∧∃N | s′(N) ∧ ¬s(N).

The unary predicate s describes the extensions in the various seman-15

tics.

2.6 Which One?

We need to be smartHolger H. Hoos, Invited Keynote Talk at ECAI2014

Features for AFs [VCG14; CGV14]20

Directed Graph (26 features)


http://research.ics.aalto.fi/software/sat/sat-to-sat/so2grounder.shtml



Implementations • Which One?

Structure:

# vertices ( |A | )

# edges ( |→ | )

# vertices / #edges ( |A |/|→ | )

# edges / #vertices ( |→ |/|A | )

density

average

Degree: stdev

attackers max

min

#

average

stdev

max

SCCs:

min

Structure:

# self-def

# unattacked

flow hierarchy

Eulerian

aperiodic

CPU-time: . . .



Undirected Graph (24 features)

Structure:

# edges

# vertices / #edges

# edges / #vertices

density

Degree:

average

stdev

max

min

SCCs:

#

average

stdev

max

min

Structure: Transitivity

3-cycles:

#

average

stdev

max

min

CPU-time: . . .

Average CPU-time, stdev, needed for extracting the featuresDirect Graph Features (DG)

Class CPU-Time # featMean stdDev

Graph Size 0.001 0.009 5

Degree 0.003 0.009 4

SCC 0.046 0.036 5

Structure 2.304 2.868 5

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

Mean stDev

Graph Size 0.001 0.003 4

Degree 0.002 0.004 4

SCC 0.011 0.009 5

Structure 0.799 0.684 1

Triangles 0.787 0.671 5

5

Best Features for Runtime Prediction [CGV14]

Determined by a greedy forward search based on the Correlation-based

Feature Selection (CFS) attribute evaluator.



Solver B1 B2 B3

AspartixM num. arguments density (DG) size max. SCC

PrefSAT density (DG) num. SCCs aperiodicity

NAD-Alg density (DG) CPU-time density CPU-time Eulerian

SSCp density (DG) num. SCCs size max SCC

Predicting the (log)Runtime [CGV14]

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

Log runtime is defined as

√∑ni=1

(log10( ti )− log10( yi )

)2

n5

Best Features for Classification [CGV14]

Determined by a greedy forward search based on the Correlation-based

Feature Selection (CFS) attribute evaluator.

C-B1 C-B2 C-B3

num. arguments density (DG) min attackers

Classification [CGV14]10

Classification (Higher is better)

C−B1 C-B2 C-B3 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%

Selecting the Best Algorithm [CGV14]

Metric: Fastest

(max. 1007)

AspartixM 106

NAD-Alg 170

PrefSAT 278

SSCp 453

EPMs Regression 755

EPMs Classification 788



Metric: IPC

(max. 1007)

NAD-Alg 210.1

AspartixM 288.3

PrefSAT 546.7

SSCp 662.4

EPMs Regression 887.7

EPMs Classification 928.1

IPC score1: for each AF, each system gets a score of T∗/T, where Tis its execution time and T∗ the best execution time among the compared

systems, or a score of 0 if it fails in that case. Runtimes below 0.01 seconds

get by default the maximal score of 1. The IPC score considers, at the5

same time, the runtimes and the solved instances

1 http://ipc.informatik.uni-freiburg.de/ .


http://ipc.informatik.uni-freiburg.de/

3 Ranking-Based Semantics

3.1 The Categoriser Semantics [BH01]

Definition 42 ([BH01]). Let Γ= ⟨A ,→⟩ be an argumentation framework.

The categoriser function Cat : A 7→]0,1] is defined as:

Cat(a1)=

1 if a−

1 =;1

1+∑a2∈a−

1Cat(a2)

otherwise5

♠

3.2 Properties for Ranking-Based Semantics[Bon+16]

Preliminary notions

Definition 43. Let Γ = ⟨A ,→⟩ and a1,a2 ∈ A . A path from a2 to a1,10

noted P(a2,a1) is a sequence s = ⟨b0, . . . ,bn⟩ of arguments such as b0 = a1,

bn = a2, and ∀i < n,⟨bi+1,bi⟩ ∈ A . We denote by lP = n the length of P.

A defender (resp. attacker) of a1 is an argument situated at the begin-

ning of an even-length (resp. odd-length) path. We denote the multiset

of defenders and attackers of a1 by R+n {a2 | ∃P(a2,a1) with lP ∈ 2N} and15

R−n = {a2 | ∃P(a2,a1) with lP ∈ 2N+ 1} respectively. The direct attack-

ers of a1 are arguments in R−1 (a1) = a−

1 . An argument a1 is defended if

R+2 (a1)= {a−

1 }− 6= ;.

A defence root (resp. attack root) is a non-attacked defender (resp.

attacker). We denote the mulitset of defence roots and attacks roots of a120

by BR+n (a1) = {a2 ∈ R+

n (a1) | a−2 = ;} and BR−

n (a1) = {a2 ∈ R−n (a1) | a−

2 =;} respectively. A path from a2 to a1 is a defence branch (resp. attackbranch) if a2 is a defence (resp. attack) root of a1. Let us note BR+(a1) =⋃

n BR+n (a1) and BR−(a1)=⋃

n BR−n (a1). ♠

Definition 44. A ranking-based semantics σ associates to any argumen-25

tation framework Γ= ⟨A ,→⟩ is a ranking ºσΓ on A , where ºσ

Γ is a preorder

(a reflexive and transitive relation) on A . a1 ºσΓ a2 means that a1 is at

least as acceptable as a2. a1 ÂσΓ a2 iff a1 ºσ

Γ a2 and a2�σΓ a1. ♠

Definition 45. A lexicographical order between two vectors of real num-

ber V = ⟨V1, . . . ,Vn⟩ and V ′ = ⟨V ′1, . . . ,V ′

n⟩, is defined as V ºlex V ′ iff ∃i ≤ n30

s.t. Vi ≥V ′i and ∀ j < i, Vj =V ′

j . ♠


Ranking-Based Semantics • Properties for Ranking-Based Semantics [Bon+16]

Definition 46. An isomorphism γ between two argumentation frame-

works Γ= ⟨A ,→⟩ and Γ′ = ⟨A ′,→′⟩ is a bijective function γ : A 7→A ′ such

that ∀a24,a25 ∈ A , ⟨a24,a25⟩ ∈→ iff ⟨γ(a24),γ(a25)⟩ ∈→′. With a slight

abuse of notation, we will note Γ′ = γ(Γ). ♠

Definition 47 ([AB13]). Let ≥S be a ranking on a set of argument A .5

For any S1,S2 ⊆ A , S1 ≥S S2 is a group comparison iff there exists an

injective mapping f from S2 to S1 such that ∀a1 ∈ S2, f (a1) Â a1. An

S1 >S S2 is a strict group comparison iff S1 ≥S S2 and (|S2| < |S1| or

∃a1 ∈ S2, f (a1)Â a1). ♠

Definition 48. Let Γ= ⟨A ,→⟩ and a1 ∈A . The defence of a1 is simple iff10

every defender of a1 attacks exactly one direct attacker of a2. The defence

of a1 is distributed iff every direct attacker of a1 is attacked by at most

one argument. ♠

Definition 49. Let Γ = ⟨A ,→⟩, a1 ∈ A . The defence branch added to a1

is P+(a1) = ⟨A ,→′⟩, with A ′ = {b0, . . . ,bn},n ∈ 2N,b0 = a1,A ∩A ′ = {a1},15

and →′= {⟨bi,bi−1⟩ | i ≤ n}. The attack branch added to a1, denoted

P−(a1) is defined similarly except that the sequence is of odd length (i.e.

n = 2N+1). ♠

Properties

Given a ranking-based semantics σ, Γ= ⟨A ,→⟩, ∀a1,a2 ∈A :20

Abstraction (Abs) [AB13]. The ranking on A should be defined only

on the basis of the attacks between arguments.

Let Γ′ = ⟨A ′,→′⟩. For any isomorphism γ s.t. Γ′ = γ(Γ), a1 ºσΓ a2 iff

γ(a1)ºσΓ′ γ(a2).

Independence (In) [MT08; AB13]. The ranking between two argu-25

ments a1 and a2 should be independent of any argument that is neither

connected to a1 nor to a2.

∀Γ′ = ⟨A ′,→′⟩ ∈ cc(Γ),1 ∀a1,a2 ∈A ′, a1 ºσΓ′ a2 ⇒ a1 ºσ

Γ a2.

Void Precedence (VP) [CL05; MT08; AB13]. A non-attacked argu-

ment is ranked strictly higher than any attacked argument.30

a−1 =; and a−

2 6= ; ⇒ a1 ºσ a2.

Self-Contradiction (SC) [MT08]. A self-attacking argument is ranked

lower than any non self-attacking argument.

⟨a1,a1⟩ 6=→ and ⟨a2,a2⟩ ∈→ ⇒ a1 ºσ a2.

1cc(Γ) denotes the set of connected components of an AF Γ.



Cardinality Precedence (CP) [AB13]. The greater the number of di-

rect attackers for an argument, the weaker the level of acceptability of

this argument.

|a−1 | < |a−

2 | ⇒ a1 ºσ a2.

Quality Precedence (QP) [AB13]. The greater the acceptability of5

one direct attacker for an argument, the weaker the level of acceptability

of this argument.

∃a3 ∈ a−2 s.t. ∀a4 ∈ a−

1 , a3 ºσ a4 ⇒ a1 ºσ a2.

Counter-Transitivity (CT) [AB13]. If the direct attackers of a2 are

at least as numerous and acceptable as those of a1, then a1 is at least as10

acceptable as a2.

a−2 ≥S a−

1 ⇒ a1 ºσ a2.

Strict Counter-Transitivity (SCT) [AB13]. If CT is satisfied and ei-

ther the direct attackers of a2 are strictly more numerous or acceptable

than those of a1, then a1 is strictly more acceptable than a2.15

a−2 >S a−

1 ⇒ a1 Âσ a2.

Defence Precedence (DP) [AB13]. For two arguments with the same

number of direct attackers, a defended argument is ranked higher than a

non-defended argument.

|a−1 | = |a−

2 |, {a−1 }− 6= ; and {a−

2 }− =; ⇒ a1 Âσ a2.20

Distributed-Defence Precedence (DDP) [AB13]. The best defense

is when each defender attacks a distinct attacker.

|a−1 | = |a−

2 | and {a−1 }− = {a−

2 }−, if the defence of a1 is simple and distributed

and the defence of a2 is simple but not distributed, then a1 Âσ a2.

Strict addition of Defence Branch (⊕DB) [CL05]. Adding a defence25

branch to any argument improves its ranking.

Given γ an isomorphism. If Γ∗ =Γ∪γ(Γ)∪P+(γ(a1)), then γ(a1)ÂσΓ+ a1.

Increase of Defence Branch (↑DB) [CL05]. Increasing the length of

a defence branch of an argument degrades its ranking.

Given γ an isomorphism. If a2 ∈ BR+(a1), a2 ∉ BR−(a1) and Γ∗ =Γ∪γ(Γ)∪30

P+(γ(a2)), then a1 ÂσΓ∗ γ(a1).

Addition of Defence Branch (+DB) [CL05]. Adding a defence branch

to an attached argument improves its ranking.

Given γ an isomorphism. If Γ∗ = Γ∪γ(Γ)∪P+(γ(a1)) and |a−1 | 6= 0, then

γ(a1)ÂσΓ+ a1.35



Increase of Attack Branch (↑AB) [CL05]. Increasing the length of

an attack branch of an argument improves its ranking.

Given γ an isomorphism. If a2 ∈ BR−(a1), a2 ∉ BR+(a1) and Γ∗ =Γ∪γ(Γ)∪P+(γ(a2)), then γ(a1)Âσ

Γ∗ a1.

Addition of Attack Branch (+AB) [CL05]. Adding an attack branch5

to any argument degrades its ranking.

Given γ an isomorphism. If Γ∗ =Γ∪γ(Γ)∪P−(γ(a1)), then a1 ÂσΓ∗ γ(a1).

Total (Tot) [Bon+16]. All pairs of arguments can be compared.

a1 ºσ a2 or a2 ºσ a1.

Non-attacked Equivalence (NaE) [Bon+16]. All the non-attacked10

argument have the same rank.

a−1 =; and a−

2 =; ⇒ a1 'σ a2.

Attack vs Full Defence (AvsFD) [Bon+16]. An argument without

any attack branch is ranked higher than an argument only attacked by

one non-attacked argument.15

Γ is acyclic, |BR−(a1)| = 0, |a−2 | = 1, and |{a−

2 }−| = 0 ⇒ a1 Âσ a2.

CP incompatible with QP [AB13]CP incompatible with AvsFD [Bon+16]CP incompatible with +DB [Bon+16]VP incompatible with ⊕DB [Bon+16]

Table 3.1: Incompatible properties

SCT implies VP [AB13]CT implies DP [AB13]SCT implies CT [Bon+16]CT implies NaE [Bon+16]⊕DB implies +DB [Bon+16]

Table 3.2: Dependencies among properties



Property Yes/No Comment

Abs YesIn YesVP Yes Implied by SCTDP Yes Implied by CTCT Yes Implied by SCTSCT YesCP NoQP NoDDP NoSC No⊕DB No Incompatible with VP+AB Yes+DB No↑AB Yes↑DB YesTot YesNaE Yes Implied by CTAvsFD No

Table 3.3: Properties satisfied by Cat [BH01]


4 Argumentation Schemes

Argumentation schemes [WRM08] are reasoning patterns which generate

arguments:

• deductive/inductive inferences that represent forms of common types

of arguments used in everyday discourse, and in special contexts5

(e.g. legal argumentation);

• neither deductive nor inductive, but defeasible, presumptive, or ab-

ductive.

Moreover, an argument satisfying a pattern may not be very strong by

itself, but may be strong enough to provide evidence to warrant rational10

acceptance of its conclusion, given that it premises are acceptable.

According to Toulmin [Tou58] such an argument can be plausible and

thus accepted after a balance of considerations in an investigation or dis-

cussion moved forward as new evidence is being collected. The investiga-

tion can then move ahead, even under conditions of uncertainty and lack15

of knowledge, using the conclusions tentatively accepted.

4.1 An example: Walton et al. ’s ArgumentationSchemes for Practical Reasoning

Suppose I am deliberating with my spouse on what to do

with our pension investment fund — whether to buy stocks,20

bonds or some other type of investments. We consult with a

financial adviser, and expert source of information who can

tell us what is happening in the stock market, and so forth at

the present time [Wal97].

Premises for practical inference:25

1. states that an agent (“I” or “my”) has a particular goal;

2. states that an agent has a particular goal.

⟨S0,S1, . . . ,Sn⟩ represents a sequence of states of affairs that can be

ordered temporally from earlier to latter. A state of affairs is meant to be

like a statement, but one describing some event or occurrence that can30

be brought about by an agent. It may be a human action, or it may be a

natural event.


Argumentation Schemes • AS and Dialogues

Practical Inference

Premises:Goal Premise Bringing about Sn is my goal

Means Premise In order to bring about Sn, I need to bring

about Si

Conclusions:Therefore, I need to bring about Si.

Critical questions:Other-Means

Question

Are there alternative possible actions to

bring about Si that could also lead to the

goal?Best-Means

Question

Is Si the best (or most favourable) of the

alternatives?Other-Goals

Question

Do I have goals other than Si whose

achievement is preferable and that

should have priority?Possibility

Question

Is it possible to bring about Si in the

given circumstances?Side Effects

Question

Would bringing about Si have known bad

consequences that ought to be taken into

account?

4.2 AS and Dialogues

Dialogue for practical reasoning: all moves (propose, prefer, justify) are co-

ordinated in a formal deliberation dialogue that has eight stages [HMP01].

1. Opening of the deliberation dialogue, and the raising of a governing

question about what is to be done.5

2. Discussion of: (a) the governing question; (b) desirable goals; (c)

any constraints on the possible actions which may be considered;

(d) perspectives by which proposals may be evaluated; and (e) any

premises (facts) relevant to this evaluation.

3. Suggesting of possible action-options appropriate to the governing10

question.

4. Commenting on proposals from various perspectives.



5. Revising of: (a) the governing question, (b) goals, (c) constraints, (d)

perspectives, and/or (e) action-options in the light of the comments

presented; and the undertaking of any information-gathering or

fact-checking required for resolution.

6. Recommending an option for action, and acceptance or non-accept-5

ance of this recommendation by each participant.

7. Confirming acceptance of a recommended option by each partici-

pant.

8. Closing of the deliberation dialogue.

Proposals are initially made at stage 3, and then evaluated at stages10

4, 5 and 6.

Especially at stage 5, much argumentation taking the form of practi-

cal reasoning would seem to be involved.

As discussed in [Wal06], there are three dialectical adequacy condi-

tions for defining the speech act of making a proposal.15

The Proponent’s Requirement (Condition 1). The proponent

puts forward a statement that describes an action and says that

both proponent and respondent (or the respondent group) should

carry out this action.

The proponent is committed to carrying out that action: the state-20

ment has the logical form of the conclusion of a practical inference,

and also expresses an attitude toward that statement.

The Respondent’s Requirement (Condition 2). The statement

is put forward with the aim of offering reasons of a kind that will

lead the respondent to become committed to it.25

The Governing Question Requirement (Condition 3). The job

of the proponent is to overcame doubts or conflicts of opinions, while

the job of the respondent is to express them. Thus the role of the

respondent is to ask questions that cast the prudential reasonable-

ness of the action in the statement into doubt, and to mount attacks30

(counter-arguments and rebuttals) against it.

Condition 3 relates to the global structure of the dialogue, whereas

conditions 1 and 2 are more localised to the part where the proposal was

made. Condition 3 relates to the global burden of proof [Wal14] and the

roles of the two parties in the dialogue as a whole.35

Speech acts [MP02], like making a proposal, are seen as types of

moves in a dialogue that are governed by rules. Three basic character-

istics of any type of move that have to be defined:



1. pre-conditions of the move;

2. the conditions defining the move itself;

3. the post-conditions that state the result of the move.

Preconditions

• At least two agents (proponent and opponent);5

• A governing question;

• Set of statements (propositions);

• The proponent proposes the proposition to the respondent if and

only if:

1. there is a set of premises that the proponent is committed to,10

and fit the premises of the argumentation scheme for practical

reasoning;

2. the proponent is advocating these premises, that is, he is mak-

ing a claim that they are true or applicable in the case at issue;

3. there is an inference from these premises fitting the argumen-15

tation scheme for practical reasoning; and

4. the proposition is the conclusion of the inference.

The Defining Conditions

The central defining condition sets out the conditions defining the struc-

ture of the move of making a proposal.20

The Goal Statement: We have a goal G.

The Means Statement: Bringing about p is necessary (or suffi-

cient) for us to bring about G.

Then the inference follows.

The Proposal Statement: We should (practically ought to) bring25

about p.



Proposal Statement in form of AS

Premises:Goal Statement We have a goal G.

The Means

Statement

Bringing about p is necessary (or suffi-

cient) for us to bring about G.

Conclusions:We should (practically ought to) bring

about p.

The Post-Conditions

The central post-condition is the response condition.

The proposal must be open to critical questioning by opponent. The

proponent should be open to answering doubts and objections correspond-5

ing to any one of the five critical questions for practical reasoning; as well

as to counter-proposals, and is in charge of giving reasons why her pro-

posal is better than the alternatives.

The response condition set by these critical questions helps to explain

how and why the maker of a proposal needs to be open to questioning and10

to requests for justification.


5 A Semantic-Web View ofArgumentation

Acknowledgement


Chris Reed. An overview can also be find at [Bex+13].5

5.1 The Argument Interchange Format [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

Figure 5.1: Original AIF Ontology [Che+06; Rah+11]

5.2 An Ontology of Arguments [Rah+11]

Please download Protégé from http://protege.stanford.edu/ and the

AIF OWL version from http://www.arg.dundee.ac.uk/wp-content/

uploads/AIF.owl10

Representation of the argument described in Figure 5.2

___jobArg : PracticalReasoning_Inference

fulfils(___jobArg, PracticalReasoning_Scheme)

hasGoalPlan_Premise(___jobArg, ___jobArgGoalPlan)

hasConclusion(___jobArg, ___jobArgConclusion)15

hasGoal_Premise(___jobArg, ___jobArgGoal)

___jobArgConclusion : EncouragedAction_Statement

fulfils(___jobArgConclusion, EncouragedAction_Desc)


http://protege.stanford.edu/

http://www.arg.dundee.ac.uk/wp-content/uploads/AIF.owl



Semantic Web Argumentation • AIF-OWL

PracticalInference

Bringing about is my goal

Sn

Si

In order to bring about I need to bring about

Sn

Therefore I needto bring about Si

hasConcDeschasPremiseDesc

hasPremiseDesc

Bringing about being richis my goal

In order to bring about being richI need to bring about having a job

fulfilsPremiseDesc

fulfilsPremiseDesc

fulfilsScheme

supports

supports

Therefore I needto bring abouthaving a job

hasConclusion

fulfils

Figure 5.2: An argument network linking instances of argument andscheme components

Symmetric attack

r → p

r pMP2A1

A2p → q

p

qMP1

neg1

Undercut attack

r MP2A3

A2 s → v

s

vMP1

cut1p

r → p

Figure 5.3: Examples of conflicts [Rah+11, Fig. 2]

claimText (___jobArgConclusion "Therefore I need to bring about hav-

ing a job")

___jobArgGoal : Goal_Statement

fulfils(___jobArgGoal, Goal_Desc)

claimText (___jobArgGoal "Bringing about being rich is my goal")5

___jobArgGoalPlan : GoalPlan_Statement

fulfils(___jobArgGoalPlan, GoalPlan_Desc)

claimText (___jobArgGoalPlan "In order to bring about being rich I

need to bring about having a job")



Relevant portion of the AIF ontology

EncouragedAction_Statement

EncouragedAction_Statement v Statement

GoalPlan_Statement

GoalPlan_Statement v Statement5

Goal_Statement

Goal_Statement v Statement

I-node

I-node ≡ Statement

I-node v Node10

I-node v ¬ S-node

Inference

Inference ≡ RA-node

Inference v ∃ fulfils Inference_Scheme

Inference v ≥ 1 hasPremise Statement15

Inference v Scheme_Application

Inference v = hasConclusion (Scheme_Application t Statement)

Inference_Scheme

Inference_Scheme v Scheme u ≥1 hasPremise_Desc Statement_Description u = hasConclusion_Desc20

(Scheme t Statement_Description)

PracticalReasoning_Inference

PracticalReasoning_Inference ≡ Presumptive_Inference u ∃ hasCon-

clusion EncouragedAction_Statement u ∃ hasGoalPlan_Premise Goal-

Plan_Statement u ∃ hasGoal_Premise Goal_Statement25

RA-node

RA-node ≡ Inference

RA-node v S-node

S-node

S-node ≡ Scheme_Application30

S-node v Node

S-node v ¬ I-node



Scheme

Scheme v Form

Scheme v ¬ Statement_Description

Scheme_Application

Scheme_Application ≡ S-node5

Scheme_Application v ∃ fulfils Scheme

Scheme_Application v Thing

Scheme_Application v ¬ Statement

Statement

Statement ≡ NegStatement10

Statement ≡ I-node

Statement v Thing

Statement v ∃ fulfils Statement_Description

Statement v ¬ Scheme_Application

Statement_Description15

Statement_Description v Form

Statement_Description v ¬ Scheme

fulfils

∃ fulfils Thing v Node

hasConclusion_Desc20

∃ hasConclusion_Desc Thing v Inference_Scheme

hasGoalPlan_Premise

v hasPremise

hasGoal_Premise

v hasPremise25

claimText

∃ claimText DatatypeLiteral v Statement

> v ∀ claimText DatatypeString

Individuals of EncouragedAction_Desc

EncouragedAction_Desc : Statement_Description30

formDescription (EncouragedAction_Desc "A should be brought about")



Individuals of GoalPlan_Desc

GoalPlan_Desc : Statement_Description

formDescription (GoalPlan_Desc "Bringing about B is the way to bring

about A")

Individuals of Goal_Desc5

Goal_Desc : Statement_Description

formDescription (Goal_Desc "The goal is to bring about A")

Individuals of PracticalReasoning_Scheme

PracticalReasoning_Scheme : PresumptiveInference_Scheme

hasPremise_Desc(PracticalReasoning_Scheme, Goal_Desc)10

hasConclusion_Desc(PracticalReasoning_Scheme, EncouragedAction_Desc)

hasPremise_Desc(PracticalReasoning_Scheme, GoalPlan_Desc)


6 A novel synthesis: CollaborativeIntelligence Spaces (CISpaces)

Acknowledgement


Alice Toniolo and Timothy J. Norman. Main reference: [Ton+15].5

6.1 Introduction

Problem

• Intelligence analysis is critical for making well-informed decisions

• Complexities in current military operations increase the amount of

information available to intelligence analysts10

CISpaces (Collaborative Intelligence Spaces)

• A toolkit developed to support collaborative intelligence analysis

• CISpaces aims to improve situational understanding of evolving sit-

uations

6.2 Intelligence Analysis15

Definition 50 ([DCD11]). The directed and coordinated acquisition and

analysis of information to assess capabilities, intent and opportunities for

exploitation by leaders at all levels. ♠

Fig. 6.1 summarises the Pirolli and Card Model [PC05].

Table 6.1 illustrates the problems of individual analysis and how col-20

laborative analysis can improve it.


CISpaces • Intelligence Analysis

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

Figure 6.1: The Pirolli & Card Model [PC05]

Individual analysis Collaborative analysis

• Scattered Information &Noise

• Hard to make connections

• Missing Information

• Cognitive biases

• Missing Expertise

• More effective and reliable

• Brings together differentexpertise, resources

• Prevent biases

Table 6.1: Individual vs. Collaborative Analysis


CISpaces • Intelligence Analysis

HarbourKish Farm

KISH

River

Water pipe

Aqueduct

KISHSHIRE

Kish Hall Hotel

Illness among young and elderly people in Kishshire caused by bacteria

Unidentified illness is affecting the local livestock in Kishshire, the rural area of Kish

Figure 6.2: Initial information assigned to Joe

PEOPLE and LIVESTOCK

illness

Water TEST shows a

BACTERIA in the water supply

Answer to POI: "GER-MAN" seen

in Kish Explosion in KISH

Hall Hotel

TIME

Tests on people/livestock POI for suspicious people

Figure 6.3: Further events happening in Kish

Example of Intelligence Analysis Process

Goal: discover potential threats in Kish

Analysts: Joe, Miles and Ella

What Joe knows is summarised by Figs. 6.2 and 6.3

Main critical points and possible conclusions during the analysis:5

• Causes of water contamination → waterborne/non-waterborne

bacteria;

• POI responsible for water contamination;

• Causes of hotel explosion.


CISpaces • Reasoning with Evidence

6.3 Reasoning with Evidence

• Identify what to believe happened from the claims constructed upon

information (the sensemaking process);

• Derive conclusions from data aggregated from explicitly requested

information (the crowdsourcing process);5

• Assess what is credible according to the history of data manipula-

tion (the provenance reasoning process).

6.4 Arguments for Sensemaking

Formal Linkage for Semantics Computation

A CISpace graph, WAT, can be transformed into a corresponding ASPIC-10

based argumentation theory. An edge in CISpaces is represented textu-

ally as 7→, an info/claim node is written pi and a link node is referred to

as `type where type= {Pro,Con}. Then, [p1, . . . ,pn 7→ `Pro 7→ pφ] indicates

that the Pro-link has p1, . . . , pn as incoming nodes and an outgoing node

pφ.15

Definition 51. A WAT is a tuple ⟨K , AS⟩ such that AS= ⟨L , ,R⟩ is con-

structed as follows:

• L is a propositional logic language, and a node corresponds to a

proposition p ∈L . The WAT set of propositions is Lw.

• The set R is formed by rules r i ∈ R corresponding to Pro links20

between nodes such that: [p1, . . . , pn 7→ `Pro 7→ pφ] is converted to

r i : p1, . . . , pn ⇒ pφ

• The contrariness function between elements is defined as: i) if [p1 7→`Con 7→ p2] and [p2 7→ `Con 7→ p1], p1 and p2 are contradictory; ii)[p1 7→ `Con 7→ p2] and p1 is the only premise of the Con link, then p125

is a contrary of p2; iii) if [p1, p3 7→ `Con 7→ p2] then a rule is added

such that p1 and p3 form an argument with conclusion ph against

p2, r i : p1, p3 ⇒ ph and ph is a contrary of p2. ♠

Definition 52. K is composed of propositions pi,

K = {p j, pi, . . . }, such that: i) let a set of rules r1, . . . , rn ∈R indicate a cycle30

such that for all pi that are consequents of a rule r exists r′ containing pi

as antecedent, then pi ∈ K if pi is an info-node; ii) otherwise, pi ∈ K if pi

is not consequent of any rule r ∈R. ♠


CISpaces • Arguments for Sensemaking

An Example of Argumentation Schemes for IntelligenceAnalysis

Intelligence analysis broadly consists of three components: Activities(Act) including actions performed by actors, and events happening in the

world; Entities (Et) including actors as individuals or groups, and objects5

such as resources; and Facts (Ft) including statements about the state of

the world regarding entities and activities.

A hypothesis in intelligence analysis is composed of activities and events

that show how the situation has evolved. The argument from cause to ef-fect (ArgCE) forms the basis of these hypotheses. The scheme, adapted10

from [WRM08], is:

Argument from cause to effect

Premises:• Typically, if C (either a fact Fti or an ac-

tivity Acti) occurs, then E (either a fact

Fti or an activity Acti) will occur• In this case, C occurs

Conclusions:In this case E will occur

Critical questions:CQCE1 Is there evidence for C to occur?

CQCE1 Is there a general rule for C causing E ?

CQCE3 Is the relationship between C and E

causal?CQCE4 Are there any exceptions to the causal

rule that prevent the effect E from occur-

ring?CQCE5 Has C happened before E ?

CQCE6 Is there any other C ′ that caused E ?

Formally:

rCE : rule(R,C ,E ),occur(C ),before(C ,E ),

ruletype(R,causal),noexceptions(R)⇒ occur(E )15


CISpaces • Arguments for Provenance

WasInformedBy

Used

WasGeneratedBy

WasAssociatedWith

ActedOnBehalfOf

WasAttributedTo

WasDerivedFrom

Entity

Actor

Activity

Figure 6.4: PROV Data Model [MM13]

Lab WaterTesting

wasGeneratedByUsed

wasAssociatedWith

pjID:Bacteria contaminates

local water Water

Sample

Generate Requirement

Water monitoring

Requirement

wasDerivedFrom

Used

wasGeneratedBy

wasInformedBy

Monitoring of water supply

used

water contamination

report

Report generation

Used wasGeneratedBy

wasAssociatedWith

wasDerivedFrom

?a1Pattern Pg

Goal

NGOlab

assistant

NGOChemical

Lab

PrimarySource

Time2014-11-13T08-16-45Z

Time2014-11-12T10-14-40Z

Time2014-11-14T05-14-10Z

?a2

?p

?ag

LEGEND

p-Agent

p-Entity

p-Activity

Node

Older p-elements Newer

Figure 6.5: Provenance of Joe’s information

6.5 Arguments for Provenance

Provenance can be used to annotate how, where, when and by whom some

information was produced [MM13]. Figure 6.4 depicts the core model for

representing provenance, and Figure 6.5 shows an example of provenance

for the pieces of information for analyst Joe w.r.t. the water contamination5

problem in Kish.

Patterns representing relevant provenance information that may war-

rant the credibility of a datum can be integrated into the analysis by ap-

plying the argument scheme for provenance (ArgPV ) [Ton+14]:


CISpaces • Arguments for Provenance

Argument Scheme for Provenance

Premises:• Given p j about activity Acti, entity Eti, or

fact Fti (ppv1)• GP (p j) includes pattern P ′

m of p-entities

Apv, p-activities Ppv, p-agents Agpv in-

volved in producing p j (ppv2)• GP (p j) infers that information p j is true

(ppv3)

Conclusions:Acti/Eti/Fti in p j may plausibly be true

(ppvcn)

Critical questions:CQPV1 Is p j consistent with other information?

CQPV2 Is p j supported by evidence?

CQPV3 Does GP (p j) contain p-elements that lead

us not to believe p j?CQPV4 Is there any other p-element that should

have been included in GP (p j) to infer that

p j is credible?


7 Natural Language Interfaces

7.1 Experiments with Humans: Scenarios [CTO14]

Scenario 1.B

The weather forecasting service of the broadcasting com-

pany AAA says that it will rain tomorrow. Meanwhile, the5

forecast service of the broadcasting company BBB says that

it will be cloudy tomorrow but that it will not rain. It is also

well known that the forecasting service of BBB is more accu-

rate than the one of AAA.

Γ1.B = ⟨S1.B,D1.B⟩, where:10

S1.B D1.B

s1 : ⇒ sAAA

s2 : ⇒ sBBB

r1 : sAAA ∧ ∼ exAAA ⇒ rainr2 : sBBB ∧ ∼ exBBB ⇒¬ rainr3 : ∼ exaccuracy ⇒ r1 ≺ r2

Γ1.B gives rise to the following set of arguments: A1.B = {a1 = ⟨s1, r1⟩,a2 =⟨s2, r2⟩,a3 = ⟨r3⟩}, where a2 A1.B-defeats a1. Therefore the set of justified

arguments (which is also the unique stable extensions) is {a2,a3}.

Scenario 1.E15

The weather forecasting service of the broadcasting com-

pany AAA says that it will rain tomorrow. Meanwhile, the

forecast service of the broadcasting company BBB says that

it will be cloudy tomorrow but that it will not rain. It is also

well known that the forecasting service of BBB is more accu-20

rate than the one of AAA. However, yesterday the trustwor-

thy newspaper CCC published an article which said that BBB

has cut the resources for its weather forecasting service in the

past months, thus making it less reliable than in the past.

Γ1.E = ⟨S1.E ,D1.E⟩, where S1.E = S1.B∪{s3 :⇒ sCCC}, and D1.E = D1.B∪25

{r4 : sCCC ∧ ∼ exCCC ⇒ cut, r5 : cut ∧ ∼ excut ⇒ exaccuracy}.

Γ1.E gives rise to the following set of arguments A1.E = A1.B ∪ {a4 =⟨s3, r4, r5⟩}. a4 is the unique justified argument, while the defensible ex-

tensions (which are also stable) are {a1,a4}, {a2,a4}.


Natural Language Interfaces • Experiments with Hu-mans: Scenarios [CTO14]

Scenario 2.B

In a TV debate, the politician AAA argues that if Region

X becomes independent then X’s citizens will be poorer than

now. Subsequently, financial expert Dr. BBB presents a doc-

ument; which scientifically shows that Region X will not be5

worse off financially if it becomes independent.

Γ2.B = ⟨S2.B,D2.B⟩, where:

S2.B D2.B

s1 : ⇒ sAAA

s2 : ⇒ sBBB

s3 : ⇒ sdoc

r1 : sAAA ∧ ∼ exAAA ⇒ poorerr2 : sBBB ∧ sdoc ∧ ∼ exBBB ∧ ∼ exdoc ⇒¬ poorerr3 : ∼ exexpert ⇒ r1 ≺ r2

Γ2.B gives rise to the following set of arguments A2.B = {a1 = ⟨s1, r1⟩,a2 =⟨s2, s3, r2⟩,a3 = ⟨r3⟩}, where a2 A2.B-defeats a1. Therefore the set of justi-10

fied arguments is {a2,a3}.

Scenario 2.E

In a TV debate, the politician AAA argues that if Region

X becomes independent then X’s citizens will be poorer than

now. Subsequently, financial expert Dr. BBB presents a doc-15

ument; which scientifically shows that Region X will not be

worse off financially if it becomes independent. After that, the

moderator of the debate reminds BBB of more recent research

by several important economists that disputes the claims in

that document.20

Γ2.E = ⟨S2.E ,D2.E⟩, where S2.E = S2.B∪{s4 :⇒ sresearch, s5 : sresearch ⇒¬sdoc}, and D2.E = D2.B.

Γ2.E gives rise to the following set of arguments A2.E = A2.B ∪ {a4 =⟨s4, s5⟩}. Therefore, there are two stable extensions which are also the

defensible extensions: {a1,a3,a4} and {a2,a3}.25

Scenario 3.B

You are planning to buy a second-hand car, and you go to

a dealership with BBB, a mechanic whom has been recom-

mended you by a friend. The salesperson AAA shows you a

car and says that it needs very little work done to it. BBB30

says it will require quite a lot of work, because in the past he

had to fix several issues in a car of the same model.



Γ3.B = ⟨S3.B,D3.B⟩, where:

S3.B D3.B

s1 : ⇒ sAAA

s2 : ⇒ sBBB

r1 : sAAA ∧ ∼ exAAA ⇒¬ workr2 : sBBB ∧ ∼ exBBB ⇒ workr3 : ∼ exprof essional ⇒ r1 ≺ r2

Γ3.B gives rise to the following set of arguments A3.B = {a1 = ⟨s1, r1⟩,a2 =⟨s2, s3, r2⟩,a3 = ⟨r3⟩}, where a2 A3.B-defeats a1. Therefore the set of justi-

fied arguments (which is also the unique stable extensions) is {a2,a3}.5

Scenario 3.E

You are planning to buy a second-hand car, and you go to

a dealership with BBB, a mechanic whom has been recom-

mended you by a friend. The salesperson AAA shows you a

car and says that it needs very little work done to it. BBB10

says it will require quite a lot of work, because in the past he

had to fix several issues in a car of the same model. While you

are at the dealership, your friend calls you to tell you that he

knows (beyond a shadow of a doubt) that BBB made unneces-

sary repairs to his car last month.15

Γ3.E = ⟨S3.E ,D3.E⟩, where S3.E = S3.B ∪ {s3 :⇒ s f riend}, and D3.E =D4.B ∪ {r4 : s f riend ∧ ∼ ex f riend ⇒ unnecc_work, r5 : unnec_work ∧ ∼exunnec_work ⇒ exprof essional}.

Γ3.E gives rise to the following set of arguments A3.E = A2.E ∪ {a4 =⟨s3, r4, r5⟩}. Similarly to Scenario 1.E, a4 is the only justified argument20

and there are two stable extensions: {a1,a4}, and {a2,a4}.

Scenario 4.B

After several dates, you would like to start a serious rela-

tionship with J but you turn to ask two close friends of yours,

AAA and BBB, for advice. You have known BBB for longer25

than you have known AAA. AAA tells you that J is lovely and

you should go ahead, while BBB suggests that you should be

very cautious because J might have a hidden agenda.

Γ4.B = ⟨S4.B,D4.B⟩, where

S4.B D4.E

s1 : ⇒ sAAA

s2 : ⇒ sBBB

r1 : sAAA ∧ ∼ exAAA ⇒ gor2 : sBBB ∧ ∼ exBBB ⇒¬ gor3 : ∼ exbest_ f riend ⇒ r1 ≺ r2

30



Γ4.B gives rise to the following set of arguments A4.B = {a1 = ⟨s1, r1⟩,a2 =⟨s2, s3, r2⟩,a3 = ⟨r3⟩}, where a2 A4.B-defeats a1. Therefore the set of justi-

fied arguments (which is also the unique stable extensions) is {a2,a3}.

Scenario 4.E

After several dates, you would like to start a serious rela-5

tionship with J. but you turn to ask two friends of yours, AAA

and BBB, for advice. You have known BBB for longer than

you have known AAA. AAA tells you that J is lovely and you

should go ahead, while BBB suggests that you should be very

cautious because J might have a hidden agenda. After some10

weeks, CCC, who is also a close friend of BBB, tells you that

BBB has been into you for years; BBB is too shy to tell you

about their feelings about you, but are still possessive of you.

Γ4.E = ⟨S4.E ,D4.E⟩, where S4.E = S4.B∪{s3 :⇒ sCCC}, and D4.E = D4.B∪{r4 : sCCC ∧ ∼ exCCC ⇒ possessive, r5 : possessive ∧ ∼ expossessive ⇒15

¬ r1 ≺ r2}.

Γ4.E gives rise to the following set of arguments A4.E = A4.B ∪ {a4 =⟨s3, r4, r5⟩}, with no justified arguments. The stable extensions are: {a1,a4}, {a2,a3}, {a2,a4}.

Results

0

15

30

45

60

PA PB PU

%

Distribution of acceptability of actors’ positions

Base cases Extended cases

Figure 7.1: Distribution of the final conclusion PA/PB/PU, comparingbase cases with extended cases, in percent.



Base Cases Extended Cases

PA PB PU PA PB PU

1, weather 5.0 50.0 45.0 15.8 21.1 63.2

2, politics 5.3 63.2 31.6 21.1 10.5 68.4

3, buying car 0.0 68.2 31.8 23.8 23.8 52.4

4, romance 12.5 68.8 18.8 48.0 36.0 16.0

Table 7.1: Distribution of the final conclusion PA/PB/PU in percent, foreach scenarios. Shading denotes the most likely conclusions.

0

15

30

45

60

U1 U2 U3

%

Distributions of motivations for PU (scenarios 1.B and 3.B)

1.B 3.B

Figure 7.2: Distribution across three categories of justification (U1: lackof information, U2: domain specific reasons; U3: other) for agreementwith the PU position in scenarios 1.B and 3.B.


Natural Language Interfaces • Lessons From Argu-ment Mining: [BR11]

Base cases Extended cases

RB†

Md∗B RE

†Md∗

E C.D.‡

Rel

evan

ce

1, weather 110.38 6.00 82.92 4.00 46.60

2, politics 107.45 6.00 69.45 4.00 47.19

3, buying car 118.05 6.50 67.45 4.00 44.38

4, romance 48.34 2.00 44.40 2.00 46.57

Agr

eem

ent 1, weather 116.38 6.00 87.18 4.00 46.60

2, politics 103.34 6.00 65.05 4.00 47.19

3, buying car 121.93 6.50 64.33 4.00 44.38

4, romance 44.94 2.00 44.20 2.00 46.57

(a)

Scenario 3.B Scenario 4.B

R3.B†

Md∗3.B R4.B

†Md∗

4.B C.D.‡

Relevance 118.05 6.50 48.34 2.00 47.79

Agreement 121.93 6.50 44.94 2.00 47.79

(b)

Table 7.2: Post-hoc analysis regarding relevance and agreement: pairwisecomparison base-extended cases (a); and between 1.B and 4.B (b). Sta-tistically significant cases (i.e. when |Rx −Ry| > C.D) are highlighted ingrey.† Mean rank as computed with the Kruskal-Wallis test∗ Median‡ Critical Difference, as computed in [SC88] cited by [Fie09] with α= 0.05.

7.2 Lessons From Argument Mining: [BR11]

Bob says: Lower taxes stimulate the economy

Bob says: The government will inevitably lower the tax

rate.

Wilma says: Why?

Challenging

Substantiating

Asserting

Asserting

Challenging

Lower taxes stimulatethe economy

An application of theargument scheme for

Argument from PositiveConsequences

The government willinevitably lower the tax

rate.

Arguing

Bob is credible

Bob is credible


Bibliography

[AB13] Leila Amgoud and Jonathan Ben-Naim. “Ranking-Based Se-

mantics for Argumentation Frameworks”. In: Scalable Un-certainty Management: 7th International Conference, SUM2013, Washington, DC, USA, September 16-18, 2013. Proceed-5

ings. Ed. by Weiru Liu, V. S. Subrahmanian, and Jef Wi-

jsen. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013,

pp. 134–147.

[Bar+14] Pietro Baroni et al. “On the Input/Output behavior of argu-

mentation frameworks”. In: Artificial Intelligence 217 (2014),10

pp. 144–197. URL: http://www.sciencedirect.com/science/

article/pii/S0004370214001131.

[BCG11] P Baroni, M Caminada, and M Giacomin. “An introduction

to argumentation semantics”. In: Knowledge Engineering Re-view 26.4 (2011), pp. 365–410.15

[Bex+13] Floris Bex et al. “Implementing the argument web”. In: Com-munications of the ACM 56.10 (Oct. 2013), p. 66.

[BG07] Pietro Baroni and Massimiliano Giacomin. “On principle-based

evaluation of extension-based argumentation semantics”. In:

Artificial Intelligence (Special issue on Argumentation in A.I.)20

171.10/15 (2007), pp. 675–700.

[BG09a] Pietro Baroni and Massimiliano Giacomin. “Semantics of Ab-

stract Argument Systems”. In: Argumentation in ArtificialIntelligence. Ed. by Guillermo Simari and Iyad Rahwan. Springer

US, 2009, pp. 25–44.25

[BG09b] Pietro Baroni and Massimiliano Giacomin. “Skepticism rela-

tions for comparing argumentation semantics”. In: Interna-tional Journal of Approximate Reasoning 50.6 (June 2009),

pp. 854–866. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2009.

02.006. URL: http://linkinghub.elsevier.com/retrieve/30

pii / S0888613X09000383 % 20http : / / dx . doi . org / 10 .

1016/j.ijar.2009.02.006%20http://dl.acm.org/

citation.cfm?id=1542547.1542704.

[BGG05] Pietro Baroni, Massimiliano Giacomin, and Giovanni Guida.

“SCC-recursiveness: a general schema for argumentation se-35

mantics”. In: Artificial Intelligence 168.1-2 (2005), pp. 165–

210.


http://www.sciencedirect.com/science/article/pii/S0004370214001131



http://dx.doi.org/10.1016/j.ijar.2009.02.006



http://linkinghub.elsevier.com/retrieve/pii/S0888613X09000383%20http://dx.doi.org/10.1016/j.ijar.2009.02.006%20http://dl.acm.org/citation.cfm?id=1542547.1542704







BIBLIOGRAPHY • BIBLIOGRAPHY

[BH01] Philippe Besnard and Anthony Hunter. “A logic-based the-

ory of deductive arguments”. In: Artificial Intelligence 128

(2001), pp. 203–235. ISSN: 00043702. DOI: 10.1016/S0004-

3702(01)00071-6. URL: http://www.sciencedirect.com/

science/article/pii/S0004370201000716.5

[BJT16] Bart Bogaerts, Tomi Janhunen, and Shahab Tasharrofi. “Declar-

ative Solver Development: Case Studies”. In: Principles ofKnowledge Representation and Reasoning: Proceedings of theFifteenth International Conference, KR 2016, Cape Town, SouthAfrica, April 25-29, 2016. 2016, pp. 74–83. URL: http://www.10

aaai.org/ocs/index.php/KR/KR16/paper/view/12822.

[Bon+16] Elise Bonzon et al. “A Comparative Study of Ranking-based

Semantics for Abstract Argumentation”. In: Proceedings ofthe 30th AAAI Conference on Artificial Intelligence (AAAI’16)1 (2016). arXiv: 1602.01059.15

[BR11] Katarzyna Budzynska and Chris Reed. Whence inference? Tech.

rep. University of Dundee, 2011.

[BS12] Stefano Bistarelli and Francesco Santini. “Modeling and Solv-

ing AFs with a Constraint-Based Tool: ConArg”. In: Theoryand Applications of Formal Argumentation. Vol. 7132. Springer,20

2012, pp. 99–116. ISBN: 978-3-642-29183-8.

[Cam06] Martin Caminada. “On the Issue of Reinstatement in Ar-

gumentation”. In: Proceedings of the 10th European Confer-ence on Logics in Artificial Intelligence (JELIA 2006). 2006,

pp. 111–123. ISBN: 3-540-39625-X.25

[Cer+14a] Federico Cerutti et al. “A SCC Recursive Meta-Algorithm for

Computing Preferred Labellings in Abstract Argumentation”.

In: 14th International Conference on Principles of KnowledgeRepresentation and Reasoning. Ed. by Chitta Baral and Giuseppe

De Giacomo. 2014, pp. 42–51. URL: http://www.aaai.org/30

ocs/index.php/KR/KR14/paper/view/7974.

[Cer+14b] Federico Cerutti et al. “Computing Preferred Extensions in

Abstract Argumentation: A SAT-Based Approach”. In: TAFA2013. Ed. by Elizabeth Black, Sanjay Modgil, and Nir Oren.

Vol. 8306. Lecture Notes in Computer Science. Springer-Verlag35

Berlin Heidelberg, 2014, pp. 176–193. URL: http://link.

springer.com/chapter/10.1007/978- 3- 642- 54373-

9_12.


http://dx.doi.org/10.1016/S0004-3702(01)00071-6

http://dx.doi.org/10.1016/S0004-3702(01)00071-6

http://dx.doi.org/10.1016/S0004-3702(01)00071-6




http://www.aaai.org/ocs/index.php/KR/KR16/paper/view/12822



http://arxiv.org/abs/1602.01059




http://link.springer.com/chapter/10.1007/978-3-642-54373-9_12






[Cer+15] Federico Cerutti et al. “Exploiting Parallelism for Hard Prob-

lems in Abstract Argumentation”. In: 29th AAAI Conference- AAAI 2015. 2015, pp. 1475–1481. URL: http://www.aaai.

org / ocs / index . php / AAAI / AAAI15 / paper / viewFile /

9451/9421.5

[CGV14] Federico Cerutti, Massimiliano Giacomin, and Mauro Vallati.

“Algorithm Selection for Preferred Extensions Enumeration”.

In: 5th Conference on Computational Models of Argument.Ed. by Simon Parsons et al. 2014, pp. 221–232. URL: http:

//ebooks.iospress.nl/volumearticle/37791.10

[Cha+15] Günther Charwat et al. “Methods for solving reasoning prob-

lems in abstract argumentation — A survey”. In: ArtificialIntelligence 220 (Mar. 2015), pp. 28–63. ISSN: 00043702. DOI:

10.1016/j.artint.2014.11.008. URL: http://www.

sciencedirect.com/science/article/pii/S0004370214001404.15

[Che+06] Carlos Iván Chesnevar et al. “Towards an argument inter-

change format”. English. In: The Knowledge Engineering Re-view 21.04 (Dec. 2006), p. 293. ISSN: 0269-8889. DOI: 10.

1017/S0269888906001044. URL: http://journals.cambridge.

org/abstract_S0269888906001044.20

[CL05] Claudette Cayrol and Marie-Christine Lagasquie-Schiex. “Grad-

uality in argumentation”. In: Journal of Artificial IntelligenceResearch 23.1 (2005), pp. 245–297.

[CTO14] Federico Cerutti, Nava Tintarev, and Nir Oren. “Formal Ar-

guments, Preferences, and Natural Language Interfaces to25

Humans: an Empirical Evaluation”. In: 21st European Con-ference on Artificial Intelligence. 2014, pp. 207–212. URL: http:

//ebooks.iospress.nl/volumearticle/36941.

[DCD11] DCDC. Understanding and Intelligence Support to Joint Op-erations. Tech. rep. 2011.30

[DS14] Jeremie Dauphin and Claudia Schulz. “Arg Teach - A Learn-

ing Tool for Argumentation Theory”. In: 2014 IEEE 26th In-ternational Conference on Tools with Artificial Intelligence.

IEEE, 2014, pp. 776–783.

[Dun+14] Paul E. Dunne et al. “Characteristics of Multiple Viewpoints35

in Abstract Argumentation”. In: Proceedings of the 14th Con-ference on Principles of Knowledge Representation and Rea-soning. 2014, pp. 72–81.


http://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/viewFile/9451/9421





http://ebooks.iospress.nl/volumearticle/37791



http://dx.doi.org/10.1016/j.artint.2014.11.008




http://dx.doi.org/10.1017/S0269888906001044

http://dx.doi.org/10.1017/S0269888906001044

http://dx.doi.org/10.1017/S0269888906001044

http://journals.cambridge.org/abstract_S0269888906001044







[Dun95] Phan Minh Dung. “On the Acceptability of Arguments and

Its Fundamental Role in Nonmonotonic Reasoning, Logic Pro-

gramming, and n-Person Games”. In: Artificial Intelligence77.2 (1995), pp. 321–357.

[Dvo+11] Wolfgang Dvorák et al. “Making Use of Advances in Answer-5

Set Programming for Abstract Argumentation Systems”. In:

Proceedings of the 19th International Conference on Applica-tions of Declarative Programming and Knowledge Manage-ment (INAP 2011). 2011.

[DW09] Paul E. Dunne and Michael Wooldridge. “Complexity of ab-10

stract argumentation”. In: Argumentation in AI. Ed. by I Rah-

wan and G Simari. Springer-Verlag, 2009. Chap. 5, pp. 85–

104.

[EGW10] Uwe Egly, Sarah Alice Gaggl, and Stefan Woltran. “Answer-

set programming encodings for argumentation frameworks”.15

In: Argument & Computation 1.2 (June 2010), pp. 147–177.

ISSN: 1946-2166. DOI: 10.1080/19462166.2010.486479.

URL: http://dx.doi.org/10.1080/19462166.2010.

486479.

[Fab13] Wolfgang Faber. “Answer Set Programming”. In: Reasoning20

Web. Semantic Technologies for Intelligent Data Access. Vol. 8067.

Lecture Notes in Computer Science. Springer Berlin Heidel-

berg, 2013, pp. 162–193.

[Fie09] Andy Field. Discovering Statistics Using SPSS (IntroducingStatistical Methods series). SAGE Publications Ltd, 2009. ISBN:25

1847879071.

[GLW16] Massimiliano Giacomin, Thomas Linsbichler, and Stefan Woltran.

“On the Functional Completeness of Argumentation Seman-

tics”. In: Knowledge Representation and Reasoning Confer-ence (KR). 2016.30

[HMP01] D Hitchcock, P McBurney, and P Parsons. “A Framework for

Deliberation Dialogues, Argument and Its Applications”. In:

Proceedings of the Fourth Biennial Conference of the OntarioSociety for the Study of Argumentation (OSSA 2001). Ed. by

H V Hansen et al. 2001.35

[MM13] L Moreau and P Missier. PROV-DM: The PROV Data Model.Available at http://www.w3.org/TR/prov-dm/. Apr. 2013.

[MP02] Peter McBurney and Simon Parsons. “Games that agents play:

A formal framework for dialogues between autonomous agents”.

In: Journal of Logic, Language and Information 11.3 (2002),40


http://dx.doi.org/10.1080/19462166.2010.486479

http://dx.doi.org/10.1080/19462166.2010.486479

http://dx.doi.org/10.1080/19462166.2010.486479

http://dx.doi.org/10.1080/19462166.2010.486479

http://www.w3.org/TR/prov-dm/


pp. 315–334. URL: http://www.springerlink.com/index/

N809NP4PPR3HFTDV.pdf.

[MT08] Paul-Amaury Matt and Francesca Toni. “A Game-Theoretic

Measure of Argument Strength for Abstract Argumentation”.

In: 11th European Conference on Logics in Artifcial Intelli-5

gence (JELIA’08). 2008, pp. 285–297.

[NAD14] Samer Nofal, Katie Atkinson, and Paul E. Dunne. “Algorithms

for decision problems in argument systems under preferred

semantics”. In: Artificial Intelligence 207 (2014), pp. 23–51.

URL: http://www.sciencedirect.com/science/article/10

pii/S0004370213001161.

[NDA12] S Nofal, P E Dunne, and K Atkinson. “On Preferred Exten-

sion Enumeration in Abstract Argumentation”. In: Proceed-ings of 3rd International Conference on Computational Mod-els of Arguments (COMMA 2012). 2012, pp. 205–216.15

[PC05] P. Pirolli and S. Card. “The sensemaking process and lever-

age points for analyst technology as identified through cogni-

tive task analysis”. In: Proceedings of the International Con-ference on Intelligence Analysis. 2005.

[Pra10] Henry Prakken. “An abstract framework for argumentation20

with structured arguments”. In: Argument & Computation1.2 (June 2010), pp. 93–124. ISSN: 1946-2166. DOI: 10.1080/

19462160903564592. URL: http://www.tandfonline.com/

doi/abs/10.1080/19462160903564592.

[Pre+14] Alun Preece et al. “Human-machine conversations to sup-25

port multi-agency missions”. In: ACM SIGMOBILE MobileComputing and Communications Review 18.1 (2014), pp. 75–

84. ISSN: 15591662. DOI: 10.1145/2581555.2581568. URL:

http://dl.acm.org/citation.cfm?id=2581555.2581568.

[PV02] Henry Prakken and Gerard Vreeswijk. “Logics for Defeasi-30

ble Argumentation”. In: Handbook of philosophical logic 4

(2002), pp. 218–319. ISSN: 0955792X. DOI: 10.1007/978-

94-017-0456-4_3. URL: http://link.springer.com/

chapter/10.1007/978-94-017-0456-4_3.

[Rah+11] Iyad Rahwan et al. “Representing and classifying arguments35

on the Semantic Web”. English. In: The Knowledge Engineer-ing Review 26.04 (Nov. 2011), pp. 487–511. ISSN: 0269-8889.

DOI: 10.1017/S0269888911000191. URL: http://journals.

cambridge.org/abstract_S0269888911000191.


http://www.springerlink.com/index/N809NP4PPR3HFTDV.pdf






http://dx.doi.org/10.1080/19462160903564592

http://dx.doi.org/10.1080/19462160903564592

http://dx.doi.org/10.1080/19462160903564592

http://www.tandfonline.com/doi/abs/10.1080/19462160903564592



http://dx.doi.org/10.1145/2581555.2581568

http://dl.acm.org/citation.cfm?id=2581555.2581568

http://dx.doi.org/10.1007/978-94-017-0456-4_3

http://dx.doi.org/10.1007/978-94-017-0456-4_3

http://dx.doi.org/10.1007/978-94-017-0456-4_3




http://dx.doi.org/10.1017/S0269888911000191





[RBW08] Francesca Rossi, Peter van Beek, and Toby Walsh. “Chap-

ter 4 Constraint Programming”. In: Handbook of KnowledgeRepresentation. Ed. by Vladimir Lifschitz van Harmelen and

Bruce Porter. Vol. 3. Foundations of Artificial Intelligence.

Elsevier, 2008, pp. 181–211. DOI: http://dx.doi.org/5

10.1016/S1574- 6526(07)03004- 0. URL: http://www.

sciencedirect.com/science/article/pii/S1574652607030040.

[SC88] Sidney Siegel and N. John Castellan Jr. Nonparametric Statis-tics for The Behavioral Sciences. McGraw-Hill Humanities/Social

Sciences/Languages, 1988. ISBN: 0070573573.10

[Ton+14] Alice Toniolo et al. “Making Informed Decisions with Prove-

nance and Argumentation Schemes”. In: Eleventh Interna-tional Workshop on Argumentation in Multi-Agent Systems(ArgMAS 2014). 2014. URL: http://www.inf.pucrs.br/

felipe.meneguzzi/download/AAMAS_14/workshops/AAMAS2014-15

W12/w12-11.pdf.

[Ton+15] Alice Toniolo et al. “Agent Support to Reasoning with Dif-

ferent Types of Evidence in Intelligence Analysis”. In: Pro-ceedings of the 14th International Conference on AutonomousAgents and Multiagent Systems (AAMAS 2015). 2015, pp. 781–20

789. URL: http://aamas2015.com/en/AAMAS_2015_USB/

aamas/p781.pdf.

[Tou58] S Toulmin. The Uses of Argument. Cambridge University Press,

Cambridge, UK, 1958.

[VCG14] Mauro Vallati, Federico Cerutti, and Massimiliano Giacomin.25

“Argumentation Frameworks Features: an Initial Study”. In:

21st European Conference on Artificial Intelligence. Ed. by

T. Shaub, G. Friedrich, and B. O’Sullivan. 2014, pp. 1117–

1118. URL: http://ebooks.iospress.nl/volumearticle/

37148.30

[Wal06] Douglas N Walton. “How to make and defend a proposal in a

deliberation dialogue”. In: Artif. Intell. Law 14.3 (Sept. 2006),

pp. 177–239. ISSN: 0924-8463. DOI: 10.1007/s10506-006-

9025-x. URL: http://portal.acm.org/citation.cfm?id=

1238120.1238122.35

[Wal14] Douglas N. Walton. Burned of Proof, Presumption and Argu-mentation. Cambridge University Press, 2014.

[Wal97] Douglas N Walton. Appeal to Expert Opinion. University Park:

Pennsylvania State University, 1997.

[WRM08] Douglas N. Walton, Chris Reed, and Fabrizio Macagno. Argu-40

mentation Schemes. Cambridge University Press, NY, 2008.


http://dx.doi.org/http://dx.doi.org/10.1016/S1574-6526(07)03004-0






http://www.inf.pucrs.br/felipe.meneguzzi/download/AAMAS_14/workshops/AAMAS2014-W12/w12-11.pdf





http://aamas2015.com/en/AAMAS_2015_USB/aamas/p781.pdf






http://dx.doi.org/10.1007/s10506-006-9025-x

http://dx.doi.org/10.1007/s10506-006-9025-x

http://dx.doi.org/10.1007/s10506-006-9025-x

http://portal.acm.org/citation.cfm?id=1238120.1238122



handout for the course abstract argumentation and interfaces to argumentative reasoning

Education