Handout for the course Abstract Argumentation and Interfaces to Argumentative Reasoning

Abstract Argumentation
and
Interfaces to Argumentative
Reasoning
Handouts
Federico Cerutti
September 2016

Contents
Contents 1
1 Dung’s AF 3
1.1 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 14
2.1 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 28
3.1 The Categoriser Semantics [BH01] . . . . . . . . . . . . . . . 28
3.2 Properties for Ranking-Based Semantics [Bon+16] . . . . . 28
4 Argumentation Schemes 33
4.1 An example: Walton et al. ’s Argumentation Schemes for
Practical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 AS and Dialogues . . . . . . . . . . . . . . . . . . . . . . . . . 34
5 Semantic Web Argumentation 38
5.1 AIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 AIF-OWL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6 CISpaces 43
6.1 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 50
7.1 Experiments with Humans: Scenarios [CTO14] . . . . . . . 50
7.2 Lessons From Argument Mining: [BR11] . . . . . . . . . . . 55
Bibliography 56

1 Dung’s Argumentation
Framework
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
→ 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 ∈ S
a 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) = }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 ∃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 an
argumentation framework AF = 〈A ,→ 〉, let S ⊆ A be a D-admissible set
of arguments, and a,b be arguments which are acceptable with respect to
S. 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 framework
AF = 〈A ,→ 〉, the set of all D-admissible sets of 〈A ,→ 〉 form a complete
partial 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).

work AF = 〈A ,→ 〉. The grounded extension of AF is the least complete20
extension of AF. GR denotes the grounded semantics. ♠
Deﬁnition 17 (Preferred Extension).

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 Yes
D-admissibility Yes Yes Yes Yes
D-strongly admissibility No Yes No No
D-reinstatement Yes Yes Yes Yes
D-I-maximality No Yes Yes Yes
D-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 labelling
of 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

[Cam06]
σ = C O σ = GR σ = P R σ = S T
EXISTSσ trivial trivial trivial NP-c
CAσ NP-c polynomial NP-c NP-c
SAσ polynomial polynomial Π
p
2 -c coNP-c
VERσ polynomial polynomial coNP-c polynomial
NEσ 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/

[Cam06]

Dung’s AF • Skepticism Relationships [BG09b]
GR
C O
P R
GR
C O
P RS T
Figure 1.2: S
⊕ relation for any argumentation framework (left) and for
argumentation framework where stable extensions exist (right).
1.5 Skepticism Relationships [BG09b]
E1
E
E2 denotes that E1 is at least as skeptical as E2.
Definition 23. Let E
be a skepticism relation between sets of exten-
sions. The skepticism relation between argumentation semantics S
is
such that for any argumentation semantics σ1 and σ2, σ1
S
σ2 iff ∀AF ∈5
Dσ1 ∩Dσ2 , EAF(σ1) E
EAF(σ2). ♠
Definition 24. Given two sets of extensions E1 and E2 of an argumenta-
tion framework AF:
• E1
E
∩+ E2 iff ∀E2 ∈ E2, ∃E1 ∈ E1: E1 ⊆ E2;
• E1
E
∪+ E2 iff ∀E1 ∈ E1, ∃E2 ∈ E2: E1 ⊆ E2. ♠10
Lemma 2. Given two argumentation semantics σ1 and σ2, if for any
argumentation framework AF EAF(σ1) ⊆ EAF(σ2), then σ1
E
∩+ σ2 and
σ1
E
∪+ σ2 (σ1
E
⊕ 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} ∈ S then there exists an b ∈ S such that 〈a,b〉 ∈
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 = | 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=i LPj
)↓
Pi
inp,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 No
Top-down decomposability Yes Yes Yes Yes
Bottom-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 F
is 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
→ 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 iff
S 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 ∈ Di;
• C = 〈C1,...,Ct〉 is a tuple of constraints, where ∀j,Cj = 〈RSj
,Sj〉,
Sj ⊆ {xi|xi is a variable}, RSj
⊆ SD
j
× SD
j
where SD
j
= {Di|Di is a
domain, and xi ∈ Sj}.15
A solution to the CSP P is A = 〈a1,...,an〉 where ∀i,ai ∈ Di and ∀j,RSj
holds on the projection of A onto the scope Sj. 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 Di = {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]:
πcf = { 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: Ii (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} → A .
i∈{1,...,k}
(Ii ∨Oi ∨Ui)∧(¬Ii ∨¬Oi)∧(¬Ii ∨¬Ui)∧(¬Oi ∨¬Ui) (2.1)
{i|φ(i)−= }
Ii (2.2)
{i|φ(i)−= }
Ii ∨
{j|φ(j)→φ(i)}
(¬Oj) (2.3)
{i|φ(i)−= } {j|φ(j)→φ(i)}
¬Ii ∨Oj (2.4)15
{i|φ(i)−= } {j|φ(j)→φ(i)}
¬I j ∨Oi (2.5)
{i|φ(i)−= }
¬Oi ∨
{j|φ(j)→φ(i)}
I j (2.6)
{i|φ(i)−= } {k|φ(k)→φ(i)}
Ui ∨¬Uk ∨
{j|φ(j)→φ(i)}
I j (2.7)
{i|φ(i)−= } {j|φ(j)→φ(i)}
(¬Ui ∨¬I j) ∧ ¬Ui ∨
{j|φ(j)→φ(i)}
Uj (2.8)
i∈{1,...k}
Ii (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 AF
PrefSAT(Γ)
1: Input: Γ = Γ
2: Output: Ep ⊆ 2A
3: Ep :=
4: cnf := ΠΓ
5: repeat
6: cnf df := cnf
7: pref cand :=
8: repeat
9: lastcompf ound := SatS(cnf df )
10: if lastcompf ound ! = ε then
11: pref cand := lastcompf ound
12: for a1 ∈ I-ARGS(lastcompf ound) do
13: cnf df := cnf df ∧ 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 df := cnf df ∧ remaining
20: end if
21: until (lastcompf ound ! = ε∧I-ARGS(lastcompf ound) ! = A )
22: if pref cand ! = then
23: Ep := Ep ∪{I-ARGS(pref cand)}
24: oppsolution := F ALSE
25: for a1 ∈ A I-ARGS(pref cand) do
26: oppsolution := oppsolution∨ Iφ−1(a1)
27: end for
28: cnf := cnf ∧ oppsolution
29: end if
30: until (pref cand ! = )
31: if Ep = then
32: Ep = { }
33: end if
34: return Ep

Parallel-SCCp [Cer+14a; Cer+15]
Based on the SCC-Recursiveness Schema [BGG05].
ab
ef
cdgh

Algorithm 1 Computing D-preferred labellings of an AF
P-PREF(Γ)
1: Input: Γ = Γ
2: Output: Ep ∈ 2L(Γ)
3: return P-SCC-REC(Γ,A )
Algorithm 2 Greedy computation of base cases
GREEDY(L,C)
1: Input: L = (L1
,...,Ln
:= {Sn
1 ,...,Sn
h
}),C ⊆ A
2: Output: M = {...,(Si,Bi),...}
3: M :=
4: for S ∈ n
i=1
Li
do in parallel
5: B := B-PR(Γ↓S,S ∩C)
6: M = M ∪{(S,B)}
7: end for
8: 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 C
GROUNDED(Γ,C)
1: Input: Γ = Γ, C ⊆ A
2: Output: (L ab,U) : U ⊆ A ,L ab ∈ LA U
3: L ab :=
4: U := A
5: repeat
6: initial f ound := ⊥
7: for a1 ∈ C do
8: if {a2 ∈ U | a2 → a1} = then
9: 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 for
18: end if
19: end for
20: until (initial f ound)
21: return(L ab,U)

Algorithm 4 Computing D-preferred labellings of an AF in C
P-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
:= {S1
1,...,S1
k
},...,Ln
:= {Sn
1 ,...,Sn
h
})
= SCCS-LIST(Γ)
7: M := {...,(Si,Bi),...} = GREEDY(L,C)
8: for l ∈ {1,...,n} do
9: El := {E
S1
l
:= (),...,E
Sk
l
:= ()}
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: ES
l
[L ab] ={{(a1,out) | a1 ∈ O} ∪{(a1,undec) | a1 ∈ S O}}
15: else
16: if I = S then
17: ES
l
[L ab] = B where (S,B) ∈ M
18: else
19: if O = then
20: ES
l
[L ab] = B-PR(Γ↓S, I ∩C)
21: else
22: ES
l
[L ab]={{(a1,out) | a1 ∈ O}}
23: ES
l
[L ab] = ES
l
[L ab]⊗P-SCC-REC(Γ↓SO, I ∩C)
24: end if
25: end if
26: end if
27: end for
28: end for
29: for S ∈ Ll
do
30: Ep :=
31: for L ab ∈ Ep do in parallel
32: Ep = Ep ∪({L ab}⊗ ES
l
[L ab])
33: end for
34: Ep := Ep
35: end for
36: end for
37: 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 ,def :
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 smart
Holger H. Hoos, Invited Keynote Talk at ECAI2014
Features for AFs [VCG14; CGV14]20
Directed Graph (26 features)

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 features
Direct Graph Features (DG)
Class CPU-Time # feat
Mean 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 0.48
PrefSAT 1.39 0.93 0.93 0.89 0.92 0.94 0.89
NAD-Alg 1.48 1.47 1.47 0.77 0.57 1.61 0.55
SSCp 1.36 0.80 0.78 0.75 0.75 0.79 0.74
Log runtime is defined as
n
i=1 log10( ti )−log10( yi )
2
n
5
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 T
is 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/ .

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 →]0,1] is defined as:
Cat(a1) =



1 if a−
1 =
1
1+ a2∈a−
1
Cat(a2)
otherwise
5
♠
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 }−
= .
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. attack
branch) 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 σ
Γ on A , where σ
Γ is a preorder
(a reflexive and transitive relation) on A . a1
σ
Γ a2 means that a1 is at
least as acceptable as a2. a1
σ
Γ a2 iff a1
σ
Γ a2 and a2
σ
Γ a1. ♠
Definition 45. A lexicographical order between two vectors of real num-
ber V = 〈V1,...,Vn〉 and V = 〈V1,...,Vn〉, is defined as V lex V iff ∃i ≤ n30
s.t. Vi ≥ Vi
and ∀j < i, Vj = Vj
. ♠

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 → 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) a1. An
S1 >S S2 is a strict group comparison iff S1 ≥S S2 and (|S2| < |S1| or
∃a1 ∈ S2, f (a1) 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
σ
Γ a2 iff
γ(a1) σ
Γ
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
σ
Γ
a2 ⇒ a1
σ
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 = ⇒ a1
σ
a2.
Self-Contradiction (SC) [MT08]. A self-attacking argument is ranked
lower than any non self-attacking argument.
〈a1,a1〉 =→ and 〈a2,a2〉 ∈→ ⇒ a1
σ
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
σ
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
σ
a4 ⇒ a1
σ
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
σ
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
σ
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 }−
= and {a−
2 }−
= ⇒ a1
σ
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
σ
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) σ
Γ+ 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
σ
Γ∗ γ(a1).
Addition of Defence Branch (+DB) [CL05]. Adding a defence branch
to an attached argument improves its ranking.
= Γ ∪ γ(Γ) ∪ P+(γ(a1)) and |a−
1 | = 0, then
γ(a1) σ
Γ+ 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) σ
Γ∗ a1.
Addition of Attack Branch (+AB) [CL05]. Adding an attack branch5
to any argument degrades its ranking.
= Γ∪γ(Γ)∪ P−(γ(a1)), then a1
σ
Γ∗ γ(a1).
Total (Tot) [Bon+16]. All pairs of arguments can be compared.
a1
σ
a2 or a2
σ
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
σ
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 Yes
In Yes
VP Yes Implied by SCT
DP Yes Implied by CT
CT Yes Implied by SCT
SCT Yes
CP No
QP No
DDP No
SC No
⊕DB No Incompatible with VP
+AB Yes
+DB No
↑AB Yes
↑DB Yes
Tot Yes
NaE Yes Implied by CT
AvsFD 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 Argumentation
Schemes 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 of
Argumentation
Acknowledgement
Chris Reed. An overview can also be find at [Bex+13].5
5.1 The Argument Interchange Format [Rah+11]
Node Graph
(argument
network)
has-a
Information
Node
(I-Node)
is-a
Scheme Node
S-Node
has-a
Edge
is-a
Rule of inference
application node
(RA-Node)
Conflict application
node (CA-Node)
Preference
application node
(PA-Node)
Derived concept
application node (e.g.
defeat)
is-a
...
ContextScheme
Conflict
scheme
contained-in
Rule of inference
scheme
Logical inference
scheme
Presumptive
inference scheme
...
is-a
Logical conflict
scheme
is-a
...
Preference
scheme
Logical preference
scheme
is-a
...
Presumptive
preference 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)

Semantic Web Argumentation • AIF-OWL
Practical
Inference
Bringing about
is my goal
Sn
Si
In order to bring about
I need to bring about
Sn
Therefore I need
to bring about Si
hasConcDeschasPremiseDesc
hasPremiseDesc
Bringing about being rich
is my goal
In order to bring about being rich
I need to bring about having a job
fulfilsPremiseDesc
fulfilsPremiseDesc
fulfilsScheme
supports
supports
Therefore I need
to bring about
having a job
hasConclusion
fulfils
Figure 5.2: An argument network linking instances of argument and
scheme components
Symmetric attack
r → p
r pMP2
A1
A2
p → q
p
qMP1
neg1
Undercut attack
r MP2
A3
A2 s → v
s
vMP1
cut1
p
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 Statement
GoalPlan_Statement
GoalPlan_Statement Statement5
Goal_Statement
Goal_Statement Statement
I-node
I-node ≡ Statement
I-node Node10
I-node ¬ S-node
Inference
Inference ≡ RA-node
Inference ∃ fulﬁls Inference_Scheme
Inference ≥ 1 hasPremise Statement15
Inference Scheme_Application
Inference = hasConclusion (Scheme_Application Statement)
Inference_Scheme
Inference_Scheme Scheme ≥
1 hasPremise_Desc Statement_Description = hasConclusion_Desc20
(Scheme Statement_Description)
PracticalReasoning_Inference
PracticalReasoning_Inference ≡ Presumptive_Inference ∃ hasCon-
clusion EncouragedAction_Statement ∃ hasGoalPlan_Premise Goal-
Plan_Statement ∃ hasGoal_Premise Goal_Statement25
RA-node
RA-node ≡ Inference
RA-node S-node
S-node
S-node ≡ Scheme_Application30
S-node Node
S-node ¬ I-node

Scheme
Scheme Form
Scheme ¬ Statement_Description
Scheme_Application
Scheme_Application ≡ S-node5
Scheme_Application ∃ fulfils Scheme
Scheme_Application Thing
Scheme_Application ¬ Statement
Statement
Statement ≡ NegStatement10
Statement ≡ I-node
Statement Thing
Statement ∃ fulfils Statement_Description
Statement ¬ Scheme_Application
Statement_Description15
Statement_Description Form
Statement_Description ¬ Scheme
fulfils
∃ fulfils Thing Node
hasConclusion_Desc20
∃ hasConclusion_Desc Thing Inference_Scheme
hasGoalPlan_Premise
hasPremise
hasGoal_Premise
hasPremise25
claimText
∃ claimText DatatypeLiteral Statement
∀ 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: Collaborative
Intelligence 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
Search
and Filter
Schematize
Build Case
Tell Story
Reevaluate
Search
for support
Search
for evidence
Search for
information
FORAGING LOOP
SENSE-MAKING LOOP
Structure
Effort
inf
Shoebox
Ev
Ev
EvEv Ev
Ev
Ev
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 different
expertise, resources
• Prevent biases
Table 6.1: Individual vs. Collaborative Analysis

CISpaces • Intelligence Analysis
Harbour
Kish 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 →, an info/claim node is written pi and a link node is referred to
as type where type = {Pro,Con}. Then, [p1,...,pn → Pro → 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 ri ∈ R corresponding to Pro links20
between nodes such that: [p1,..., pn → Pro → pφ] is converted to
ri : p1,..., pn ⇒ pφ
• The contrariness function between elements is defined as: i) if [p1 →
Con → p2] and [p2 → Con → p1], p1 and p2 are contradictory; ii)
[p1 → Con → p2] and p1 is the only premise of the Con link, then p125
is a contrary of p2; iii) if [p1, p3 → Con → p2] then a rule is added
such that p1 and p3 form an argument with conclusion ph against
p2, ri : p1, p3 ⇒ ph and ph is a contrary of p2. ♠
Definition 52. K is composed of propositions pi,
K = {pj, 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 Intelligence
Analysis
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 Water
Testing
wasGeneratedBy
Used
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
NGO
lab
assistant
NGO
Chemical
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 pj about activity Acti, entity Eti, or
fact Fti (ppv1)
• GP(pj) includes pattern Pm of p-entities
Apv, p-activities Ppv, p-agents Agpv in-
volved in producing pj (ppv2)
• GP(pj) infers that information pj is true
(ppv3)
Conclusions:
Acti/Eti/Fti in pj may plausibly be true
(ppvcn)
Critical questions:
CQPV1 Is pj consistent with other information?
CQPV2 Is pj supported by evidence?
CQPV3 Does GP(pj) contain p-elements that lead
us not to believe pj?
CQPV4 Is there any other p-element that should
have been included in GP(pj) to infer that
pj 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 ⇒ rain
r2 : sBBB ∧ ∼ exBBB ⇒ ¬ rain
r3 : ∼ 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}.

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