Handouts for the IJCAI 2017 tutorial on Argumentation. This document is a collection of technical definitions as well as examples of various topics addressed in the tutorial. It is not supposed to be an exhaustive compendium of twenty years of research in argumentation theory. This material is derived from a variety of publications from many researchers who hold the copyright and any other intellectual property of their work. Original publications are thoroughly cited and reported in the bibliography at the end of the document. Errors and misunderstandings rest with the author of this tutorial: please send an email to federico.cerutti@acm.org for reporting any.

1. Abstract
Handouts for the IJCAI 2017 tutorial on Argumentation. This document is
a collection of technical definitions as well as examples of various topics ad-
dressed in the tutorial. It is not supposed to be an exhaustive compendium of
twenty years of research in argumentation theory.
This material is derived from a variety of publications from many researchers
who hold the copyright and any other intellectual property of their work.
Original publications are thoroughly cited and reported in the bibliography
at the end of the document. Errors and misunderstandings rest with the au-
thor of this tutorial: please send an email to federico.cerutti@acm.org for
reporting any.

2. Argumentation in Artificial Intelligence:
From Theory to Practice
Federico Cerutti
August 2017

3. Chapter 1
Dung’s Argumentation
Framework
Acknowledgement
This handout include material from a number of collaborators including Pietro5
Baroni, Massimiliano Giacomin, and Stefan 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 directed10
graph where the nodes are arguments and the edges are drawn from attack-
ing 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. given E ⊆ A ,15
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. Similarly,
b → S ≡ ∃a ∈ S : b → a.
1.1 Principles for Extension-based Semantics:
[BG07]20
Definition 2.

4. 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 . ♠
Definition 3. Given an argumentation framework AF = 〈A ,→ 〉, an argu-25
ment a ∈ A is D-acceptable w.r.t. a set S ⊆ A if and only if ∀b ∈ A b → a ⇒
S → b.
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5. Dung’s AF • Acceptability of Arguments [PV02; BG09a]
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-characteristic function of
AF. ♠
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-ac-5
ceptable w.r.t. S. The set of all the D-admissible sets of AF is denoted as
AS (AF). ♠
Dσ = {AF|Eσ(AF) = }
Definition 5.

6. 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)) iff10
∀b ∈ A , b → a, ∃c ∈ S {a} : c → b and D-sd(c,S {a}). ♠
Definition 7.

7. A semantics σ satisfies the D-strongly admissibility principle
if and only if ∀AF ∈ Dσ, ∀E ∈ Eσ(AF) it holds that
a ∈ E ⊃ D-sd(a,E) ♠
Definition 8.

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.

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-maximality principle
if and only if ∀AF ∈ Dσ Eσ(AF) is D-I-maximal. ♠
Definition 10. Given an argumentation framework AF = 〈A ,→ 〉, a non-15
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. The re-
striction of AF to S ⊆ A is the argumentation framework AF↓S = 〈S,→
∩(S × S)〉. ♠20
Definition 12.

10. 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
. ♠
1.2 Acceptability of Arguments [PV02; BG09a]
Definition 13. Given a semantics σ and an argumentation framework 〈A ,→ 〉,25
an argument AF ∈ Dσ is:
• skeptically justified iff ∀E ∈ Eσ(AF), a ∈ S;
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11. Dung’s AF • (Some) Semantics [Dun95]
• credulously justified iff ∃E ∈ Eσ(AF), a ∈ S. ♠
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;5
• overruled iff it is not credulously justified. ♠
1.3 (Some) Semantics [Dun95]
Lemma 1 (Dung’s Fundamental Lemma, [Dun95, Lemma 10]). Given an ar-
gumentation framework AF = 〈A ,→ 〉, let S ⊆ A be a D-admissible set of ar-
guments, 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 or-
der with respect to set inclusion. ♣15
Definition 15 (Complete Extension).

12. Given an argumentation framework
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).

13. Given an argumentation framework
AF = 〈A ,→ 〉. The grounded extension of AF is the least complete extension20
of AF. GR denotes the grounded semantics. ♠
Definition 17 (Preferred Extension).

14. Given an argumentation framework
AF = 〈A ,→ 〉. A preferred extension of AF is a maximal (w.r.t. set inclusion)
complete extension of AF. P R denotes the preferred semantics. ♠
Definition 18. Given an argumentation framework AF = 〈A ,→ 〉 and S ⊆ A ,25
S+
{a ∈ A | ∃b ∈ S ∧ b → a}. ♠
Definition 19 (Stable Extension).

15. Given an argumentation framework AF =
〈A ,→ 〉. S ⊆ A is a stable extension of AF iff S is a preferred extension and
S+
= A S. S T denotes the stable semantics. ♠
1.4 Labelling-Based Semantics Representation30
[Cam06]
Definition 20. Let ∆ = Γ be an argumentation framework. A labelling L ab ∈
L(∆) is a complete labelling of ∆ iff it satisfies the following conditions for any
a1 ∈ A :
• L ab(a1) = in ⇔ ∀a2 ∈ a−
1 L ab(a2) = out;35
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16. 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
• 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 be an argumentation framework. A labelling L ab ∈
L(∆) is the grounded labelling of ∆ if it is the complete labelling of ∆ minimiz-5
ing the set of arguments labelled in, and it is a preferred labelling of ∆ if it is
a complete labelling of ∆ maximizing the set of arguments labelled in. ♠
In order to show the connection between extensions and labellings, let us
recall the definition of the function Ext2Lab, returning the labelling corre-
sponding to a D-conflict-free set of arguments S.10
Definition 22. Given an AF ∆ = Γ and a D-conflict-free set S ⊆ A , the corre-
sponding labelling Ext2Lab(S) is defined as Ext2Lab(S) ≡ L ab, where
• L ab(a1) = in ⇔ a1 ∈ S
• L ab(a1) = out ⇔ ∃ a2 ∈ S s.t. a2 → a1
• L ab(a1) = undec ⇔ a1 ∉ S ∧ a2 ∈ S s.t. a2 → a1 ♠15
[Cam06] shows that there is a bijective correspondence between the com-
plete, grounded, preferred extensions and the complete, grounded, preferred
labellings, respectively.
Proposition 1. Given an an AF ∆ = Γ, L ab is a complete (grounded, pre-
ferred) labelling of ∆ if and only if there is a complete (grounded, preferred)20
extension S of ∆ such that L ab = Ext2Lab(S). ♣
The set of complete labellings of ∆ is denoted as LC O (∆), the set of pre-
ferred labellings as LP R(∆), while LGR(∆) denotes the set including the
grounded labelling.
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17. Dung’s AF • Decomposability and Transparancy [Bar+14]
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]
1.5 Decomposability and Transparancy [Bar+14]
Definition 23. Given an argumentation framework AF = (A ,→),
a labelling-based semantics σ associates with AF a subset of L(AF), denoted
as Lσ(AF). ♠
Definition 24. Given AF = (A ,→) and a set Args ⊆ A , the input of Args, de-5
noted as Argsinp, is the set {B ∈ A Args | ∃A ∈ Args,(B, A) ∈→}, the condition-
ing relation of Args, denoted as ArgsR
, is defined as → ∩(Argsinp ×Args). ♠
Definition 25. An argumentation framework with input is a tuple
(AF,I ,LI ,RI ), including an argumentation framework AF = (A ,→), a set
of arguments I such that I ∩A = , a labelling LI ∈ LI and a relation RI ⊆10
I ×A . A local function assigns to any argumentation framework with input a
(possibly empty) set of labellings of AF, i.e.
F(AF,I ,LI ,RI ) ∈ 2L(AF)
. ♠
Definition 26. Given an argumentation framework with input
(AF,I ,LI ,RI ), the standard argumentation framework w.r.t.15
(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 27. Given a semantics σ, the canonical local function of σ (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 argumentation frame-20
work w.r.t. (AF,I ,LI ,RI ). ♠
Definition 28. A semantics σ is complete-compatible iff the following condi-
tions hold:
1. For any argumentation framework AF = (A ,→), every labelling L ∈
Lσ(AF) satisfies the following conditions:25
• 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) = out
• if C ∈ A is self-defeating, and there are no attackers of C besides
C itself, then L(C) = undec30
2. for any set of arguments I and any labelling LI ∈ LI , the argumen-
tation framework AF = (I ,→ ), where I = I ∪{A | A ∈ out(LI )} and
→ = {(A , A) | A ∈ out(LI )}∪{(A, A) | A ∈ undec(LI )}, admits a (unique)
labelling, i.e. |Lσ(AF )| = 1. ♠
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18. Dung’s AF • Decomposability and Transparancy [Bar+14]
Definition 29. A semantics σ is fully decomposable (or simply decomposable)
iff there is a local function F such that for every argumentation 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 30. A complete-compatible semantics σ is top-down decomposable
iff for any argumentation framework AF = (A ,→) and any partition P =
{P1,...Pn} of A , it holds that Lσ(AF) ⊆ U (P , AF,Fσ). ♠
Definition 31. A complete-compatible semantics σ is bottom-up decompos-
able iff for any argumentation framework AF = (A ,→) and any partition10
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.
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19. Chapter 2
Argumentation Schemes
Argumentation schemes [WRM08] are reasoning patterns which generate ar-
guments:
• deductive/inductive inferences that represent forms of common types5
of arguments used in everyday discourse, and in special contexts (e.g.
legal argumentation);
• neither deductive nor inductive, but defeasible, presumptive, or abduc-
tive.
Moreover, an argument satisfying a pattern may not be very strong by10
itself, but may be strong enough to provide evidence to warrant rational ac-
ceptance 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 discussion
moved forward as new evidence is being collected. The investigation can then15
move ahead, even under conditions of uncertainty and lack of knowledge,
using the conclusions tentatively accepted.
2.1 An example: Walton et al. ’s Argumentation
Schemes for Practical Reasoning
Suppose I am deliberating with my spouse on what to do with20
our pension investment fund — whether to buy stocks, bonds or
some other type of investments. We consult with a financial ad-
viser, and expert source of information who can tell us what is
happening in the stock market, and so forth at the present time
[Wal97].25
Premises for practical inference:
1. states that an agent (“I” or “my”) has a particular goal;
2. states that an agent has a particular goal.
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20. Argumentation Schemes • AS and Dialogues
〈S0,S1,...,Sn〉 represents a sequence of states of affairs that can be or-
dered temporally from earlier to latter. A state of affairs is meant to be like a
statement, but one describing some event or occurrence that can be brought
about by an agent. It may be a human action, or it may be a natural event.
5
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 al-
ternatives?
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 ac-
count?
2.2 AS and Dialogues
Dialogue for practical reasoning: all moves (propose, prefer, justify) are coor-
dinated 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.10
2. Discussion of: (a) the governing question; (b) desirable goals; (c) any
constraints on the possible actions which may be considered; (d) per-
spectives by which proposals may be evaluated; and (e) any premises
(facts) relevant to this evaluation.
3. Suggesting of possible action-options appropriate to the governing ques-15
tion.
4. Commenting on proposals from various perspectives.
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21. Argumentation Schemes • AS and Dialogues
5. Revising of: (a) the governing question, (b) goals, (c) constraints, (d)
perspectives, and/or (e) action-options in the light of the comments pre-
sented; and the undertaking of any information-gathering or fact-checking
required for resolution.
6. Recommending an option for action, and acceptance or non-acceptance5
of this recommendation by each participant.
7. Confirming acceptance of a recommended option by each participant.
8. Closing of the deliberation dialogue.
Proposals are initially made at stage 3, and then evaluated at stages 4, 5
and 6.10
Especially at stage 5, much argumentation taking the form of practical
reasoning would seem to be involved.
As discussed in [Wal06], there are three dialectical adequacy conditions
for defining the speech act of making a proposal.
The Proponent’s Requirement (Condition 1). The proponent puts15
forward a statement that describes an action and says that both pro-
ponent and respondent (or the respondent group) should carry out this
action.
The proponent is committed to carrying out that action: the statement
has the logical form of the conclusion of a practical inference, and also20
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.
The Governing Question Requirement (Condition 3). The job of25
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 reasonableness of the action
in the statement into doubt, and to mount attacks (counter-arguments
and rebuttals) against it.30
Condition 3 relates to the global structure of the dialogue, whereas con-
ditions 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.
Speech acts [MP02], like making a proposal, are seen as types of moves in35
a dialogue that are governed by rules. Three basic characteristics 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.40
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22. Argumentation Schemes • AS and Dialogues
Preconditions
• At least two agents (proponent and opponent);
• A governing question;
• Set of statements (propositions);
• The proponent proposes the proposition to the respondent if and only if:5
1. there is a set of premises that the proponent is committed to, and
fit the premises of the argumentation scheme for practical reason-
ing;
2. the proponent is advocating these premises, that is, he is making
a claim that they are true or applicable in the case at issue;10
3. there is an inference from these premises fitting the argumenta-
tion 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 structure15
of the move of making a proposal.
The Goal Statement: We have a goal G.
The Means Statement: Bringing about p is necessary (or sufficient)
for us to bring about G.
Then the inference follows.20
The Proposal Statement: We should (practically ought to) bring about
p.
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23. Argumentation Schemes • AS and Dialogues
Proposal Statement in form of AS
Premises:
Goal Statement We have a goal G.
The Means State-
ment
Bringing about p is necessary (or sufficient)
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 propo-
nent should be open to answering doubts and objections corresponding to any5
one of the five critical questions for practical reasoning; as well as to counter-
proposals, and is in charge of giving reasons why her proposal 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 and to re-10
quests for justification.
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24. Chapter 3
A Semantic-Web View of
Argumentation
Acknowledgement
This handout include material from a number of collaborators including Chris5
Reed. An overview can also be find at [Bex+13].
3.1 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 3.1: Original AIF Ontology [Che+06; Rah+11]
3.2 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/10
AIF.owl
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25. 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 3.2: An argument network linking instances of argument and scheme
components
3.2.1 Representation of the argument described in Fig-
ure 3.2
___jobArg : PracticalReasoning_Inference
fulfils(___jobArg, PracticalReasoning_Scheme)
hasGoalPlan_Premise(___jobArg, ___jobArgGoalPlan)5
hasConclusion(___jobArg, ___jobArgConclusion)
hasGoal_Premise(___jobArg, ___jobArgGoal)
___jobArgConclusion : EncouragedAction_Statement
fulfils(___jobArgConclusion, EncouragedAction_Desc)
claimText (___jobArgConclusion "Therefore I need to bring about having10
a job")
___jobArgGoal : Goal_Statement
fulfils(___jobArgGoal, Goal_Desc)
claimText (___jobArgGoal "Bringing about being rich is my goal")
___jobArgGoalPlan : GoalPlan_Statement15
fulfils(___jobArgGoalPlan, GoalPlan_Desc)
claimText (___jobArgGoalPlan "In order to bring about being rich I need
to bring about having a job")
3.2.2 Relevant portion of the AIF ontology
EncouragedAction_Statement20
EncouragedAction_Statement Statement
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26. Semantic Web Argumentation • AIF-OWL
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 3.3: Examples of conflicts [Rah+11, Fig. 2]
GoalPlan_Statement
GoalPlan_Statement Statement
Goal_Statement
Goal_Statement Statement
I-node5
I-node ≡ Statement
I-node Node
I-node ¬ S-node
Inference
Inference ≡ RA-node10
Inference ∃ fulfils Inference_Scheme
Inference ≥ 1 hasPremise Statement
Inference Scheme_Application
Inference = hasConclusion (Scheme_Application Statement)
Inference_Scheme15
Inference_Scheme Scheme ≥
1 hasPremise_Desc Statement_Description = hasConclusion_Desc
(Scheme Statement_Description)
PracticalReasoning_Inference
PracticalReasoning_Inference ≡ Presumptive_Inference ∃ hasConclu-20
sion EncouragedAction_Statement ∃ hasGoalPlan_Premise GoalPlan_Statement ∃ has-
Goal_Premise Goal_Statement
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27. Semantic Web Argumentation • AIF-OWL
RA-node
RA-node ≡ Inference
RA-node S-node
S-node
S-node ≡ Scheme_Application5
S-node Node
S-node ¬ I-node
Scheme
Scheme Form
Scheme ¬ Statement_Description10
Scheme_Application
Scheme_Application ≡ S-node
Scheme_Application ∃ fulfils Scheme
Scheme_Application Thing
Scheme_Application ¬ Statement15
Statement
Statement ≡ NegStatement
Statement ≡ I-node
Statement Thing
Statement ∃ fulfils Statement_Description20
Statement ¬ Scheme_Application
Statement_Description
Statement_Description Form
Statement_Description ¬ Scheme
fulfils25
∃ fulfils Thing Node
hasConclusion_Desc
∃ hasConclusion_Desc Thing Inference_Scheme
hasGoalPlan_Premise
hasPremise30
hasGoal_Premise
hasPremise
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28. Semantic Web Argumentation • AIF-OWL
claimText
∃ claimText DatatypeLiteral Statement
∀ claimText DatatypeString
Individuals of EncouragedAction_Desc
EncouragedAction_Desc : Statement_Description5
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")10
Individuals of Goal_Desc
Goal_Desc : Statement_Description
formDescription (Goal_Desc "The goal is to bring about A")
Individuals of PracticalReasoning_Scheme
PracticalReasoning_Scheme : PresumptiveInference_Scheme15
hasPremise_Desc(PracticalReasoning_Scheme, Goal_Desc)
hasConclusion_Desc(PracticalReasoning_Scheme, EncouragedAction_Desc)
hasPremise_Desc(PracticalReasoning_Scheme, GoalPlan_Desc)
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