The document discusses the evolution of argumentation in artificial intelligence, reflecting on twenty years since Dung's foundational framework. It explores various argumentation schemes, semantics, and algorithms, addressing the theoretical and practical aspects of argumentative reasoning. Additionally, it touches on applications in multi-agent systems and the complexity of different argumentation semantics.

1. argumentation in artificial intelligence
20 Years After Dung’s Work
.
Federico Cerutti†
xxvi • vii • mmxv
†
University of Aberdeen

2. P. Baroni
U. Brescia
T. J. M. Bench-Capon
U. Liverpool
C. Cayrol
IRIT
P. E. Dunne
U. Liverpool
M. Giacomin
U. Brescia
A. Hunter
UCL
H. Li
U. Aberdeen
S. Modgil
KCL
T. J. Norman
U. Aberdeen
N. Oren
U. Aberdeen
C. Reed
U. Dundee
G. R. Simari
U. Nacional der Sur
A. Toniolo
U. Aberdeen
M. Vallati
U. Huddersfield
S. Woltran
TU Wien
J. Leite
New U. Lisbon
S. Parson
KCL
M. Thimm
U. Koblenz

3. This tutorial was sponsored by the U.S. Army Research Laboratory and the U.K.
Ministry of Defence, under Agreement Number W911NF-06-3-0001. The views
and conclusions contained in this document are those of the author(s) and
should not be interpreted as representing the official policies, either expressed
or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K.
Ministry of Defence or the U.K. Government. The U.S. and U.K. Governments are
authorized to reproduce and distribute reprints for Government purposes
notwithstanding any copyright notation hereon.
The tutor acknowledges the contribution of the Santander Universities Network
in supporting his travel

4. outline
∙ Introduction Why bother?
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

5. outline
∙ Introduction
∙ Dung’s AF Syntax, semantics, current state of research
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

6. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes Arguments in human experience
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

7. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation AIF, OVA+, and other tools
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

8. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks Abstract, instantiated, probabilistic frameworks: kite-level view
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

9. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces „One Ring to bring them all and in the darkness bind them”
∙ Algorithms and Implementations
∙ The frontier

10. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations …and how to choose among them
∙ The frontier

11. outline
∙ Introduction
∙ Dung’s AF
∙ Argumentation Schemes
∙ A Semantic-Web view of Argumentation
∙ Frameworks
∙ CISpaces
∙ Algorithms and Implementations
∙ The frontier

12. what is missing
A lot
Dialogues
Argumentation and trust
Argumentation in multi-agent systems
Several approaches to represent arguments
Several extensions to Dung’s framework
Several frontier approaches
…

13. ..why bother?

14. There is no milk in the shop
and the milk you have is sour.
Beer Milk
1 0

15. There is a coffee machine and
fresh coffee in the cupboard.
Beer makes you sick
Beer Milk Coffee?
0 0 1

16. There is fresh milk in your
bag because you went to the
shop earlier.
The Principal is visiting later
today, so you had better not
alcohol
Beer Milk
0 1

17. There is no milk in the shop
and the milk you have is sour.
There is a coffee machine and
fresh coffee in the cupboard.
Beer makes you sick
There is fresh milk in your
bag because you went to the
shop earlier.
The Principal is visiting later
today, so you had better not
alcohol
Beer Milk Coffee?
1 0
0 0 1
0 1

18. You should drink milk
You should drink beer
There is no milk in the shop
and the milk you have is sour.
There is a coffee machine and
fresh coffee in the cupboard.
Beer makes you sick
You should drink coffee
There is fresh milk in your
bag because you went to the
shop earlier.
The Principal is
visiting later today, so
you had better not

19. ..dung’s argumentation framework

20. [Dun95]

21. Definition 1
A Dung argumentation framework AF is a pair
⟨A, → ⟩
where A is a set of arguments, and → is a binary relation on A i.e. →⊆ A × A.

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

23. (some) semantics properties
[BG07] [BCG11]

24. (some) semantics properties
∙ Conflict-freeness (Def. 2)
an attacking and an attacked argument can not stay together (∅ is c.f. by def.)
∙ Admissibility (Def. 5)
∙ Strong-Admissibility (Def. 7)
∙ Reinstatement (Def. 8)
∙ I-Maximality (Def. 9)
∙ Directionality (Def. 12)

25. (some) semantics properties
∙ Conflict-freeness (Def. 2)
∙ Admissibility (Def. 5)
the extension should be able to defend itself, „fight fire with fire” (∅ is adm. by def.)
∙ Strong-Admissibility (Def. 7)
∙ Reinstatement (Def. 8)
∙ I-Maximality (Def. 9)
∙ Directionality (Def. 12)

26. (some) semantics properties
∙ Conflict-freeness (Def. 2)
∙ Admissibility (Def. 5)
∙ Strong-Admissibility (Def. 7)
no self-defeating arguments (∅ is strong adm. by def.)
∙ Reinstatement (Def. 8)
∙ I-Maximality (Def. 9)
∙ Directionality (Def. 12)

27. (some) semantics properties
∙ Conflict-freeness (Def. 2)
∙ Admissibility (Def. 5)
∙ Strong-Admissibility (Def. 7)
∙ Reinstatement (Def. 8)
if you defend some argument you should take it on board (∅ satisfies the principle
only if there are no unattacked arguments)
∙ I-Maximality (Def. 9)
∙ Directionality (Def. 12)

28. (some) semantics properties
∙ Conflict-freeness (Def. 2)
∙ Admissibility (Def. 5)
∙ Strong-Admissibility (Def. 7)
∙ Reinstatement (Def. 8)
∙ I-Maximality (Def. 9)
no extension is a proper subset of another one
∙ Directionality (Def. 12)

29. (some) semantics properties
∙ Conflict-freeness (Def. 2)
∙ Admissibility (Def. 5)
∙ Strong-Admissibility (Def. 7)
∙ Reinstatement (Def. 8)
∙ I-Maximality (Def. 9)
∙ Directionality (Def. 12)
a (set of) argument(s) is affected only by its ancestors in the attack relation

30. You should drink milk
You should drink beer
There is no milk in the shop
and the milk you have is sour.
There is a coffee machine and
fresh coffee in the cupboard.
Beer makes you sick
You should drink coffee
There is fresh milk in your
bag because you went to the
shop earlier.
The Principal is
visiting later today, so
you had better not

31. You should drink milk
You should drink beer
There is no milk in the shop
and the milk you have is sour.
There is a coffee machine and
fresh coffee in the cupboard.
Beer makes you sick
You should drink coffee
There is fresh milk in your
bag because you went to the
shop earlier.
The Principal is
visiting later today, so
you had better not
b
a
c
d
f
e
gh

32. complete extension (def. 15)
Admissibility and reinstatement
Set of conflict-free arguments s.t. each defended argument is included
b a
c
d
f e
gh



{a, c, d, e, g},
{a, b, c, e, g},
{a, c, e, g}




33. grounded extension (def. 16)
Strong Admissibility
Minimum complete extension
b a
c
d
f e
gh


 {a, c, e, g}




34. preferred extension (def. 17)
Admissibility and maximality
Maximum complete extensions
b a
c
d
f e
gh



{a, c, d, e, g},
{a, b, c, e, g}




35. stable extension (def. 17)
„orror vacui:” the absence of odd-length cycles is a sufficient condition for existence of
stable extensions
Complete extensions attacking all the arguments outside
b a
c
d
f e
gh



{a, c, d, e, g},
{a, b, c, e, g}




36. complete labellings (def. 20)
Max. UNDEC ≡ Grounded
b a
c
d
f e
gh


 {a, c, e, g}




37. complete labellings (def. 20)
Max. IN ≡ Preferred
b a
c
d
f e
gh



{a, c, d, e, g}




38. complete labellings (def. 20)
Max. IN ≡ Preferred
b a
c
d
f e
gh



{a, b, c, e, g}




39. complete labellings (def. 20)
No UNDEC ≡ Stable
b a
c
d
f e
gh



{a, c, d, e, g}




40. complete labellings (def. 20)
No UNDEC ≡ Stable
b a
c
d
f e
gh



{a, b, c, e, g}




41. properties of semantics
CO GR PR ST
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

42. complexity
[DW09]

43. complexity
σ = CO σ = GR σ = PR σ = ST
existsσ trivial trivial trivial np-c
caσ np-c polynomial np-c np-c
saσ polynomial polynomial Πp
2 -c conp-c
verσ polynomial polynomial conp-c polynomial
neσ np-c polynomial np-c np-c

44. an exercise
a
b c d
e
f
g
h
i
l
m
no
p

45. an exercise
a
b c d
e
f
g
h
i
l
m
no
p
ECO(∆) =



{a, c},
{a, c, f},
{a, c, m},
{a, c, f, m},
{a, c, f, l},
{a, c, g, m}




46. an exercise
a
b c d
e
f
g
h
i
l
m
no
p
EGR(∆) =



{a, c}




47. an exercise
a
b c d
e
f
g
h
i
l
m
no
p
EPR(∆) =



{a, c, f, m},
{a, c, f, l},
{a, c, g, m}




48. an exercise
a
b c d
e
f
g
h
i
l
m
no
p
EST (∆) =







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

50. skepticisms and comparisons of sets of extensions
[BG09b]

51. skepticisms and comparisons of sets of extensions
..GR.
CO
.
PR
.
ST
⪯S
⊕ relation
Comparing extensions individually:
E1 ⪯E
∩+ E2 iff ∀E2 ∈ E2, ∃E1 ∈ E1: E1 ⊆ E2 and E1 ⪯E
∪+ E2 iff ∀E1 ∈ E1, ∃E2 ∈ E2: E1 ⊆ E2

52. signatures
[Dun+14]

53. signatures
The signature of a semantics is the collection of all possible sets of extensions an AF can
possess under a semantics (Def. 25).
S ⊆ 2A
:
∙ ArgsS =
∪
S∈S S;
∙ PairsS = {⟨a, b⟩ | ∃S ∈ S s.t. {a, b} ⊆ S}.
• • • • •
S = { { a, d, e },
{ b, c, e },
{ a, b } }
ArgsS = {a, b, c, d, e} PairsS = {⟨a, b⟩, ⟨a, d⟩, ⟨a, e⟩, ⟨b, c⟩, ⟨b, e⟩, ⟨c, e⟩, ⟨d, e⟩}

54. signatures
∙ Incomparable (Def. 26): A ⊆ B iff A = B
„Maximal”
∙ Tight (Def. 27): if S ∪ {a} ̸∈ S then ∃b ∈ S s.t. ⟨a, b⟩ ̸∈ PairsS
∙ Adm-Closed (Def. 28): if ⟨a, b⟩ ∈ PairsS ∀a, b ∈ A ∪ B, A ∪ B ∈ S
Stable iff incomparable and tight
Preferred iff non-empty, incomparable and adm-closed

55. signatures
∙ Incomparable (Def. 26): A ⊆ B iff A = B
∙ Tight (Def. 27): if S ∪ {a} ̸∈ S then ∃b ∈ S s.t. ⟨a, b⟩ ̸∈ PairsS
if an argument does not occur in some extension there must be a reason for that
(typically a conflict)
∙ Adm-Closed (Def. 28): if ⟨a, b⟩ ∈ PairsS ∀a, b ∈ A ∪ B, A ∪ B ∈ S
Stable iff incomparable and tight
Preferred iff non-empty, incomparable and adm-closed

56. signatures
∙ Incomparable (Def. 26): A ⊆ B iff A = B
∙ Tight (Def. 27): if S ∪ {a} ̸∈ S then ∃b ∈ S s.t. ⟨a, b⟩ ̸∈ PairsS
∙ Adm-Closed (Def. 28): if ⟨a, b⟩ ∈ PairsS ∀a, b ∈ A ∪ B, A ∪ B ∈ S
„Admissibility”
Stable iff incomparable and tight
Preferred iff non-empty, incomparable and adm-closed

57. signatures
S = { { a, d, e },
{ b, c, e },
{ a, b } }
incomparable and adm-closed (⟨a, b⟩ ∈ PairsS ∀a, b ∈ A ∪ B, A ∪ B ∈ S)

58. signatures
S = { { a, d, e },
{ b, c, e },
{ a, b } }
incomparable and adm-closed (⟨a, b⟩ ∈ PairsS ∀a, b ∈ A ∪ B, A ∪ B ∈ S)
a
b
c
d
f e

59. exercise
S = { { a, d, e },
{ b, c, e },
{ a, b, d } }
Does an AF ∆ having EPR(∆) = S exist?

60. exercise
S = { { a, d, e },
{ b, c, e },
{ a, b, d } }
Does an AF ∆ having EPR(∆) = S exist?
No
PairsS = {⟨a, b⟩, ⟨a, d⟩, ⟨a, e⟩, ⟨b, c⟩, ⟨b, e⟩, ⟨c, e⟩, ⟨d, e⟩, ⟨b, d⟩}
b, d ∈ { a, d, e } ∪ { a, b, d }
but { a, d, e } ∪ { a, b, d } = { a, b, d, e } /∈ S

61. decomposability
[Bar+14]

62. decomposability
AF1
AF2
AF3
Is it possible to consider a (partial) argumentation framework as a black-box and focus
only on the input/output interface?

63. decomposability
A semantics is:
∙ Fully decomposable (Def. 35):
∙ any combination of “local” labellings gives rise to a global labelling;
∙ any global labelling arises from a set of “local” labellings
∙ Top-Down decomposable (Def. 36):
combining “local” labellings you get all global labellings, possibly more
∙ Bottom-Up decomposable (Def. 37):
combining “local” labellings you get only global labellings, possibly less

64. decomposability
A semantics is:
∙ Fully decomposable (Def. 35):
∙ any combination of “local” labellings gives rise to a global labelling;
∙ any global labelling arises from a set of “local” labellings
∙ Top-Down decomposable (Def. 36):
combining “local” labellings you get all global labellings, possibly more
∙ Bottom-Up decomposable (Def. 37):
combining “local” labellings you get only global labellings, possibly less

65. decomposability
A semantics is:
∙ Fully decomposable (Def. 35):
∙ any combination of “local” labellings gives rise to a global labelling;
∙ any global labelling arises from a set of “local” labellings
∙ Top-Down decomposable (Def. 36):
combining “local” labellings you get all global labellings, possibly more
∙ Bottom-Up decomposable (Def. 37):
combining “local” labellings you get only global labellings, possibly less

66. decomposability
A semantics is:
∙ Fully decomposable (Def. 35):
∙ any combination of “local” labellings gives rise to a global labelling;
∙ any global labelling arises from a set of “local” labellings
∙ Top-Down decomposable (Def. 36):
combining “local” labellings you get all global labellings, possibly more
∙ Bottom-Up decomposable (Def. 37):
combining “local” labellings you get only global labellings, possibly less
CO ST GR PR
Full decomposability Yes Yes No No
Top-down decomposability Yes Yes Yes Yes
Bottom-up decomposability Yes Yes No No

67. ..argumentation schemes

68. what is an argument?
The Argument Clinic

69. what is an argument?
Argumentation is a verbal,
social, and rational activity aimed
at convincing a reasonable critic of
the acceptability of a standpoint by
putting forward a constellation of
propositions justifying or refuting
the proposition expressed in the
standpoint.
Some elements of dialogue in the handout, but they
will not be considered here.

70. [WRM08]

71. practical inference: an example of argumentation scheme
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.

72. practical inference: an example of argumentation scheme
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 Q. Are there alternative possible actions to bring about Si that
could also lead to the goal?
Best-Means Q. Is Si the best (or most favourable) of the alternatives?
Other-Goals Q. Do I have goals other than Si whose achievement is prefer-
able and that should have priority?
Possibility Q. Is it possible to bring about Si in the given circumstances?
Side Effects Q. Would bringing about Si have known bad consequences that
ought to be taken into account?

73. an example
Goal
Bringing about being rich is my goal I want to be rich
Means/Plan
In order to bring about being rich I need
to bring about having a job
To be rich I need a job
Action
Therefore I need to bring about having a
job
Therefore I have to search
for a job.

74. an example
http://ova.arg-tech.org/
with
http://homepages.abdn.ac.uk/f.cerutti/pages/research/
tutorialijcai2015/rich.html

75. ..a semantic-web view of argumentation

76. [Rah+11]

77. 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

78. AIF-OWL

79. [Bex+13]

80. On-line analysis of Moral Maze

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

82. ..abstract argumentation frameworks

83. Value Based AF
Extended AF AFRA
Bipolar AF

84. value based argumentation framework
[BA09]

85. value based argumentation framework
..a2
LC, FC
.. a3
LC, FH
..
a1
LC
a1 Hal should not take insulin, thus
allowing Carla to be alive (value of
Life for Carla LC);
a2 Hal should take insulin and
compensate Carla, thus both of
them stay alive (value of Life for
Carla, and the Freedom — of using
money — for Carla FC);
a3 Hal should take insulin and that
Carla should buy insulin, thus
both of them stay alive (value of
Life for Carla, and the Freedom —
of using money — for Hal FH).

86. Value Based AF
Extended AF AFRA
Bipolar AF

87. extended argumentation framework
[Mod09]

88. extended argumentation framework
a1 “Today will be dry in London since
the BBC forecast sunshine”;
a2 “Today will be wet in London since
CNN forecast rain”;
a3 “But the BBC are more trustworthy
than CNN”;
a4 “However, statistically CNN are
more accurate forecasters than
the BBC”;
a5 “Basing a comparison on statistics
is more rigorous and rational than
basing a comparison on your
instincts about their relative
trustworthiness”.

89. Value Based AF
Extended AF AFRA
Bipolar AF

90. afra: argumentation framework with recursive attacks
[Bar+11]

91. afra: argumentation framework with recursive attacks
a1 There is a last minute offer for
Gstaad: therefore I should go to
Gstaad;
a2 There is a last minute offer for
Cuba: therefore I should go to
Cuba;
a3 I do like to ski;
a4 The weather report informs that in
Gstaad there were no snowfalls
since one month: therefore it is
not possible to ski in Gstaad;
a5 It is anyway possible to ski in
Gstaad, thanks to a good amount
of artificial snow.

92. Value Based AF
Extended AF AFRA
Bipolar AF

93. bipolar argumentation framework
[CL05]

94. bipolar argumentation framework
..a3. a2. a1.
a4
a1 in favour of m, with premises
{s, f, (s ∧ f) → m};
a2 in favour of ¬s, with premises
{w, w → ¬s};
a3 in favour of ¬w, with premises
{b, b → ¬w};
a4 in favour of f, with premises
{l, l → f}
m Mary (who is small) is the killer
f the killer is female
s the killer is small
w a witness says that the killer is tall
b the witness is short-sighted
l the killer has long hair and wear
lipstick

95. ..structured argumentation frameworks

96. DeLP ABA
ASPIC+
Deductive
Argumentation
Logic for Clinical
Knowledge

97. delp: defeasible logic programming
[SL92] [GS14]

98. delp: defeasible logic programming
Π non-defeasible knowledge ⟨Π, ∆⟩ ∆ defeasible knowledge
facts i.e. atomic information
strict rules Lo ←− L1, . . . , Ln defeasible rules Lo −< L1, . . . , Ln
Def. 40
Let H be a ground literal: ⟨A, H⟩ is an argument structure if:
∙ there exists a defeasible derivation*
for H from ⟨Π, A⟩;
∙ there are no defeasible derivations from ⟨Π, A⟩ of contradictory literals;
∙ and there is no proper subset A′
⊂ A such that A′
satisfies (1) and (2).
*A defeasible derivation for Q from ⟨Π, ∆⟩, is L1, L2, . . . , Ln = Q s.t.: (i) Li is a fact; or (ii) ∃Ri ∈ ⟨Π, ∆⟩ with
head Li and body B1, . . . , Bk, and every literal of the body is an element Lj of the sequence with j < i.

99. delp: defeasible logic programming
Def. 41
⟨B, S⟩ is a counter-argument for ⟨A, H⟩ at literal P, if there exists a sub-argument ⟨C, P⟩ of
⟨A, H⟩ such that P and S disagree, that is, there exist two contradictory literals that have a
strict derivation from Π ∪ {S, P}. The literal P is referred as the counter-argument point
and ⟨C, P⟩ as the disagreement sub-argument.
Def. 42
Let ⟨B, S⟩ be a counter-argument for ⟨A, H⟩ at point P, and ⟨C, P⟩ the disagreement
sub-argument.
If ⟨B, S⟩ ≻*
⟨C, P⟩, then ⟨B, S⟩ is a proper defeater for ⟨A, H⟩.
If ⟨B, S⟩ ⊁ ⟨C, P⟩ and ⟨C, P⟩ ⊁ ⟨B, S⟩, then ⟨B, S⟩ is a blocking defeater for ⟨A, H⟩.
⟨B, S⟩ is a defeater for ⟨A, H⟩ if ⟨B, S⟩ is either a proper or blocking defeater for ⟨A, H⟩.
*≻ is an argument comparison criterion.

100. delp: defeasible logic programming
Π1 ∆1



cloudy
dry_season
waves
vacation
¬working ←− vacation






surf −< nice, spare_time
nice −< waves
spare_time −< ¬busy
¬busy −< ¬working
¬nice −< rain
rain −< cloudy
¬rain −< dry_season




101. delp: defeasible logic programming
Π1



cloudy
dry_season
waves
vacation
¬working ←− vacation



A0 =



surf −< nice, spare_time
nice −< waves
spare_time −< ¬busy
¬busy −< ¬working



A1 = {¬nice −< rain; rain −< cloudy}
A2 = {nice −< waves}
A3 = {rain −< cloudy}
A4 = {¬rain −< dry_season}

102. DeLP ABA
ASPIC+
Deductive
Argumentation
Logic for Clinical
Knowledge

103. assumption based argumentation framework
[Bon+97] [Ton14]

104. assumption based argumentation framework
⟨L, R, A, ⟩
L R A ⊆ L : A → L
language set of rules assumptions contrariness
Def. 45
An argument for the claim σ ∈ L supported by A ⊆ A (A ⊢ σ) is a deduction for σ
supported by A (and some R ⊆ R).*
Def. 46
An argument A1 ⊢ σ1 attacks an argument A2 ⊢ σ2 iff σ1 is the contrary of one of the
assumptions in A2.
*A (finite) tree with nodes labelled by sentences in L or by τ /∈ L, the root labelled by σ, leaves either τ
or sentences in A, non-leaves σ′ with, as children, the elements of the body of some rule in R with head σ′.

105. assumption based argumentation framework
R = { innocent(X) ←− notGuilty(X);
killer(oj) ←− DNAshows(oj), DNAshows(X) ⊃ killer(X);
DNAshows(X) ⊃ killer(X) ←− DNAfromReliableEvidence(X);
evidenceUnreliable(X) ←− collected(X, Y), racist(Y);
DNAshows(oj) ←−;
collected(oj, mary) ←−;
racist(mary) ←− }
A = { notGuilty(oj);
DNAfromReliableEvidence(oj) }
notGuilty(oj) = killer(oj),
DNAfromReliableEvidence(oj) = evidenceUnreliale(oj).

106. assumption based argumentation framework

107. DeLP ABA
ASPIC+
Deductive
Argumentation
Logic for Clinical
Knowledge

108. aspic+
[Pra10] [MP13] [MP14]

109. aspic+
Def. 47
An argumentation system is as tuple AS = ⟨L, R, ν⟩ where:
∙ : L → 2L
: a contrariness function s.t. if φ ∈ ψ and:
∙ ψ /∈ φ, then φ is a contrary of ψ;
∙ ψ ∈ φ, then φ is a contradictory of ψ (φ = –ψ);
∙ R = Rd ∪ Rs: strict (Rs) and defeasible (Rd) inference rules s.t. Rd ∩ Rs = ∅;
∙ ν : Rd → L, is a partial function.*
P ⊆ L is consistent iff ∄φ, ψ ∈ P s.t. φ ̸∈ ψ, otherwise is inconsistent.
A knowledge base in an AS is Kn ∪ Kp = K ⊆ L; {Kn, Kp} is a partition of K; Kn contains
axioms that cannot be attacked; Kp contains ordinary premises that can be attacked.
An argumentation theory is a pair AT = ⟨AS, K⟩.
*Informally, ν(r) is a wff in L which says that the defeasible rule r is applicable.

110. aspic+
Def. 48
An argument a on the basis of a AT = ⟨AS, K⟩, AS = ⟨L, R, ν⟩ is:
1. φ if φ ∈ K with: Prem(a) = {φ}; Conc(a) = φ; Sub(a) = {φ};
Rules(a) = DefRules(a) = ∅; TopRule(a) = undefined.
2. a1, . . . , an −→ / =⇒ ψ if a1, . . . , an, with n ≥ 0, are arguments such that there exists a
strict/defeasible rule r = Conc(a1), . . . , Conc(an) −→ / =⇒ ψ ∈ Rs/Rd.
Prem(a) =
∪n
i=1 Prem(ai); Conc(a) = ψ;
Sub(a) =
∪n
i=1 Sub(ai) ∪ {a};
Rules(a) =
∪n
i=1 Rules(ai) ∪ {r};
DefRules(a) = {d | d ∈ Rules(a) ∩ Rd};
TopRule(a) = r
a is strict if DefRules(a) = ∅, otherwise defeasible; firm if Prem(a) ⊆ Kn, otherwise
plausible.

111. aspic+
Def. 49
Given a and b arguments, a defeats b iff a undercuts, successfully rebuts or successfully
undermines b, where:
∙ a undercuts b (on b′
) iff Conc(a) /∈ ν(r) for some b′
∈ Sub(b) s.t.
r = TopRule(b′
) ∈ Rd;
∙ a successfully rebuts b (on b′
) iff Conc(a) /∈ φ for some b′
∈ Sub(b) of the form
b′′
1 , . . . , b′′
n =⇒ –φ, and a b′
;
∙ a successfully undermines b (on φ) iff Conc(a) /∈ φ, and φ ∈ Prem(b) ∩ Kp, and
a φ.
Def. 50
AF is the abstract argumentation framework defined by AT = ⟨AS, K⟩ if A is the smallest
set of all finite arguments constructed from K; and → is the defeat relation on A.

112. aspic+
Rationality postulates
P1: direct consistency iff
{Conc(a) | a ∈ S} is
consistent;
P2: indirect consistency iff
Cl({Conc(a) | a ∈ S}) is
consistent;
P3: closure iff {Conc(a) | a ∈ S} =
Cl({Conc(a) | a ∈ S});
P4: sub-argument closure iff
∀a ∈ S, Sub(a) ⊆ S.
∙ close under transposition
If φ1, . . . , φn −→ ψ ∈ Rs, then ∀i = 1 . . . n,
φ1, . . . , φi−1, ¬ψ, φi+1, . . . , φn =⇒ ¬φi ∈ Rs.
∙ Cl(Kn) is consistent;
∙ the argument ordering ⪯ is reasonable, namely:
∙ ∀a, b, if a is strict and firm, and b is plausible or
defeasible, then a b;
∙ ∀a, b, if b is strict and firm, then b a;
∙ ∀a, a′
, b such that a′
is a strict continuation of
{a}, if a b then a′
b, and if b a, then
b a′
;
∙ given a finite set of arguments {a1, . . . , an}, let
a+i
be some strict continuation of
{a1, . . . , ai−1, ai+1, . . . , an}. Then it is not the case
that ∀i, a+i
ai.

113. aspic+
Kp = { Snores;
Professor }
Rd = { Snores =⇒d1
Misbehaves;
Misbehaves =⇒d2
AccessDenied;
Professor =⇒d3
AccessAllowed }
AccesAllowed = −AccessDenied
Snores <′
Professor; d1 < d2; d1 < d3; d3 < d2.

114. aspic+

115. aspic+
http://toast.arg-tech.org/4214

116. DeLP ABA
ASPIC+
Deductive
Argumentation
Logic for Clinical
Knowledge

117. deductive argumentation
[BH01] [GH11] [BH14]

118. deductive argumentation
Def. 53
A deductive argument is an ordered pair ⟨Φ, α⟩ where Φ ⊢i α. Φ is the support, or
premises, or assumptions of the argument, and α is the claim, or conclusion, of the
argument.
consistency constraint when Φ is consistent (not essential, cf. paraconsistent logic).
minimality constraint when there is no Ψ ⊂ Φ such that Ψ ⊢ α
Def. 56
If ⟨Φ, α⟩ and ⟨Ψ, β⟩ are arguments, then
∙ ⟨Φ, α⟩ rebuts ⟨Ψ, β⟩ iff α ⊢ ¬β
∙ ⟨Φ, α⟩ undercuts ⟨Ψ, β⟩ iff α ⊢ ¬ ∧ Ψ

119. deductive argumentation
Def. 55
A classical logic argument from a set of formulae ∆ is a pair ⟨Φ, α⟩ such that
Φ ⊆ ∆ Φ ̸⊢ ⊥ Φ ⊢ α there is no Φ′
⊂ Φ such that Φ′
⊢ α.
Def. 57
Let a and b be two classical arguments. We define the following types of classical attack.
a is a direct undercut of b if ¬Claim(a) ∈ Support(b)
a is a classical defeater of b if Claim(a) ⊢ ¬
∧
Support(b)
a is a classical direct defeater of b if ∃ϕ ∈ Support(b) s.t. Claim(a) ⊢ ¬ϕ
a is a classical undercut of b if ∃Ψ ⊆ Support(b) s.t. Claim(a) ≡ ¬
∧
Ψ
a is a classical direct undercut of b if ∃ϕ ∈ Support(b) s.t. Claim(a) ≡ ¬ϕ
a is a classical canonical undercut of b if Claim(a) ≡ ¬
∧
Support(b).
a is a classical rebuttal of b if Claim(a) ≡ ¬Claim(b).
a is a classical defeating rebuttal of b if Claim(a) ⊢ ¬Claim(b).

120. deductive argumentation
..
bp(high)
ok(diuretic)
bp(high) ∧ ok(diuretic) → give(diuretic)
¬ok(diuretic) ∨ ¬ok(betablocker)
give(diuretic) ∧ ¬ok(betablocker)
.
bp(high)
ok(betablocker)
bp(high) ∧ ok(betablocker) → give(betablocker)
¬ok(diuretic) ∨ ¬ok(betablocker)
give(betablocker) ∧ ¬ok(diuretic)
.
symptom(emphysema),
symptom(emphysema) → ¬ok(betablocker)
¬ok(betablocker)
...

121. DeLP ABA
ASPIC+
Deductive
Argumentation
Logic for Clinical
Knowledge

122. a logic for clinical knowledge
[HW12] [Wil+15]

123. a logic for clinical knowledge
Def. 58
Given treatments τ1 and τ2, X ⊆ evidence, there are three kinds of inductive argument:
1. ⟨X, τ1 > τ2⟩: evidence in X supports the claim that treatment τ1 is superior to τ2.
2. ⟨X, τ1 ∼ τ2⟩: evidence in X supports the claim that treatment τ1 is equivalent to τ2
3. ⟨X, τ1 < τ2⟩: evidence in X supports the claim that treatment τ1 is inferior to τ2.
Def. 59
If the claim of argument ai is ϵi and the claim of argument aj is ϵj then ai conflicts with aj
whenever:
1. ϵi = τ1 > τ2, and ( ϵj = τ1 ∼ τ2 or ϵj = τ1 < τ2 ).
2. ϵi = τ1 ∼ τ2, and ( ϵj = τ1 > τ2 or ϵj = τ1 < τ2 ).
3. ϵi = τ1 < τ2, and ( ϵj = τ1 > τ2 or ϵj = τ1 ∼ τ2 ).

124. a logic for clinical knowledge
Def. 60
For any pair of arguments ai and aj, and a preference relation R, ai attacks aj with respect
to R iff ai conflicts with aj and it is not the case that aj is strictly preferred to ai according
to R.
A domain-specific benefit preference relation is defined in [HW12]
Def. 61 (Meta arguments)
For a ∈ Arg(evidence), if there is an e ∈ support(a) such that:
∙ e is not statistically significant, and e is not a side-effect, then this is an attacker:
⟨Not statistically significant⟩;
∙ e is a non-randomised and non-blind trial, then this is an attacker:
⟨Non-randomized & non-blind trials⟩;
∙ e is a meta-analysis that concerns a narrow patient group, then this is an attacker:
⟨Meta-analysis for a narrow patient group⟩.

125. a logic for clinical knowledge
ID Left Right Indicator Risk ratio Outcome p
e1 CP*
NT†
Pregnancy 0.05 superior 0.01
e2 CP NT Ovarian cancer 0.99 superior 0.07
e3 CP NT Breast cancer 1.04 inferior 0.01
e4 CP NT DVT 1.02 inferior 0.05
N.B.: Fictional data.
*Contraceptive pill.
†No Treatment.

126. a logic for clinical knowledge
..
⟨{e1}, CP > NT⟩
.
⟨{e2}, CP > NT⟩
. ⟨{e1, e2}, CP > NT⟩.
⟨{e3}, CP < NT⟩
.
⟨{e4}, CP < NT⟩
. ⟨{e3, e4}, CP < NT⟩.
⟨Notstatistically
significant⟩
ID Left Right Indicator Risk ratio Outcome p
e1 CP NT Pregnancy 0.05 superior 0.01
e2 CP NT Ovarian cancer 0.99 superior 0.07
e3 CP NT Breast cancer 1.04 inferior 0.01
e4 CP NT DVT 1.02 inferior 0.05

127. ..probabilistic argumentation frameworks

128. epistemic approach
[Thi12] [Hun13]

129. epistemic approach
[HT14] [BGV14]

130. epistemic approach
An epistemic probability distribution*
for an argumentation framework ∆ = ⟨A, → ⟩ is:
P : A → [0, 1]
Def. 65
For an argumentation framework AF = ⟨A, →⟩ and a probability assignment P, the
epistemic extension is
{a ∈ A | P(a) > 0.5}
*In the tutorial a way to compute it for arguments based on classical deduction.

131. epistemic approach
COH: P is coherent if for every a, b ∈ A, if a attacks b then P(a) ≤ 1 − P(b).
SFOU: P is semi-founded if P(a) ≥ 0.5 for every unattacked a ∈ A.
FOU: P is founded if P(a) = 1 for every unattacked a ∈ A.
SOPT: P is semi-optimistic if P(a) ≥ 1 −
∑
b∈a− P(b) for every a ∈ A with at least one attacker.
OPT: P is optimistic if P(a) ≥ 1 −
∑
b∈a− P(b) for every a ∈ A.
JUS: P is justifiableif P is coherent and optimistic.
TER: P is ternary if P(a) ∈ {0, 0.5, 1} for every a ∈ A.
RAT: P is rational if for every a, b ∈ A, if a attacks b then P(a) > 0.5 implies P(b) ≤ 0.5.
NEU: P is neutral if P(a) = 0.5 for every a ∈ A.
INV: P is involutary if for every a, b ∈ A, if a attacks b, then P(a) = 1 − P(b).
Let the event “a is accepted” be denoted as a, and let be Eac(S) = {a|a ∈ S}. Then P is weakly
p-justifiable iff ∀a ∈ A, ∀b ∈ a−
, P(a) ≤ 1 − P(b).

132. epistemic approach
Def. 67
Restriction on complete*
probability function P Classical semantics
No restriction complete extensions
No arguments a such that P(a) = 0.5 stable
Maximal no. of a such that P(a) = 1 preferred
Maximal no. of a such that P(a) = 0 preferred
Maximal no. of a such that P(a) = 0.5 grounded
Minimal no. of a such that P(a) = 1 grounded
Minimal no. of a such that P(a) = 0 grounded
Minimal no. of a such that P(a) = 0.5 semi-stable
*Coherent, founded, and ternary. http://arxiv.org/abs/1405.3376

133. structural approach
[Hun14]

134. structural approach
P : {∆′
⊑ ∆} → [0, 1]
Subframework Probability
∆1 a ↔ b 0.09
∆2 a 0.81
∆3 b 0.01
∆4 0.09
PGR({a, b}) = = 0.00
PGR({a}) = P(∆2) = 0.81
PGR({b}) = P(∆3) = 0.01
PGR({}) = P(∆1) + P(∆4) = 0.18

135. a computational framework
[Li15]

136. a computational framework
Convert to
ASPIC+Argumentation
System
•Logical Language
•Inference Rules
•Contrariness Function
•......
Structured
Argumentation
Framework
(SAF)
DAF
DAFEAF
Extended
Evidential
Framework
(EEAF)
Probabilistic
Extended
Evidential
Framework
Convert to
Convert to
Extended
Evidential
Framework
(EEAF)
Model
Probabilistic
Extended
Evidential
Framework
Associate
Probabilities
Convert toPrEAF
Associate
Probabilities
Semantics
Preserved
PrAF
Associate
Probabilities

137. ..cispaces

138. [Ton+15]

139. CISpaces

140. What is the cause of the illness?

141. Analyst Joe
?
Illness among peopleLivestock illness
Possible
Connection
CONTAMINATED
WATER SUPPLY
Is this information credible?
Are there alternative explanations?
Is there evidence for the
contamination of the water supply?
Analysts must reason with different types of evidence

142. research foci
Attributes of the problem domain
∙ Intelligence analysis is critical for making well-informed decisions
∙ Large amount of conflicting incomplete information
∙ Reasoning with different types of evidence
Research Question
How to develop agents to support to reasoning with different types of evidence in a
combined approach throughout the process of analysis?

143. intelligence analysis
Def. 73
The application of individual and collective cognitive methods to evaluate, integrate,
interpret information about situations and events to provide warning for potential
threats or identify opportunities.
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
Effective if:
TIMELY
TARGETED
and TRUSTED

144. collaboration among analysts
Team of Analysts: More effective, Prevent Bias, Different Expertise and Resources
Challenges at
different stages
of analysis
Schematize Build Case
Search
for support
Search
for evidence
Shoebox
Evidence File
Hyp1 Hyp2
Hypotheses
Share data and analysis
Integrate and annotate
Assess credibility
inf
inf
inf
Gather information Identify Plausible Hypotheses
Mitigate Cognitive Biases

145. cispaces agent support
Interface
Communication layer
ToolBox
WorkBoxInfoBox ReqBox
ChatBox
Sensemaking
Agent
Crowd-sourcing
Agent
Provenance
Agent
analyst
CISpaces Interface: Working space and access to agent support
Sensemaking Agent: Support collaborative analysis of arguments
Crowd-sourcing Agent: Enable participation of large groups of contributors
Provenance Agent: Assess the credibility of information

146. Interface
Communication layer
ToolBox
WorkBoxInfoBox ReqBox
ChatBox
Sensemaking
Agent
Crowd-sourcing
Agent
Provenance
Agent
analyst
Provenance
Agent
Sensemaking
Agent

147. sensemaking agent (smag) - analysis construction
∙ Annotation of Pro links;
∙ Suggests CQs (Con links) to prevent cognitive biases.
Causal – Distribution of Activities
∙ Typically, if C occurs, then E
will occur
∙ In this case, C occurs
⇒ Therefore, in this case E will
occur
Association – Element Connections
∙ An activity occurs, and an entity may be
involved
∙ To perform the activity some property H
is required
∙ The entity fits the property H
⇒ Therefore, the entity is associated with
the activity

148. smag analysis construction (cont.)
E is an expert in D
E asserts A in D
A is true
Lab Expert on
water toxins and
chemicals asserts
There is a bacteria
contaminating the
water supply
Water supply in
Kish is
contaminated
Pro
Expert Opinion
Cause to effect
Identification...
V
Analyst annotates pro links and
nodes → match to an argument
scheme.
E is an expert in D
Lab Expert on
water toxins and
chemicals asserts
There is a bacteria
contaminating the
water supply
Water supply in
Kish is
contaminated
Expert
Opinion
E asserts A in D
A is true
∙ E is an expert in domain D containing A,
∙ E asserts that A is true,
⇒ Therefore, A may plausibly be true.
E is an expert in D
Lab Expert on
water toxins and
chemicals asserts
CQ1: Is E an expert in D?
CQ2: Is E reliable?V
Con
CQ2
The expert is not
reliable
Analyst select CQs. CISpaces shows
a negative answer to a CQ to prevent
cognitive biases.

149. smag hypotheses identification
controversial standpoints as extensions
1. Transforming the current workbox view into an argumentation framework
q0,q1=>q2
PREMISE PREMISE
q0
q1
q2
q3
q4
q1,q3=>q4
Contradictory
statements:
q2-q4
CAUSE TO
EFFECT
ASPIC+ argumentation framework:
Premises: q0, q1, q3
Rules: q0, q1 ⇒ q2; q1, q3 ⇒ q4;
Negation: q2 − q4
Arguments:
A0 : q0, A1 : q1, A2 : q3
A4 : A0, A1 ⇒ q2
A5 : A0, A2 ⇒ q4
2. ASPIC+
/Dung’s AF implementation identifies the sets of acceptable arguments:

150. smag hypotheses identification (cont.)
3. CISpaces shows what conclusions can be supported
∙ Labelled according to extensions computed
∙ Arguments shared through the Argument Interchange Format (AIF)
Unidentified
illness affects
the local
livestock in
Kish
Non-
waterborne
bacteria were
engineered and
released in the
water supply
Illness among
young and elderly
people in Kish
caused by bacteria
Toxic
Bacteria
contaminate
the local water
system in Kish
NGO Lab
reports
examined the
contamination
NON-
waterborne
bacteria
contaminate the
water supply
There are
bacteria in the
water supply
Waterborne
bacteria
contaminate
the water
supply
V
V
V
V
VWaterborne
bacteria have
formed by a
sewage leakage
in the water
supply pipes
V

151. Interface
Communication layer
ToolBox
WorkBoxInfoBox ReqBox
ChatBox
Sensemaking
Agent
Crowd-sourcing
Agent
Provenance
Agent
analyst
Provenance
Agent
Crowd-sourcing
Agent

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

153. cwsag results import
Q0-Answer
Clear (Con)
Q1-Answer
21.1 (Pro)
Q0-AGAINST
Water Contaminated
Q1-FOR
Water Contaminated
CONTRADICTORY

154. Interface
Communication layer
ToolBox
WorkBoxInfoBox ReqBox
ChatBox
Sensemaking
Agent
Crowd-sourcing
Agent
Provenance
Agent
analyst
Provenance
Agent
Provenance
Agent

155. N
S
E
W
image info ij
observation
Observer Messenger Informer
message
info ik
Gang
heading
South
Gang
Crossing
North Border
N
S
E
W
Surveillance
BORDER L1-L2
Image
Processing
Analyst Joe
BORDER L1-L2
GP(ij)
GP(ik)

156. argument from provenance
- Given a provenance chain GP(ij) of ij, information ij:
- (Where?) was derived from an entity A
- (Who?) was associated with actor AG
- (What?) was generated by activity P1
- (How?) was informed by activity P2
- (Why?) was generated to satisfy goal X
- (When?) was generated at time T
- (Which?) was generated by using some entities A1,…, AN
- where A, AG, P1, …belong to GP(ij)
- the stated elements of GP(ij) infer that information ij is true,
⇒ Therefore, information ij may plausibly be taken to be true.
CQA1: Is ij consistent with other information?
CQA2: Is ij supported by evidence?
CQA3: Does GP(ij) contain other elements that lead us not to believe ij?
CQA4: Are there provenance elements that should have been included for believing ij?

157. argument for provenance preference
- Given information ij and ik,
- and their known parts of the provenance chains GP(ij) and GP(ik),
- if there exists a criterion Ctr such that GP(ij) ≪Ctr GP(ik), then ij ≪ ik
- a criterion Ctr′
leads to assert that GP(ij) ≪Ctr′ GP(ik)
⇒ Therefore, ik should be preferred to ij.
Trustworthiness Reliability Timeliness Shortest path
CQB1: Does a different criterion Ctr1, such that GP(ij) ≫Ctr1
GP(ik) lead ij ≪ ik not being valid?
CQB2: Is there any exception to criterion Ctr such that even if a provenance chain GP(ik) is preferred to
GP(ij), information ik is not preferred to information ij?
CQB3: Is there any other reason for believing that the preference ij ≪ ik is not valid?

158. pvag provenance analysis & import
IMPORT ANALYSIS
Primary Source Pattern
Provenance
Explanation
US Patrol
Report
Extract
Used wasGeneratedBy
US Team
Patrol
wasAssociatedWith
wasDerivedFrom
INFO:
Livestock
illness
prov: time
2015-04-27T02:27:40Z
Farm Daily
Report
Prepare
Used wasGeneratedBy
Kish
Farmer
wasAssociatedWith
wasDerivedFrom
type PrimarySource
Annotate
wasGeneratedBy
wasAssociatedWith
Livestock
Pictures
Used
Livestock
Information
IMPORT OF
PREFERENCES?

159. theories/technologies integrated
∙ Argument representation:
∙ Argument Schemes and Critical questions (domain specific)
∙ „Bipolar-like” graph for user consumption
∙ AIF (extension for provenance)
∙ ASPIC(+)
∙ Arguments based on preferences (partially under development)
∙ Theoretical framework for acceptability status:
∙ AF
∙ PrAF (case study for [Li15])
∙ AFRA for preference handling (under development)
∙ Computational machinery: jArgSemSAT

160. ..algorithms and implementations

161. [Cha+15]

162. ad-hoc procedures
ArgTools
[NAD14]

163. ad-hoc procedures

164. csp-based approach
ConArg
[BS12]

165. csp-based approach
A Constraint Satisfaction Problem (CSP) P is a triple P = ⟨X, D, C⟩ such that:
∙ X = ⟨x1, . . . , xn⟩ is a tuple of variables;
∙ D = ⟨D1, . . . , Dn⟩ a tuple of domains such that ∀i, xi ∈ Di;
∙ C = ⟨C1, . . . , Ct⟩ is a tuple of constraints, where ∀j, Cj = ⟨RSj
, Sj⟩,
Sj ⊆ {xi|xi is a variable}, RSj
⊆ SD
j × SD
j where SD
j = {Di|Di is a
domain, and xi ∈ Sj}.
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.

166. csp-based approach
Given an AF:
1. create a variable for each argument whose domain is always {0, 1} — ∀ai ∈ A, ∃xi ∈ X
such that Di = {0, 1};
2. describe constraints associated to different definitions of Dung’s argumentation
framework: e.g.
{a1, a2} ⊆ A is D-conflict-free iff ¬(x1 = 1 ∧ x2 = 1);
3. solve the CSP problem.

167. asp-based approach
ASPARTIX-D / ASPARTIX-V / DIAMOND
[EGW10] [Dvo+11]

168. asp-based approach
πST = { in(X) ← not out(X), arg(X);
out(X) ← not in(X), arg(X);
← in(X), in(Y), defeat(X, Y);
defeated(X) ← in(Y), defeat(Y, X);
← out(X), not defeated(X)}.
Tests for subset-maximality exploit the metasp optimisation frontend for the
ASP-package gringo/claspD.

169. sat-based approaches
Cegartix
[Dvo+12]
ArgSemSAT/jArgSemSAT/LabSATSolver
[Cer+14b]

170. sat-based approaches
[Dvo+12]
∧
a→b
(¬xa ∨ ¬xb)∧
∧
b→c

¬xc ∨
∨
a→b
xa



171. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
C1
Lab(a1) = in ⇔ ∀a2 ∈ a−
1 Lab(a2) = out
Lab(a1) = out ⇔ ∃a2 ∈ a−
1 : Lab(a2) = in
Lab(a1) = undec ⇔ ∀a2 ∈ a−
1 Lab(a2) ̸= in ∧ ∃a3 ∈ a−
1 :
Lab(a3) = undec

172. sat-based approaches
[Cer+14b]
∧
i∈{1,...,k}
(
(Ii ∨ Oi ∨ Ui) ∧ (¬Ii ∨ ¬Oi)∧(¬Ii ∨ ¬Ui) ∧ (¬Oi ∨ ¬Ui)
)
∧
∧
{i|ϕ(i)−=∅}
(Ii ∧ ¬Oi ∧ ¬Ui) ∧
∧
{i|ϕ(i)−̸=∅}


Ii ∨



∨
{j|ϕ(j)→ϕ(i)}
(¬Oj)





 ∧
∧
{i|ϕ(i)−̸=∅}



∧
{j|ϕ(j)→ϕ(i)}
¬Ii ∨ Oj


 ∧
∧
{i|ϕ(i)−̸=∅}



∧
{j|ϕ(j)→ϕ(i)}
¬Ij ∨ Oi


 ∧
∧
{i|ϕ(i)−̸=∅}


¬Oi ∨



∨
{j|ϕ(j)→ϕ(i)}
Ij





 ∧
∧
{i|ϕ(i)−̸=∅}



∧
{k|ϕ(k)→ϕ(i)}


Ui ∨ ¬Uk ∨



∨
{j|ϕ(j)→ϕ(i)}
Ij








 ∧
∧
{i|ϕ(i)−̸=∅}






∧
{j|ϕ(j)→ϕ(i)}
(¬Ui ∨ ¬Ij)


 ∧


¬Ui ∨



∨
{j|ϕ(j)→ϕ(i)}
Uj










173. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
Ca
1
Lab(a1) = in ⇔ ∀a2 ∈ a−
1 Lab(a2) = out
Lab(a1) = out ⇔ ∃a2 ∈ a−
1 : Lab(a2) = in

174. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
Cb
1
Lab(a1) = out ⇔ ∃a2 ∈ a−
1 : Lab(a2) = in
Lab(a1) = undec ⇔ ∀a2 ∈ a−
1 Lab(a2) ̸= in ∧ ∃a3 ∈ a−
1 :
Lab(a3) = undec

175. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
Cc
1
Lab(a1) = in ⇔ ∀a2 ∈ a−
1 Lab(a2) = out
Lab(a1) = undec ⇔ ∀a2 ∈ a−
1 Lab(a2) ̸= in ∧ ∃a3 ∈ a−
1 :
Lab(a3) = undec

176. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
C2
Lab(a1) = in ⇒ ∀a2 ∈ a−
1 Lab(a2) = out
Lab(a1) = out ⇒ ∃a2 ∈ a−
1 : Lab(a2) = in
Lab(a1) = undec ⇒ ∀a2 ∈ a−
1 Lab(a2) ̸= in ∧ ∃a3 ∈ a−
1 :
Lab(a3) = undec

177. sat-based approaches
[Cer+14b]
If a1 is not attacked, Lab(a1) = in
C3
Lab(a1) = in ⇐ ∀a2 ∈ a−
1 Lab(a2) = out
Lab(a1) = out ⇐ ∃a2 ∈ a−
1 : Lab(a2) = in
Lab(a1) = undec ⇐ ∀a2 ∈ a−
1 Lab(a2) ̸= in ∧ ∃a3 ∈ a−
1 :
Lab(a3) = undec

178. sat-based approaches
[Cer+14b]
50
60
70
80
90
100
50 100 150 200IPCnormalisedto100
Number of arguments
IPC normalised to 100 with respect to the number of arguments
C1
Ca
1
Cb
1
Cc
1
C2
C3

179. iccma 2015
The First International Competition on Computational Models of Argumentation
http://argumentationcompetition.org/
Results announced yesterday

180. iccma 2015

181. iccma 2015

182. iccma 2015

183. a parallel algorithm
[BGG05] [Cer+14a] [Cer+15]

184. a parallel algorithm

185. a parallel algorithm

186. a parallel algorithm
a b
e f
c d g h

187. a parallel algorithm
a b
e f
c d g h

188. a parallel algorithm
a b
e f
c d g h
Level 1 Level 2

189. a parallel algorithm
a b
e f
c d g h
Level 1 Level 2



⟨{a, c, e}, {b, d, f}, {}⟩,
⟨{a, c, f}, {b, d, e}, {}⟩,
⟨{a, d, e}, {b, c, f}, {}⟩,
⟨{a, d, f}, {b, c, e}, {}⟩




190. a parallel algorithm
a b
e f
c d g h
Level 1 Level 2
Moving to the the last level,
B1: no argument in S3 is attacked from “outside” for Lab ∈
{
⟨{a, c, e}, {b, d, f}, {}⟩,
⟨{a, c, f}, {b, d, e}, {}⟩
}
B2: g is attacked by d Lab ∈
{
⟨{a, d, e}, {b, c, f}, {}⟩,
⟨{a, d, f}, {b, c, e}, {}⟩
}
Cases B1 and B2 are computed in parallel.

191. a parallel algorithm
a b
e f
c d g h
Level 1 Level 2



⟨{a, c, e, g}, {b, d, f, h}, {}⟩,
⟨{a, c, e, h}, {b, d, f, g}, {}⟩,
⟨{a, c, f, g}, {b, d, e, h}, {}⟩,
⟨{a, c, f, h}, {b, d, e, g}, {}⟩,
⟨{a, d, e, h}, {b, c, f, g}, {}⟩,
⟨{a, d, f, h}, {b, c, e, g}, {}⟩




192. We need to be smart
Holger H. Hoos, Invited Keynote Talk at ECAI2014

193. [VCG14] [CGV14]

194. features from an argumentation graph
Directed Graph (26 features)
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: …

195. how hard is to get the features?
Direct Graph Features (DG) Undirect Graph Features (UG)
Class CPU-Time # feat Class CPU-Time # feat
Mean stdDev Mean stDev
Graph Size 0.001 0.009 5 Graph Size 0.001 0.003 4
Degree 0.003 0.009 4 Degree 0.002 0.004 4
SCC 0.046 0.036 5 Components 0.011 0.009 5
Structure 2.304 2.868 5 Structure 0.799 0.684 1
Triangles 0.787 0.671 5
Average CPU-time, stdev, needed for extracting the features of a given class.

196. protocol: some numbers
∙ |SCCS∆| in 1 : 100;
∙ |A| in 10 : 5, 000;
∙ | → | in 25 : 270, 000 (Erdös-Rényi, p uniformly distributed) ;
∙ Overall 10, 000 AFs.
∙ Cutoff time of 900 seconds (value also for crashed, timed-out or ran out of memory).
∙ EPMs both for Regression (Random forests) and Classification (M5-Rules) using WEKA;
∙ Evaluation using a 10-fold cross-validation approach on a uniform random
permutation of instances.

197. result 1: best features for prediction
Solver B1 B2 B3
AspartixM number of arguments density of directed graph size of max. SCC
PrefSAT density of directed graph number of SCCs aperiodicity
NAD-Alg density of directed graph CPU-time for density CPU-time for Eulerian
SSCp density of directed graph number of SCCs size of the max SCC
Determined by a greedy forward search based on the Correlation-based Feature
Selection (CFS) attribute evaluator.
AF structure SCCs CPU-time for feature extraction

198. result 2: predicting (log)runtime
RSME of Regression (Lower is better)
B1 B2 B3 DG UG SCC All
AspartixM 0.66 0.49 0.49 0.48 0.49 0.52 0.48
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
∑n
i=1
(
log10( ti ) − log10( yi )
)2
n
AF structure SCCs CPU-time for feature extraction Undirect Graph

199. result 3: best features for classification
C-B1 C-B2 C-B3
number of arguments density of directed graph min attackers
Determined by a greedy forward search based on the Correlation-based Feature
Selection (CFS) attribute evaluator.
AF structure Attackers

200. result 4: classification, i.e. selecting the best solver for a given af
Classification (Higher is better)
|A| density min attackers DG UG SCC All
Accuracy 48.5% 70.1% 69.9% 78.9% 79.0% 55.3% 79.5%
Prec. AspartixM 35.0% 64.6% 63.7% 74.5% 74.9% 42.2% 76.1%
Prec. PrefSAT 53.7% 67.8% 68.1% 79.6% 80.5% 60.4% 80.1%
Prec. NAD-Alg 26.5% 69.2% 69.0% 81.7% 85.1% 35.3% 86.0%
Prec. SSCp 54.3% 73.0% 72.7% 76.6% 76.8% 57.8% 77.2%
AF structure Attackers Undirect Graph SCCs

201. result 5: algorithm selection
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
*Scale of (log)relative performance

202. ..the frontier

203. belief revision and argumentation
[FKS09] [FGS13]

204. belief revision and argumentation
Potential cross-fertilisation
Argumentation in Belief Revision
∙ Justification-based truth maintenance
system
∙ Assumption-based truth maintenance
system
Some conceptual differences:
in revision, external beliefs are
compared with internal beliefs and,
after a selection process, some
sentences are discarded, other
ones are accepted. [FKS09]
Belief Revision in Argumentation
∙ Changing by adding or deleting an
argument.
∙ Changing by adding or deleting a set of
arguments.
∙ Changing the attack (and/or defeat)
relation among arguments.
∙ Changing the status of beliefs (as
conclusions of arguments).
∙ Changing the type of an argument (from
strict to defeasible, or vice versa).

205. abstract dialectical framework
[Bre+13]

206. abstract dialectical framework
Dependency Graph + Acceptance Conditions

207. argumentation and social networks
[LM11] [ET13]

208. argumentation and social networks
a:The Wonder-Phone is the
best new generation
phone.
+20 -20
b: No, the Magic-Phone is
the best new generation
phone.
+ 20 - 20
c: here is a [link] to a review
of the Magic-Phone giving
poor scores due to bad
battery performance
+60 -10.
d: author of c is ignorant, since
subsequent reviews noted that
only one of the first editions
had such problems: [links].
+10 -40
e: d is wrong. I found out
c) knows about that but
withheld the information.
Here's a [link] to another
thread proving it!
+40 -10

209. argumentation and social networks
a:The Wonder-Phone is the best
new generation phone.
+20 -20 b: No, the Magic-Phone is the
best new generation phone.
+ 20 - 20
c: here is a [link] to a review
of the Magic-Phone giving
poor scores due to bad
battery performance
+60 -10.
d: author of c is ignorant, since
subsequent reviews noted that
only one of the first editions had
such problems: [links].
+10 -40
e: d is wrong. I found out c)
knows about that but
withheld the information.
Here's a [link] to another
thread proving it!
+40 -10

210. argumentation and social networks
a:The Wonder-Phone is the best
new generation phone.
+20 -20
b: No, the Magic-Phone is the best
new generation phone.
+ 20 - 20
c: here is a [link] to a review of the Magic-
Phone giving poor scores due to bad
battery performance
+60 -10.
d: author of c is ignorant, since subsequent
reviews noted that only one of the first editions
had such problems: [links].
+10 -40
e: d is wrong. I found out c)
knows about that but
withheld the information.
Here's a [link] to another
thread proving it!
+40 -10

211. argumentation and social networks
http://www.quaestio-it.com/

212. argument mining
[CV12] [Bud+14]

213. argument mining
http://www-sop.inria.fr/NoDE/
http://corpora.aifdb.org/

214. natural language interfaces
[CTO14] [Cam+14]

215. natural language interfaces
a1 : σA ⇒ γ
a2 : σB ⇒ ¬γ
a3 : ⇒ a1 a2
First Scenario
a1: Alice suggests to move in together with Jane
a2: Stacy suggests otherwise because Jane might have a hidden agenda
a3: Stacy is your best friend
a1 a2 don’t know
% agreement 12.5 68.8 18.8
• • • • •
Second Scenario
a1: TV1 suggests that tomorrow will rain
a2: TV2 suggests that tomorrow will be cloudy but will not rain
a3: TV2 is generally more accurate than TV1
a1 a2 don’t know
% agreement 5.0 50.0 45.0

216. natural language interfaces
Scrutable Autonomous Systems (in particular from 7’ 30”)

217. ..conclusion

218. Hal’s Argument

219. ..credits

220. credits
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