Handout: Argumentation in Artificial Intelligence: From Theory to Practice

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. Cardiff University, 2017 Page 1

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; Cardiff University, 2017 Page 2

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 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).

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 Cardiff University, 2017 Page 3

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 corresponding 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 corresponding 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 complete, grounded, preferred extensions and the complete, grounded, preferred labellings, respectively. Proposition 1. Given an an AF ∆ = Γ, L ab is a complete (grounded, preferred) 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 preferred labellings as LP R(∆), while LGR(∆) denotes the set including the grounded labelling. Cardiff University, 2017 Page 4

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 conditions 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 argumentation 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. ♠ Cardiff University, 2017 Page 5

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 decomposable 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. Cardiff University, 2017 Page 6

19. Chapter 2 Argumentation Schemes Argumentation schemes [WRM08] are reasoning patterns which generate arguments: • 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 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 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. Cardiff University, 2017 Page 7

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 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? 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) 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 governing ques-15 tion. 4. Commenting on proposals from various perspectives. Cardiff University, 2017 Page 8

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 proponent 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 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. 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 Cardiff University, 2017 Page 9

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 reasoning; 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 argumentation 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. Cardiff University, 2017 Page 10

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 proponent 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. Cardiff University, 2017 Page 11

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 Cardiff University, 2017 Page 12

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 Cardiff University, 2017 Page 13

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 Cardiff University, 2017 Page 14

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 Cardiff University, 2017 Page 15

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) Cardiff University, 2017 Page 16

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