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Abstract: Introduction to abstract argumentation and semantics, signatures and decomposability. Complexity of reasoning problems on an abstract argumentation framework and state-of-the-art solvers. Graphical interfaces to reasoning problems and natural language interfaces, with introduction on Natural Language Generation. Course held as part of The Second Summer School on Argumentation: Computational and Linguistic Perspectives September 2016 http://ssa2016.west.uni-koblenz.de/

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Abstract: Introduction to abstract argumentation and semantics, signatures and decomposability. Complexity of reasoning problems on an abstract argumentation framework and state-of-the-art solvers. Graphical interfaces to reasoning problems and natural language interfaces, with introduction on Natural Language Generation. Course held as part of The Second Summer School on Argumentation: Computational and Linguistic Perspectives September 2016 http://ssa2016.west.uni-koblenz.de/

- 1. Abstract Argumentation and Interfaces to Argumentative Reasoning Handouts Federico Cerutti September 2016
- 2. Contents Contents 1 1 Dung’s AF 3 1.1 Principles for Extension-based Semantics: [BG07] . . . . . 3 1.2 Acceptability of Arguments [PV02; BG09a] . . . . . . . . . . 4 1.3 (Some) Semantics [Dun95] . . . . . . . . . . . . . . . . . . . . 5 1.4 Labelling-Based Semantics Representation [Cam06] . . . . 6 1.5 Skepticism Relationships [BG09b] . . . . . . . . . . . . . . . 9 1.6 Signatures [Dun+14] . . . . . . . . . . . . . . . . . . . . . . . 9 1.7 Decomposability and Transparancy [Bar+14] . . . . . . . . 12 1.8 Extension-based I/O Characterisation [GLW16] . . . . . . . 13 2 Implementations 14 2.1 Ad Hoc Procedures . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Constraint Satisfaction Programming . . . . . . . . . . . . . 14 2.3 Answer Set Programming . . . . . . . . . . . . . . . . . . . . 15 2.4 Propositional Satisﬁability Problems . . . . . . . . . . . . . 15 2.5 Second-order Solver [BJT16] . . . . . . . . . . . . . . . . . . 23 2.6 Which One? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Ranking-Based Semantics 28 3.1 The Categoriser Semantics [BH01] . . . . . . . . . . . . . . . 28 3.2 Properties for Ranking-Based Semantics [Bon+16] . . . . . 28 4 Argumentation Schemes 33 4.1 An example: Walton et al. ’s Argumentation Schemes for Practical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 AS and Dialogues . . . . . . . . . . . . . . . . . . . . . . . . . 34 5 Semantic Web Argumentation 38 5.1 AIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.2 AIF-OWL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6 CISpaces 43 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.2 Intelligence Analysis . . . . . . . . . . . . . . . . . . . . . . . 43 6.3 Reasoning with Evidence . . . . . . . . . . . . . . . . . . . . . 46 6.4 Arguments for Sensemaking . . . . . . . . . . . . . . . . . . 46 6.5 Arguments for Provenance . . . . . . . . . . . . . . . . . . . . 48 Cardiff University, 2016 Page 1
- 3. 7 Natural Language Interfaces 50 7.1 Experiments with Humans: Scenarios [CTO14] . . . . . . . 50 7.2 Lessons From Argument Mining: [BR11] . . . . . . . . . . . 55 Bibliography 56 Cardiff University, 2016 Page 2
- 4. 1 Dung’s Argumentation Framework Acknowledgement This handout include material from a number of collaborators including Pietro Baroni, Massimiliano Giacomin, Thomas Linsbichler, and Stefan5 Woltran. Deﬁnition 1 ([Dun95]). A Dung argumentation framework AF is a pair 〈A ,→ 〉 where A is a set of arguments, and → is a binary relation on A i.e. →⊆ A ×A . ♠ An argumentation framework has an obvious representation as a di-10 rected graph where the nodes are arguments and the edges are drawn from attacking to attacked arguments. The set of attackers of an argument a1 will be denoted as a− 1 {a2 : a2 → a1}, the set of arguments attacked by a1 will be denoted as a+ 1 {a2 : a1 → a2}. We also extend these notations to sets of arguments, i.e. given15 E ⊆ A , E− {a2 | ∃a1 ∈ E,a2 → a1} and E+ {a2 | ∃a1 ∈ E,a1 → a2}. With a little abuse of notation we deﬁne S → a ≡ ∃a ∈ S : a → b. Simi- larly, b → S ≡ ∃a ∈ S : b → a. Given Γ = 〈A ,→〉 and Γ = 〈A ,→ 〉, Γ∪Γ = 〈A ∪A ,→ ∪ → 〉. 1.1 Principles for Extension-based Semantics:20 [BG07] Deﬁnition 2.
- 5. Given an argumentation framework AF = 〈A ,→ 〉, a set S ⊆ A is D-conﬂict-free, denoted as D-cf(S), if and only if a,b ∈ S such that a → b. A semantics σ satisﬁes the D-conﬂict-free principle if and only if ∀AF,∀E ∈ Eσ(AF) E is D-conﬂict-free . ♠25 Deﬁnition 3. Given an argumentation framework AF = 〈A ,→ 〉, an ar- gument a ∈ A is D-acceptable w.r.t. a set S ⊆ A if and only if ∀b ∈ A b → a ⇒ S → b. The function FAF : 2A → 2A which, given a set S ⊆ A , returns the set of the D-acceptable arguments w.r.t. S, is called the D-characteristic30 function of AF. ♠ Cardiff University, 2016 Page 3
- 6. Dung’s AF • Acceptability of Arguments [PV02; BG09a] Deﬁnition 4. Given an argumentation framework AF = 〈A ,→ 〉, a set S ⊆ A is D-admissible (S ∈ AS (AF)) if and only if D-cf(S) and ∀a ∈ S a is D-acceptable w.r.t. S. The set of all the D-admissible sets of AF is denoted as AS (AF). ♠ Dσ = {AF|Eσ(AF) = }5 Deﬁnition 5.
- 7. A semantics σ satisﬁes the D-admissibility principle if and only if ∀AF ∈ Dσ Eσ(AF) ⊆ AS (AF), namely ∀E ∈ Eσ(AF) it holds that: a ∈ E ⇒ (∀b ∈ A ,b → a ⇒ E → b). ♠ Deﬁnition 6. Given an argumentation framework AF = 〈A ,→ 〉, a ∈ A and S ⊆ A , we say that a is D-strongly-defended by S (denoted as D-sd(a,S)) iff ∀b ∈ A , b → a, ∃c ∈ S {a} : c → b and D-sd(c,S {a}). ♠ Deﬁnition 7.
- 8. A semantics σ satisﬁes the D-strongly admissibility prin- ciple if and only if ∀AF ∈ Dσ, ∀E ∈ Eσ(AF) it holds that a ∈ E ⊃ D-sd(a,E) ♠ Deﬁnition 8.
- 9. 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.
- 10. A set of extensions E is D-I-maximal if and only if ∀E1,E2 ∈ E , if E1 ⊆ E2 then E1 = E2. A semantics σ satisﬁes the D-I-maximality10 principle if and only if ∀AF ∈ Dσ Eσ(AF) is D-I-maximal. ♠ Deﬁnition 10. Given an argumentation framework AF = 〈A ,→ 〉, a non- empty set S ⊆ A is D-unattacked if and only if ∃a ∈ (A S) : a → S. The set of D-unattacked sets of AF is denoted as US (AF). ♠ Deﬁnition 11. Let AF = 〈A ,→ 〉 be an argumentation framework. The15 restriction of AF to S ⊆ A is the argumentation framework AF↓S = 〈S,→ ∩(S × S)〉. ♠ Deﬁnition 12.
- 11. A semantics σ satisﬁes the D-directionality principle if and only if ∀AF = 〈A ,→ 〉,∀S ∈ US (AF),AE σ(AF,S) = Eσ(AF↓S), where AE σ(AF,S) {(E ∩ S) | E ∈ Eσ(AF)} ⊆ 2S . ♠20 1.2 Acceptability of Arguments [PV02; BG09a] Deﬁnition 13. Given a semantics σ and an argumentation framework 〈A ,→ 〉, an argument AF ∈ Dσ is: • skeptically justiﬁed iff ∀E ∈ Eσ(AF), a ∈ S; • credulously justiﬁed iff ∃E ∈ Eσ(AF), a ∈ S. ♠25 Cardiff University, 2016 Page 4
- 12. Dung’s AF • (Some) Semantics [Dun95] Deﬁnition 14. Given a semantics σ and an argumentation framework 〈A ,→ 〉, an argument AF ∈ Dσ is: • justiﬁed iff it is skeptically justiﬁed; • defensible iff it is credulously justiﬁed but not skeptically justiﬁed; • overruled iff it is not credulously justiﬁed. ♠5 1.3 (Some) Semantics [Dun95] Lemma 1 (Dung’s Fundamental Lemma, [Dun95, Lemma 10]). Given an argumentation framework AF = 〈A ,→ 〉, let S ⊆ A be a D-admissible set of arguments, and a,b be arguments which are acceptable with respect to S. Then:10 1. S = S ∪{a} is D-admissible; and 2. b is D-acceptable with respect to S . ♣ Theorem 1 ([Dun95, Theorem 11]). Given an argumentation framework AF = 〈A ,→ 〉, the set of all D-admissible sets of 〈A ,→ 〉 form a complete partial order with respect to set inclusion. ♣15 Deﬁnition 15 (Complete Extension).
- 13. Given an argumentation frame- work AF = 〈A ,→ 〉, S ⊆ A is a D-complete extension iff S is D-conﬂict-free and S = FAF(S). C O denotes the complete semantics. ♠ Deﬁnition 16 (Grounded Extension).
- 14. Given an argumentation frame- work AF = 〈A ,→ 〉. The grounded extension of AF is the least complete20 extension of AF. GR denotes the grounded semantics. ♠ Deﬁnition 17 (Preferred Extension).
- 15. Given an argumentation frame- work AF = 〈A ,→ 〉. A preferred extension of AF is a maximal (w.r.t. set inclusion) complete extension of AF. P R denotes the preferred seman- tics. ♠25 Deﬁnition 18. Given an argumentation framework AF = 〈A ,→ 〉 and S ⊆ A , S+ {a ∈ A | ∃b ∈ S ∧ b → a}. ♠ Deﬁnition 19 (Stable Extension).
- 16. Given an argumentation framework AF = 〈A ,→ 〉. S ⊆ A is a stable extension of AF iff S is a preferred exten- sion and S+ = A S. S T denotes the stable semantics. ♠30 Cardiff University, 2016 Page 5
- 17. Dung’s AF • Labelling-Based Semantics Representation [Cam06] C O GR P R S T D-conﬂict-free Yes Yes Yes Yes D-admissibility Yes Yes Yes Yes D-strongly admissibility No Yes No No D-reinstatement Yes Yes Yes Yes D-I-maximality No Yes Yes Yes D-directionality Yes Yes Yes No Table 1.1: Satisfaction of general properties by argumentation semantics [BG07; BCG11] S T P R C O GR Figure 1.1: Relationships among argumentation semantics 1.4 Labelling-Based Semantics Representation [Cam06] Deﬁnition 20. Let Γ = Γ be an argumentation framework. A labelling L ab ∈ L(Γ) is a complete labelling of Γ iff it satisﬁes the following condi- tions for any a1 ∈ A :5 • L ab(a1) = in ⇔ ∀a2 ∈ a− 1 L ab(a2) = out; • L ab(a1) = out ⇔ ∃a2 ∈ a− 1 : L ab(a2) = in. ♠ The grounded and preferred labelling can then be deﬁned on the basis of complete labellings. Deﬁnition 21. Let Γ = Γ be an argumentation framework. A labelling10 L ab ∈ L(Γ) is the grounded labelling of Γ if it is the complete labelling of Γ minimizing the set of arguments labelled in, and it is a preferred labelling of Γ if it is a complete labelling of Γ maximizing the set of arguments labelled in. ♠ In order to show the connection between extensions and labellings, let15 us recall the deﬁnition of the function Ext2Lab, returning the labelling corresponding to a D-conﬂict-free set of arguments S. Deﬁnition 22. Given an AF Γ = Γ and a D-conﬂict-free set S ⊆ A , the cor- responding labelling Ext2Lab(S) is deﬁned as Ext2Lab(S) ≡ L ab, where • L ab(a1) = in ⇔ a1 ∈ S20 • L ab(a1) = out ⇔ ∃ a2 ∈ S s.t. a2 → a1 Cardiff University, 2016 Page 6
- 18. Dung’s AF • Labelling-Based Semantics Representation [Cam06] σ = C O σ = GR σ = P R σ = S T EXISTSσ trivial trivial trivial NP-c CAσ NP-c polynomial NP-c NP-c SAσ polynomial polynomial Π p 2 -c coNP-c VERσ polynomial polynomial coNP-c polynomial NEσ NP-c polynomial NP-c NP-c Table 1.2: Complexity of decision problems by argumentation semantics [DW09] • L ab(a1) = undec ⇔ a1 ∉ S ∧ a2 ∈ S s.t. a2 → a1 ♠ [Cam06] shows that there is a bijective correspondence between the complete, grounded, preferred extensions and the complete, grounded, preferred labellings, respectively. Proposition 1. Given an an AF Γ = Γ, L ab is a complete (grounded, pre-5 ferred) labelling of Γ if and only if there is a complete (grounded, preferred) extension S of Γ such that L ab = Ext2Lab(S). ♣ The set of complete labellings of Γ is denoted as LC O (Γ), the set of preferred labellings as LP R(Γ), while LGR(Γ) denotes the set including the grounded labelling.10 Remark 1.
- 19. To exercise yourself, try Arg Teach [DS14] at http://www-argteach. doc.ic.ac.uk/ Cardiff University, 2016 Page 7
- 20. Dung’s AF • Labelling-Based Semantics Representation [Cam06] Cardiff University, 2016 Page 8
- 21. Dung’s AF • Skepticism Relationships [BG09b] GR C O P R GR C O P RS T Figure 1.2: S ⊕ relation for any argumentation framework (left) and for argumentation framework where stable extensions exist (right). 1.5 Skepticism Relationships [BG09b] E1 E E2 denotes that E1 is at least as skeptical as E2. Deﬁnition 23. Let E be a skepticism relation between sets of exten- sions. The skepticism relation between argumentation semantics S is such that for any argumentation semantics σ1 and σ2, σ1 S σ2 iff ∀AF ∈5 Dσ1 ∩Dσ2 , EAF(σ1) E EAF(σ2). ♠ Deﬁnition 24. Given two sets of extensions E1 and E2 of an argumenta- tion framework AF: • E1 E ∩+ E2 iff ∀E2 ∈ E2, ∃E1 ∈ E1: E1 ⊆ E2; • E1 E ∪+ E2 iff ∀E1 ∈ E1, ∃E2 ∈ E2: E1 ⊆ E2. ♠10 Lemma 2. Given two argumentation semantics σ1 and σ2, if for any argumentation framework AF EAF(σ1) ⊆ EAF(σ2), then σ1 E ∩+ σ2 and σ1 E ∪+ σ2 (σ1 E ⊕ σ2). ♣ 1.6 Signatures [Dun+14] Let A be a countably inﬁnite domain of arguments, and15 AFA = {〈A ,→〉 | A ⊆ A,→⊆ A ×A }. Deﬁnition 25. The signature Σσ of a semantics σ is deﬁned as Σσ = {σ(F) | F ∈ AFA} (i.e. the collection of all possible sets of extensions an AF can possess under a semantics). ♠20 Given S ⊆ 2A , ArgsS = S∈S S, PairsS = {〈a,b〉 | ∃S ∈ S s.t. {a,b} ⊆ S}. S is called an extension-set if ArgsS is ﬁnite. Deﬁnition 26. Let S ⊆ 2A . S is incomparable if ∀S,S ∈ S, S ⊆ S implies S = S . ♠ Cardiff University, 2016 Page 9
- 22. Dung’s AF • Signatures [Dun+14] Deﬁnition 27. An extension-set S ⊆ 2A is tight if ∀S ∈ S and a ∈ ArgsS it holds that if S ∪ {a} ∈ S then there exists an b ∈ S such that 〈a,b〉 ∈ PairsS. ♠ Deﬁnition 28. S ⊆⊆ 2A is adm-closed if for each A,B ∈ S the following holds: if 〈a,b〉 ∈ PairsS for each a,b ∈ A ∪B, then also A ∪B ∈ S. ♠5 Proposition 2. For each F ∈ AFA: • S T (F) is incomparable and tight; • P R(F) is non-empty, incomparable and adm-closed. ♣ Theorem 2. The signatures for S T and P R are: • ΣS T = {S | S is incomparable and tight};10 • ΣP R = {S = | S is incomparable and adm-closed}. ♣ Cardiff University, 2016 Page 10
- 23. Dung’s AF • Signatures [Dun+14] Consider S = { { a,d, e }, { b, c, e }, { a,b,d } } Cardiff University, 2016 Page 11
- 24. Dung’s AF • Decomposability and Transparancy [Bar+14] 1.7 Decomposability and Transparancy [Bar+14] Deﬁnition 29. Given an argumentation framework AF = (A ,→), a labelling-based semantics σ associates with AF a subset of L(AF), de- noted as Lσ(AF). ♠ Deﬁnition 30. Given AF = (A ,→) and a set Args ⊆ A , the input of Args,5 denoted as Argsinp, is the set {B ∈ A Args | ∃A ∈ Args,(B, A) ∈→}, the con- ditioning relation of Args, denoted as ArgsR , is deﬁned as → ∩(Argsinp × Args). ♠ Deﬁnition 31. An argumentation framework with input is a tuple (AF,I ,LI ,RI ), including an argumentation framework AF = (A ,→), a10 set of arguments I such that I ∩A = , a labelling LI ∈ LI and a rela- tion RI ⊆ I × A . A local function assigns to any argumentation frame- work with input a (possibly empty) set of labellings of AF, i.e. F(AF,I ,LI ,RI ) ∈ 2L(AF) . ♠ Deﬁnition 32. Given an argumentation framework with input15 (AF,I ,LI ,RI ), the standard argumentation framework w.r.t. (AF,I ,LI ,RI ) is deﬁned as AF = (A ∪ I ,→ ∪R I ), where I = I ∪ {A | A ∈ out(LI )} and R I = RI ∪ {(A , A) | A ∈ out(LI )} ∪ {(A, A) | A ∈ undec(LI )}. ♠ Deﬁnition 33. Given a semantics σ, the canonical local function of σ20 (also called local function of σ) is deﬁned as Fσ(AF,I ,LI ,RI ) = {Lab↓A | Lab ∈ Lσ(AF )}, where AF = (A ,→) and AF is the standard argumenta- tion framework w.r.t. (AF,I ,LI ,RI ). ♠ Deﬁnition 34. A semantics σ is complete-compatible iff the following conditions hold:25 1. For any argumentation framework AF = (A ,→), every labelling L ∈ Lσ(AF) satisﬁes the following conditions: • if A ∈ A is initial, then L(A) = in • if B ∈ A and there is an initial argument A which attacks B, then L(B) = out30 • if C ∈ A is self-defeating, and there are no attackers of C be- sides C itself, then L(C) = undec 2. for any set of arguments I and any labelling LI ∈ LI , the ar- gumentation framework AF = (I ,→ ), where I = I ∪ {A | A ∈ out(LI )} and → = {(A , A) | A ∈ out(LI )}∪{(A, A) | A ∈ undec(LI )},35 admits a (unique) labelling, i.e. |Lσ(AF )| = 1. ♠ Cardiff University, 2016 Page 12
- 25. Dung’s AF • Extension-based I/O Characterisation [GLW16] Deﬁnition 35. A semantics σ is fully decomposable (or simply decom- posable) iff there is a local function F such that for every argumenta- tion framework AF = (A ,→) and every partition P = {P1,...Pn} of A , Lσ(AF) = U (P , AF,F) where U (P , AF,F) {LP1 ∪ ... ∪ LPn | LPi ∈ F(AF↓Pi ,Pi inp,( j=1···n,j=i LPj )↓ Pi inp,Pi R )}. ♠5 Deﬁnition 36. A complete-compatible semantics σ is top-down decom- posable iff for any argumentation framework AF = (A ,→) and any parti- tion P = {P1,...Pn} of A , it holds that Lσ(AF) ⊆ U (P , AF,Fσ). ♠ Deﬁnition 37. A complete-compatible semantics σ is bottom-up decom- posable iff for any argumentation framework AF = (A ,→) and any parti-10 tion P = {P1,...Pn} of A , it holds that Lσ(AF) ⊇ U (P , AF,Fσ). ♠ C O S T GR P R Full decomposability Yes Yes No No Top-down decomposability Yes Yes Yes Yes Bottom-up decomposability Yes Yes No No Table 1.3: Decomposability properties of argumentation semantics. 1.8 Extension-based I/O Characterisation [GLW16] Deﬁnition 38. Given input arguments I and output arguments O with I ∩O = , an I/O-gadget is an AF F = (A,R) such that I,O ⊆ A and I− F = . ♠15 Deﬁnition 39. Given an I/O-gadget F = (A,R) the injection of J ⊆ I to F is the AF (F, J) = (A ∪{z},R ∪{(z, i) | i ∈ (I J)}). ♠ Deﬁnition 40. An I/O-speciﬁcation consists of two sets I,O ⊆ A and a total function f : 2I → 22O . ♠ Deﬁnition 41. The I/O-gadget F satisﬁes I/O-speciﬁcation f under se-20 mantics σ iff ∀J ⊆ I : σ( (F, J))|O = f(J). ♠ Theorem 3. An I/O-speciﬁcation f is satisﬁable under σ iff S T : P R: ∀J ⊆ I : |f(J)| ≥ 1 C O: ∀J ⊆ I : |f(J)| ≥ 1∧ f(J) ∈ f(J) GR: ∀J ⊆ I : |f(J)| = 1 ♣ Cardiff University, 2016 Page 13
- 26. 2 Implementations Acknowledgement This handout include material from a number of collaborators including Massimiliano Giacomin, Mauro Vallati, and Stefan Woltran. Comprehensive survey recently published in [Cha+15].5 2.1 Ad Hoc Procedures NAD-Alg [NDA12; NAD14] 2.2 Constraint Satisfaction Programming A Constraint Satisfaction Problem (CSP) P [BS12; RBW08] is a triple P = 〈X,D,C〉 such that:10 • X = 〈x1,...,xn〉 is a tuple of variables; • D = 〈D1,...,Dn〉 a tuple of domains such that ∀i,xi ∈ Di; • C = 〈C1,...,Ct〉 is a tuple of constraints, where ∀j,Cj = 〈RSj ,Sj〉, Sj ⊆ {xi|xi is a variable}, RSj ⊆ SD j × SD j where SD j = {Di|Di is a domain, and xi ∈ Sj}.15 A solution to the CSP P is A = 〈a1,...,an〉 where ∀i,ai ∈ Di and ∀j,RSj holds on the projection of A onto the scope Sj. If the set of solutions is empty, the CSP is unsatisﬁable. Cardiff University, 2016 Page 14
- 27. Implementations • Answer Set Programming CONArg2 [BS12] In [BS12], the authors propose a mapping from AFs to CSPs. Given an AF Γ, they ﬁrst create a variable for each argument whose domain is always {0,1} — ∀ai ∈ A ,∃xi ∈ X such that Di = {0,1}. Subsequently, they describe constraints associated to different deﬁ-5 nitions of Dung’s argumentation framework: for instance {a1,a2} ⊆ A is D-conﬂict-free iff ¬(x1 = 1∧ x2 = 1). 2.3 Answer Set Programming Answer Set Programming (ASP) [Fab13] is a declarative problem solving paradigm. In ASP, representation is done using a rule-based language,10 while reasoning is performed using implementations of general-purpose algorithms, referred to as ASP solvers. AspartixM [EGW10; Dvo+11] AspartixM [Dvo+11] expresses argumentation semantics in Answer Set Programming (ASP): a single program is used to encode a particular ar-15 gumentation semantics, and the instance of an argumentation framework is given as an input database. Tests for subset-maximality exploit the metasp optimisation frontend for the ASP-package gringo/claspD. Given an AF Γ, Aspartix encodes the requirements for a “semantics” (e.g. the D-conﬂict-free requirements) in an ASP program whose database20 considers: {arg(a) | a ∈ A }∪{defeat(a1,a2) | 〈a1,a2〉 ∈→} The following program fragment is thus used to check the D-conﬂict- freeness [Dvo+11]: πcf = { in(X) ← not out(X),arg(X); out(X) ← not in(X),arg(X); ← in(X),in(Y ),defeat(X,Y )}. 25 πS T = { in(X) ← not out(X),arg(X); out(X) ← not in(X),arg(X); ← in(X),in(Y ),defeat(X,Y ); defeated(X) ← in(Y ),defeat(Y , X); ← out(X),not defeated(X)}. 2.4 Propositional Satisﬁability Problems In the propositional satisﬁability problem (SAT) the goal is to determine whether a given Boolean formula is satisﬁable. A variable assignment that satisﬁes a formula is a solution.30 Cardiff University, 2016 Page 15
- 28. Implementations • Propositional Satisﬁability Problems In SAT, formulae are commonly expressed in Conjunctive Normal Form (CNF). A formula in CNF is a conjunction of clauses, where clauses are disjunctions of literals, and a literal is either positive (a variable) or neg- ative (the negation of a variable). If at least one of the literals in a clause is true, then the clause is satisﬁed, and if all clauses in the formula are5 satisﬁed then the formula is satisﬁed and a solution has been found. PrefSAT [Cer+14b] Requirements for complete labelling as a CNF [Cer+14b]: for each argu- ment ai ∈ A , three propositional variables are considered: Ii (which is true iff L ab(ai) = in), Oi (which is true iff L ab(ai) = out), Ui (which is10 true iff L ab(ai) = undec). Given |A | = k and φ : {1,...,k} → A . i∈{1,...,k} (Ii ∨Oi ∨Ui)∧(¬Ii ∨¬Oi)∧(¬Ii ∨¬Ui)∧(¬Oi ∨¬Ui) (2.1) {i|φ(i)−= } Ii (2.2) {i|φ(i)−= } Ii ∨ {j|φ(j)→φ(i)} (¬Oj) (2.3) {i|φ(i)−= } {j|φ(j)→φ(i)} ¬Ii ∨Oj (2.4)15 {i|φ(i)−= } {j|φ(j)→φ(i)} ¬I j ∨Oi (2.5) {i|φ(i)−= } ¬Oi ∨ {j|φ(j)→φ(i)} I j (2.6) {i|φ(i)−= } {k|φ(k)→φ(i)} Ui ∨¬Uk ∨ {j|φ(j)→φ(i)} I j (2.7) {i|φ(i)−= } {j|φ(j)→φ(i)} (¬Ui ∨¬I j) ∧ ¬Ui ∨ {j|φ(j)→φ(i)} Uj (2.8) i∈{1,...k} Ii (2.9)20 Cardiff University, 2016 Page 16
- 29. Implementations • Propositional Satisﬁability Problems As noticed in [Cer+14b], the conjunction of the above formulae is re- dundant. However, the non-redundant CNFs are not equivalent from an empirical evaluation [Cer+14b]: the overall performance is signiﬁcantly affected by the chosen conﬁguration pair CNF encoding–SAT solver. Cardiff University, 2016 Page 17
- 30. Implementations • Propositional Satisﬁability Problems Algorithm 1 Enumerating the D-preferred extensions of an AF PrefSAT(Γ) 1: Input: Γ = Γ 2: Output: Ep ⊆ 2A 3: Ep := 4: cnf := ΠΓ 5: repeat 6: cnf df := cnf 7: pref cand := 8: repeat 9: lastcompf ound := SatS(cnf df ) 10: if lastcompf ound ! = ε then 11: pref cand := lastcompf ound 12: for a1 ∈ I-ARGS(lastcompf ound) do 13: cnf df := cnf df ∧ Iφ−1(a1) 14: end for 15: remaining := F ALSE 16: for a1 ∈ A I-ARGS(lastcompf ound) do 17: remaining := remaining ∨ Iφ−1(a1) 18: end for 19: cnf df := cnf df ∧ remaining 20: end if 21: until (lastcompf ound ! = ε∧I-ARGS(lastcompf ound) ! = A ) 22: if pref cand ! = then 23: Ep := Ep ∪{I-ARGS(pref cand)} 24: oppsolution := F ALSE 25: for a1 ∈ A I-ARGS(pref cand) do 26: oppsolution := oppsolution∨ Iφ−1(a1) 27: end for 28: cnf := cnf ∧ oppsolution 29: end if 30: until (pref cand ! = ) 31: if Ep = then 32: Ep = { } 33: end if 34: return Ep Cardiff University, 2016 Page 18
- 31. Implementations • Propositional Satisﬁability Problems Parallel-SCCp [Cer+14a; Cer+15] Based on the SCC-Recursiveness Schema [BGG05]. ab ef cdgh Cardiff University, 2016 Page 19
- 32. Implementations • Propositional Satisﬁability Problems Algorithm 1 Computing D-preferred labellings of an AF P-PREF(Γ) 1: Input: Γ = Γ 2: Output: Ep ∈ 2L(Γ) 3: return P-SCC-REC(Γ,A ) Algorithm 2 Greedy computation of base cases GREEDY(L,C) 1: Input: L = (L1 ,...,Ln := {Sn 1 ,...,Sn h }),C ⊆ A 2: Output: M = {...,(Si,Bi),...} 3: M := 4: for S ∈ n i=1 Li do in parallel 5: B := B-PR(Γ↓S,S ∩C) 6: M = M ∪{(S,B)} 7: end for 8: return M BOUNDCOND(Γ,Si,L ab) returns (O, I) where O = {a1 ∈ Si | ∃a2 ∈ S ∩ a− 1 : L ab(a2) = in} and I = {a1 ∈ Si | ∀ a2 ∈ S ∩ a− 1 ,L ab(a2) = out}, with S ≡ S1 ∪...∪ Si−1. Cardiff University, 2016 Page 20
- 33. Implementations • Propositional Satisﬁability Problems Algorithm 3 Determining the D-grounded labelling of an AF in a set C GROUNDED(Γ,C) 1: Input: Γ = Γ, C ⊆ A 2: Output: (L ab,U) : U ⊆ A ,L ab ∈ LA U 3: L ab := 4: U := A 5: repeat 6: initial f ound := ⊥ 7: for a1 ∈ C do 8: if {a2 ∈ U | a2 → a1} = then 9: initial f ound := 10: L ab := L ab ∪{(a1,in)} 11: U := U a1 12: C := C a1 13: for a2 ∈ (U ∩a+ 1 ) do 14: L ab := L ab ∪{(a2,out)} 15: U := U a2 16: C := C a2 17: end for 18: end if 19: end for 20: until (initial f ound) 21: return(L ab,U) Cardiff University, 2016 Page 21
- 34. Implementations • Propositional Satisﬁability Problems Algorithm 4 Computing D-preferred labellings of an AF in C P-SCC-REC(Γ,C) 1: Input: Γ = Γ, C ⊆ A 2: Output: Ep ∈ 2L(Γ) 3: (L ab,U) = GROUNDED(Γ,C) 4: Ep := {L ab} 5: Γ = Γ↓U 6: L:= (L1 := {S1 1,...,S1 k },...,Ln := {Sn 1 ,...,Sn h }) = SCCS-LIST(Γ) 7: M := {...,(Si,Bi),...} = GREEDY(L,C) 8: for l ∈ {1,...,n} do 9: El := {E S1 l := (),...,E Sk l := ()} 10: for S ∈ Ll do in parallel 11: for L ab ∈ Ep do in parallel 12: (O, I) := L-COND(Γ,S,Ll ,L ab) 13: if I = then 14: ES l [L ab] ={{(a1,out) | a1 ∈ O} ∪{(a1,undec) | a1 ∈ S O}} 15: else 16: if I = S then 17: ES l [L ab] = B where (S,B) ∈ M 18: else 19: if O = then 20: ES l [L ab] = B-PR(Γ↓S, I ∩C) 21: else 22: ES l [L ab]={{(a1,out) | a1 ∈ O}} 23: ES l [L ab] = ES l [L ab]⊗P-SCC-REC(Γ↓SO, I ∩C) 24: end if 25: end if 26: end if 27: end for 28: end for 29: for S ∈ Ll do 30: Ep := 31: for L ab ∈ Ep do in parallel 32: Ep = Ep ∪({L ab}⊗ ES l [L ab]) 33: end for 34: Ep := Ep 35: end for 36: end for 37: return Ep Cardiff University, 2016 Page 22
- 35. Implementations • Second-order Solver [BJT16] 2.5 Second-order Solver [BJT16] http://research.ics.aalto.fi/software/sat/sat-to-sat/so2grounder. shtml Given a representation of an argumentation framework such as: • a(X) holds iff X is an argument;5 • r(X,Y ) holds iff X attacks Y ; then: • TCF = { N,M | r(N,M) ∧ s(N) ∧ s(M).} • TAD = ∀N | att(N) ⇐⇒ ( a(N) ∧ ∃M | r(M,N) ∧ s(M) ). ∀N | def (N) ⇐⇒ ( a(N) ∧ ∀M | r(M,N) =⇒ att(M) ). • TFP = {TAD. ∀N | s(N) ⇐⇒ def (N).}10 • TGR = TFP. s ,att ,def : TFP[s/s ,def /def ,att/att ] ∧ ( ∀N | s (N) =⇒ s(N) ) ∧ ( ∃N | s(N)∧¬s (N) ) • TST = {TAD. ∀N | a(N) =⇒ ( s(N) ⇐⇒ ¬att(N) ).} • TCO = {TFP. TCF.} • TPR = TCO. s ,att, ,def : TCO[s/s ,def /def ,att/att ] ∧ ( ∀N | s(N) =⇒ s (N) ) ∧ ∃N | s (N) ∧ ¬s(N). The unary predicate s describes the extensions in the various seman-15 tics. 2.6 Which One? We need to be smart Holger H. Hoos, Invited Keynote Talk at ECAI2014 Features for AFs [VCG14; CGV14]20 Directed Graph (26 features) Cardiff University, 2016 Page 23
- 36. Implementations • Which One? Structure: # vertices ( |A | ) # edges ( | → | ) # vertices / #edges ( |A |/| → | ) # edges / #vertices ( | → |/|A | ) density average Degree: stdev attackers max min # average stdev max SCCs: min Structure: # self-def # unattacked ﬂow hierarchy Eulerian aperiodic CPU-time: . . . Cardiff University, 2016 Page 24
- 37. Implementations • Which One? Undirected Graph (24 features) Structure: # edges # vertices / #edges # edges / #vertices density Degree: average stdev max min SCCs: # average stdev max min Structure: Transitivity 3-cycles: # average stdev max min CPU-time: . . . Average CPU-time, stdev, needed for extracting the features Direct Graph Features (DG) Class CPU-Time # feat Mean stdDev Graph Size 0.001 0.009 5 Degree 0.003 0.009 4 SCC 0.046 0.036 5 Structure 2.304 2.868 5 Undirect Graph Features (UG) Class CPU-Time # feat Mean stDev Graph Size 0.001 0.003 4 Degree 0.002 0.004 4 SCC 0.011 0.009 5 Structure 0.799 0.684 1 Triangles 0.787 0.671 5 5 Best Features for Runtime Prediction [CGV14] Determined by a greedy forward search based on the Correlation-based Feature Selection (CFS) attribute evaluator. Cardiff University, 2016 Page 25
- 38. Implementations • Which One? Solver B1 B2 B3 AspartixM num. arguments density (DG) size max. SCC PrefSAT density (DG) num. SCCs aperiodicity NAD-Alg density (DG) CPU-time density CPU-time Eulerian SSCp density (DG) num. SCCs size max SCC Predicting the (log)Runtime [CGV14] RSME of Regression (Lower is better) B1 B2 B3 DG UG SCC All AspartixM 0.66 0.49 0.49 0.48 0.49 0.52 0.48 PrefSAT 1.39 0.93 0.93 0.89 0.92 0.94 0.89 NAD-Alg 1.48 1.47 1.47 0.77 0.57 1.61 0.55 SSCp 1.36 0.80 0.78 0.75 0.75 0.79 0.74 Log runtime is deﬁned as n i=1 log10( ti )−log10( yi ) 2 n 5 Best Features for Classiﬁcation [CGV14] Determined by a greedy forward search based on the Correlation-based Feature Selection (CFS) attribute evaluator. C-B1 C-B2 C-B3 num. arguments density (DG) min attackers Classiﬁcation [CGV14]10 Classiﬁcation (Higher is better) C −B1 C-B2 C-B3 DG UG SCC All Accuracy 48.5% 70.1% 69.9% 78.9% 79.0% 55.3% 79.5% Prec. AspartixM 35.0% 64.6% 63.7% 74.5% 74.9% 42.2% 76.1% Prec. PrefSAT 53.7% 67.8% 68.1% 79.6% 80.5% 60.4% 80.1% Prec. NAD-Alg 26.5% 69.2% 69.0% 81.7% 85.1% 35.3% 86.0% Prec. SSCp 54.3% 73.0% 72.7% 76.6% 76.8% 57.8% 77.2% Selecting the Best Algorithm [CGV14] Metric: Fastest (max. 1007) AspartixM 106 NAD-Alg 170 PrefSAT 278 SSCp 453 EPMs Regression 755 EPMs Classiﬁcation 788 Cardiff University, 2016 Page 26
- 39. Implementations • Which One? Metric: IPC (max. 1007) NAD-Alg 210.1 AspartixM 288.3 PrefSAT 546.7 SSCp 662.4 EPMs Regression 887.7 EPMs Classiﬁcation 928.1 IPC score1 : for each AF, each system gets a score of T∗ /T, where T is its execution time and T∗ the best execution time among the compared systems, or a score of 0 if it fails in that case. Runtimes below 0.01 seconds get by default the maximal score of 1. The IPC score considers, at the5 same time, the runtimes and the solved instances 1 http://ipc.informatik.uni-freiburg.de/ . Cardiff University, 2016 Page 27
- 40. 3 Ranking-Based Semantics 3.1 The Categoriser Semantics [BH01] Deﬁnition 42 ([BH01]). Let Γ = 〈A ,→〉 be an argumentation framework. The categoriser function Cat : A →]0,1] is deﬁned as: Cat(a1) = 1 if a− 1 = 1 1+ a2∈a− 1 Cat(a2) otherwise 5 ♠ 3.2 Properties for Ranking-Based Semantics [Bon+16] Preliminary notions Deﬁnition 43. Let Γ = 〈A ,→〉 and a1,a2 ∈ A . A path from a2 to a1,10 noted P(a2,a1) is a sequence s = 〈b0,...,bn〉 of arguments such as b0 = a1, bn = a2, and ∀i < n,〈bi+1,bi〉 ∈ A . We denote by lP = n the length of P. A defender (resp. attacker) of a1 is an argument situated at the begin- ning of an even-length (resp. odd-length) path. We denote the multiset of defenders and attackers of a1 by R+ n {a2 | ∃P(a2,a1) with lP ∈ 2N} and15 R− n = {a2 | ∃P(a2,a1) with lP ∈ 2N + 1} respectively. The direct attack- ers of a1 are arguments in R− 1 (a1) = a− 1 . An argument a1 is defended if R+ 2 (a1) = {a− 1 }− = . A defence root (resp. attack root) is a non-attacked defender (resp. attacker). We denote the mulitset of defence roots and attacks roots of a120 by BR+ n (a1) = {a2 ∈ R+ n (a1) | a− 2 = } and BR− n (a1) = {a2 ∈ R− n (a1) | a− 2 = } respectively. A path from a2 to a1 is a defence branch (resp. attack branch) if a2 is a defence (resp. attack) root of a1. Let us note BR+ (a1) = n BR+ n (a1) and BR− (a1) = n BR− n (a1). ♠ Deﬁnition 44. A ranking-based semantics σ associates to any argumen-25 tation framework Γ = 〈A ,→〉 is a ranking σ Γ on A , where σ Γ is a preorder (a reﬂexive and transitive relation) on A . a1 σ Γ a2 means that a1 is at least as acceptable as a2. a1 σ Γ a2 iff a1 σ Γ a2 and a2 σ Γ a1. ♠ Deﬁnition 45. A lexicographical order between two vectors of real num- ber V = 〈V1,...,Vn〉 and V = 〈V1,...,Vn〉, is deﬁned as V lex V iff ∃i ≤ n30 s.t. Vi ≥ Vi and ∀j < i, Vj = Vj . ♠ Cardiff University, 2016 Page 28
- 41. Ranking-Based Semantics • Properties for Ranking- Based Semantics [Bon+16] Deﬁnition 46. An isomorphism γ between two argumentation frame- works Γ = 〈A ,→〉 and Γ = 〈A ,→ 〉 is a bijective function γ : A → A such that ∀a24,a25 ∈ A , 〈a24,a25〉 ∈→ iff 〈γ(a24),γ(a25)〉 ∈→ . With a slight abuse of notation, we will note Γ = γ(Γ). ♠ Deﬁnition 47 ([AB13]). Let ≥S be a ranking on a set of argument A .5 For any S1,S2 ⊆ A , S1 ≥S S2 is a group comparison iff there exists an injective mapping f from S2 to S1 such that ∀a1 ∈ S2, f (a1) a1. An S1 >S S2 is a strict group comparison iff S1 ≥S S2 and (|S2| < |S1| or ∃a1 ∈ S2, f (a1) a1). ♠ Deﬁnition 48. Let Γ = 〈A ,→〉 and a1 ∈ A . The defence of a1 is simple iff10 every defender of a1 attacks exactly one direct attacker of a2. The defence of a1 is distributed iff every direct attacker of a1 is attacked by at most one argument. ♠ Deﬁnition 49. Let Γ = 〈A ,→〉, a1 ∈ A . The defence branch added to a1 is P+(a1) = 〈A ,→ 〉, with A = {b0,...,bn},n ∈ 2N,b0 = a1,A ∩ A = {a1},15 and → = {〈bi,bi−1〉 | i ≤ n}. The attack branch added to a1, denoted P−(a1) is deﬁned similarly except that the sequence is of odd length (i.e. n = 2N+1). ♠ Properties Given a ranking-based semantics σ, Γ = 〈A ,→〉, ∀a1,a2 ∈ A :20 Abstraction (Abs) [AB13]. The ranking on A should be deﬁned only on the basis of the attacks between arguments. Let Γ = 〈A ,→ 〉. For any isomorphism γ s.t. Γ = γ(Γ), a1 σ Γ a2 iff γ(a1) σ Γ γ(a2). Independence (In) [MT08; AB13]. The ranking between two argu-25 ments a1 and a2 should be independent of any argument that is neither connected to a1 nor to a2. ∀Γ = 〈A ,→ 〉 ∈ cc(Γ),1 ∀a1,a2 ∈ A , a1 σ Γ a2 ⇒ a1 σ Γ a2. Void Precedence (VP) [CL05; MT08; AB13]. A non-attacked argu- ment is ranked strictly higher than any attacked argument.30 a− 1 = and a− 2 = ⇒ a1 σ a2. Self-Contradiction (SC) [MT08]. A self-attacking argument is ranked lower than any non self-attacking argument. 〈a1,a1〉 =→ and 〈a2,a2〉 ∈→ ⇒ a1 σ a2. 1cc(Γ) denotes the set of connected components of an AF Γ. Cardiff University, 2016 Page 29
- 42. Ranking-Based Semantics • Properties for Ranking- Based Semantics [Bon+16] Cardinality Precedence (CP) [AB13]. The greater the number of di- rect attackers for an argument, the weaker the level of acceptability of this argument. |a− 1 | < |a− 2 | ⇒ a1 σ a2. Quality Precedence (QP) [AB13]. The greater the acceptability of5 one direct attacker for an argument, the weaker the level of acceptability of this argument. ∃a3 ∈ a− 2 s.t. ∀a4 ∈ a− 1 , a3 σ a4 ⇒ a1 σ a2. Counter-Transitivity (CT) [AB13]. If the direct attackers of a2 are at least as numerous and acceptable as those of a1, then a1 is at least as10 acceptable as a2. a− 2 ≥S a− 1 ⇒ a1 σ a2. Strict Counter-Transitivity (SCT) [AB13]. If CT is satisﬁed and ei- ther the direct attackers of a2 are strictly more numerous or acceptable than those of a1, then a1 is strictly more acceptable than a2.15 a− 2 >S a− 1 ⇒ a1 σ a2. Defence Precedence (DP) [AB13]. For two arguments with the same number of direct attackers, a defended argument is ranked higher than a non-defended argument. |a− 1 | = |a− 2 |, {a− 1 }− = and {a− 2 }− = ⇒ a1 σ a2.20 Distributed-Defence Precedence (DDP) [AB13]. The best defense is when each defender attacks a distinct attacker. |a− 1 | = |a− 2 | and {a− 1 }− = {a− 2 }− , if the defence of a1 is simple and distributed and the defence of a2 is simple but not distributed, then a1 σ a2. Strict addition of Defence Branch (⊕DB) [CL05]. Adding a defence25 branch to any argument improves its ranking. Given γ an isomorphism. If Γ∗ = Γ∪γ(Γ)∪ P+(γ(a1)), then γ(a1) σ Γ+ a1. Increase of Defence Branch (↑DB) [CL05]. Increasing the length of a defence branch of an argument degrades its ranking. Given γ an isomorphism. If a2 ∈ BR+ (a1), a2 ∉ BR− (a1) and Γ∗ = Γ∪γ(Γ)∪30 P+(γ(a2)), then a1 σ Γ∗ γ(a1). Addition of Defence Branch (+DB) [CL05]. Adding a defence branch to an attached argument improves its ranking. Given γ an isomorphism. If Γ∗ = Γ ∪ γ(Γ) ∪ P+(γ(a1)) and |a− 1 | = 0, then γ(a1) σ Γ+ a1.35 Cardiff University, 2016 Page 30
- 43. Ranking-Based Semantics • Properties for Ranking- Based Semantics [Bon+16] Increase of Attack Branch (↑AB) [CL05]. Increasing the length of an attack branch of an argument improves its ranking. Given γ an isomorphism. If a2 ∈ BR− (a1), a2 ∉ BR+ (a1) and Γ∗ = Γ∪γ(Γ)∪ P+(γ(a2)), then γ(a1) σ Γ∗ a1. Addition of Attack Branch (+AB) [CL05]. Adding an attack branch5 to any argument degrades its ranking. Given γ an isomorphism. If Γ∗ = Γ∪γ(Γ)∪ P−(γ(a1)), then a1 σ Γ∗ γ(a1). Total (Tot) [Bon+16]. All pairs of arguments can be compared. a1 σ a2 or a2 σ a1. Non-attacked Equivalence (NaE) [Bon+16]. All the non-attacked10 argument have the same rank. a− 1 = and a− 2 = ⇒ a1 σ a2. Attack vs Full Defence (AvsFD) [Bon+16]. An argument without any attack branch is ranked higher than an argument only attacked by one non-attacked argument.15 Γ is acyclic, |BR− (a1)| = 0, |a− 2 | = 1, and |{a− 2 }− | = 0 ⇒ a1 σ a2. CP incompatible with QP [AB13] CP incompatible with AvsFD [Bon+16] CP incompatible with +DB [Bon+16] VP incompatible with ⊕DB [Bon+16] Table 3.1: Incompatible properties SCT implies VP [AB13] CT implies DP [AB13] SCT implies CT [Bon+16] CT implies NaE [Bon+16] ⊕DB implies +DB [Bon+16] Table 3.2: Dependencies among properties Cardiff University, 2016 Page 31
- 44. Ranking-Based Semantics • Properties for Ranking- Based Semantics [Bon+16] Property Yes/No Comment Abs Yes In Yes VP Yes Implied by SCT DP Yes Implied by CT CT Yes Implied by SCT SCT Yes CP No QP No DDP No SC No ⊕DB No Incompatible with VP +AB Yes +DB No ↑AB Yes ↑DB Yes Tot Yes NaE Yes Implied by CT AvsFD No Table 3.3: Properties satisﬁed by Cat [BH01] Cardiff University, 2016 Page 32
- 45. 4 Argumentation Schemes Argumentation schemes [WRM08] are reasoning patterns which generate arguments: • deductive/inductive inferences that represent forms of common types of arguments used in everyday discourse, and in special contexts5 (e.g. legal argumentation); • neither deductive nor inductive, but defeasible, presumptive, or ab- ductive. Moreover, an argument satisfying a pattern may not be very strong by itself, but may be strong enough to provide evidence to warrant rational10 acceptance of its conclusion, given that it premises are acceptable. According to Toulmin [Tou58] such an argument can be plausible and thus accepted after a balance of considerations in an investigation or dis- cussion moved forward as new evidence is being collected. The investiga- tion can then move ahead, even under conditions of uncertainty and lack15 of knowledge, using the conclusions tentatively accepted. 4.1 An example: Walton et al. ’s Argumentation Schemes for Practical Reasoning Suppose I am deliberating with my spouse on what to do with our pension investment fund — whether to buy stocks,20 bonds or some other type of investments. We consult with a ﬁnancial adviser, and expert source of information who can tell us what is happening in the stock market, and so forth at the present time [Wal97]. Premises for practical inference:25 1. states that an agent (“I” or “my”) has a particular goal; 2. states that an agent has a particular goal. 〈S0,S1,...,Sn〉 represents a sequence of states of affairs that can be ordered temporally from earlier to latter. A state of affairs is meant to be like a statement, but one describing some event or occurrence that can30 be brought about by an agent. It may be a human action, or it may be a natural event. Cardiff University, 2016 Page 33
- 46. Argumentation Schemes • AS and Dialogues Practical Inference Premises: Goal Premise Bringing about Sn is my goal Means Premise In order to bring about Sn, I need to bring about Si Conclusions: Therefore, I need to bring about Si. Critical questions: Other-Means Question Are there alternative possible actions to bring about Si that could also lead to the goal? Best-Means Question Is Si the best (or most favourable) of the alternatives? Other-Goals Question Do I have goals other than Si whose achievement is preferable and that should have priority? Possibility Question Is it possible to bring about Si in the given circumstances? Side Effects Question Would bringing about Si have known bad consequences that ought to be taken into account? 4.2 AS and Dialogues Dialogue for practical reasoning: all moves (propose, prefer, justify) are co- ordinated in a formal deliberation dialogue that has eight stages [HMP01]. 1. Opening of the deliberation dialogue, and the raising of a governing question about what is to be done.5 2. Discussion of: (a) the governing question; (b) desirable goals; (c) any constraints on the possible actions which may be considered; (d) perspectives by which proposals may be evaluated; and (e) any premises (facts) relevant to this evaluation. 3. Suggesting of possible action-options appropriate to the governing10 question. 4. Commenting on proposals from various perspectives. Cardiff University, 2016 Page 34
- 47. 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 presented; and the undertaking of any information-gathering or fact-checking required for resolution. 6. Recommending an option for action, and acceptance or non-accept-5 ance of this recommendation by each participant. 7. Conﬁrming acceptance of a recommended option by each partici- pant. 8. Closing of the deliberation dialogue. Proposals are initially made at stage 3, and then evaluated at stages10 4, 5 and 6. Especially at stage 5, much argumentation taking the form of practi- cal reasoning would seem to be involved. As discussed in [Wal06], there are three dialectical adequacy condi- tions for deﬁning the speech act of making a proposal.15 The Proponent’s Requirement (Condition 1). The proponent puts forward a statement that describes an action and says that both proponent and respondent (or the respondent group) should carry out this action. The proponent is committed to carrying out that action: the state-20 ment has the logical form of the conclusion of a practical inference, and also expresses an attitude toward that statement. The Respondent’s Requirement (Condition 2). The statement is put forward with the aim of offering reasons of a kind that will lead the respondent to become committed to it.25 The Governing Question Requirement (Condition 3). The job of the proponent is to overcame doubts or conﬂicts of opinions, while the job of the respondent is to express them. Thus the role of the respondent is to ask questions that cast the prudential reasonable- ness of the action in the statement into doubt, and to mount attacks30 (counter-arguments and rebuttals) against it. Condition 3 relates to the global structure of the dialogue, whereas conditions 1 and 2 are more localised to the part where the proposal was made. Condition 3 relates to the global burden of proof [Wal14] and the roles of the two parties in the dialogue as a whole.35 Speech acts [MP02], like making a proposal, are seen as types of moves in a dialogue that are governed by rules. Three basic character- istics of any type of move that have to be deﬁned: Cardiff University, 2016 Page 35
- 48. Argumentation Schemes • AS and Dialogues 1. pre-conditions of the move; 2. the conditions deﬁning the move itself; 3. the post-conditions that state the result of the move. Preconditions • At least two agents (proponent and opponent);5 • A governing question; • Set of statements (propositions); • The proponent proposes the proposition to the respondent if and only if: 1. there is a set of premises that the proponent is committed to,10 and ﬁt the premises of the argumentation scheme for practical reasoning; 2. the proponent is advocating these premises, that is, he is mak- ing a claim that they are true or applicable in the case at issue; 3. there is an inference from these premises ﬁtting the argumen-15 tation scheme for practical reasoning; and 4. the proposition is the conclusion of the inference. The Deﬁning Conditions The central deﬁning condition sets out the conditions deﬁning the struc- ture of the move of making a proposal.20 The Goal Statement: We have a goal G. The Means Statement: Bringing about p is necessary (or sufﬁ- cient) for us to bring about G. Then the inference follows. The Proposal Statement: We should (practically ought to) bring25 about p. Cardiff University, 2016 Page 36
- 49. Argumentation Schemes • AS and Dialogues Proposal Statement in form of AS Premises: Goal Statement We have a goal G. The Means Statement Bringing about p is necessary (or sufﬁ- cient) for us to bring about G. Conclusions: We should (practically ought to) bring about p. The Post-Conditions The central post-condition is the response condition. The proposal must be open to critical questioning by opponent. The proponent should be open to answering doubts and objections correspond-5 ing to any one of the ﬁve critical questions for practical reasoning; as well as to counter-proposals, and is in charge of giving reasons why her pro- posal is better than the alternatives. The response condition set by these critical questions helps to explain how and why the maker of a proposal needs to be open to questioning and10 to requests for justiﬁcation. Cardiff University, 2016 Page 37
- 50. 5 A Semantic-Web View of Argumentation Acknowledgement This handout include material from a number of collaborators including Chris Reed. An overview can also be ﬁnd at [Bex+13].5 5.1 The Argument Interchange Format [Rah+11] Node Graph (argument network) has-a Information Node (I-Node) is-a Scheme Node S-Node has-a Edge is-a Rule of inference application node (RA-Node) Conflict application node (CA-Node) Preference application node (PA-Node) Derived concept application node (e.g. defeat) is-a ... ContextScheme Conflict scheme contained-in Rule of inference scheme Logical inference scheme Presumptive inference scheme ... is-a Logical conflict scheme is-a ... Preference scheme Logical preference scheme is-a ... Presumptive preference scheme is-a uses uses uses Figure 5.1: Original AIF Ontology [Che+06; Rah+11] 5.2 An Ontology of Arguments [Rah+11] Please download Protégé from http://protege.stanford.edu/ and the AIF OWL version from http://www.arg.dundee.ac.uk/wp-content/ uploads/AIF.owl10 Representation of the argument described in Figure 5.2 ___jobArg : PracticalReasoning_Inference fulﬁls(___jobArg, PracticalReasoning_Scheme) hasGoalPlan_Premise(___jobArg, ___jobArgGoalPlan) hasConclusion(___jobArg, ___jobArgConclusion)15 hasGoal_Premise(___jobArg, ___jobArgGoal) ___jobArgConclusion : EncouragedAction_Statement fulﬁls(___jobArgConclusion, EncouragedAction_Desc) Cardiff University, 2016 Page 38
- 51. Semantic Web Argumentation • AIF-OWL Practical Inference Bringing about is my goal Sn Si In order to bring about I need to bring about Sn Therefore I need to bring about Si hasConcDeschasPremiseDesc hasPremiseDesc Bringing about being rich is my goal In order to bring about being rich I need to bring about having a job fulfilsPremiseDesc fulfilsPremiseDesc fulfilsScheme supports supports Therefore I need to bring about having a job hasConclusion fulfils Figure 5.2: An argument network linking instances of argument and scheme components Symmetric attack r → p r pMP2 A1 A2 p → q p qMP1 neg1 Undercut attack r MP2 A3 A2 s → v s vMP1 cut1 p r → p Figure 5.3: Examples of conﬂicts [Rah+11, Fig. 2] claimText (___jobArgConclusion "Therefore I need to bring about hav- ing a job") ___jobArgGoal : Goal_Statement fulﬁls(___jobArgGoal, Goal_Desc) claimText (___jobArgGoal "Bringing about being rich is my goal")5 ___jobArgGoalPlan : GoalPlan_Statement fulﬁls(___jobArgGoalPlan, GoalPlan_Desc) claimText (___jobArgGoalPlan "In order to bring about being rich I need to bring about having a job") Cardiff University, 2016 Page 39
- 52. Semantic Web Argumentation • AIF-OWL Relevant portion of the AIF ontology EncouragedAction_Statement EncouragedAction_Statement Statement GoalPlan_Statement GoalPlan_Statement Statement5 Goal_Statement Goal_Statement Statement I-node I-node ≡ Statement I-node Node10 I-node ¬ S-node Inference Inference ≡ RA-node Inference ∃ fulﬁls Inference_Scheme Inference ≥ 1 hasPremise Statement15 Inference Scheme_Application Inference = hasConclusion (Scheme_Application Statement) Inference_Scheme Inference_Scheme Scheme ≥ 1 hasPremise_Desc Statement_Description = hasConclusion_Desc20 (Scheme Statement_Description) PracticalReasoning_Inference PracticalReasoning_Inference ≡ Presumptive_Inference ∃ hasCon- clusion EncouragedAction_Statement ∃ hasGoalPlan_Premise Goal- Plan_Statement ∃ hasGoal_Premise Goal_Statement25 RA-node RA-node ≡ Inference RA-node S-node S-node S-node ≡ Scheme_Application30 S-node Node S-node ¬ I-node Cardiff University, 2016 Page 40
- 53. Semantic Web Argumentation • AIF-OWL Scheme Scheme Form Scheme ¬ Statement_Description Scheme_Application Scheme_Application ≡ S-node5 Scheme_Application ∃ fulﬁls Scheme Scheme_Application Thing Scheme_Application ¬ Statement Statement Statement ≡ NegStatement10 Statement ≡ I-node Statement Thing Statement ∃ fulﬁls Statement_Description Statement ¬ Scheme_Application Statement_Description15 Statement_Description Form Statement_Description ¬ Scheme fulﬁls ∃ fulﬁls Thing Node hasConclusion_Desc20 ∃ hasConclusion_Desc Thing Inference_Scheme hasGoalPlan_Premise hasPremise hasGoal_Premise hasPremise25 claimText ∃ claimText DatatypeLiteral Statement ∀ claimText DatatypeString Individuals of EncouragedAction_Desc EncouragedAction_Desc : Statement_Description30 formDescription (EncouragedAction_Desc "A should be brought about") Cardiff University, 2016 Page 41
- 54. Semantic Web Argumentation • AIF-OWL Individuals of GoalPlan_Desc GoalPlan_Desc : Statement_Description formDescription (GoalPlan_Desc "Bringing about B is the way to bring about A") Individuals of Goal_Desc5 Goal_Desc : Statement_Description formDescription (Goal_Desc "The goal is to bring about A") Individuals of PracticalReasoning_Scheme PracticalReasoning_Scheme : PresumptiveInference_Scheme hasPremise_Desc(PracticalReasoning_Scheme, Goal_Desc)10 hasConclusion_Desc(PracticalReasoning_Scheme, EncouragedAction_Desc) hasPremise_Desc(PracticalReasoning_Scheme, GoalPlan_Desc) Cardiff University, 2016 Page 42
- 55. 6 A novel synthesis: Collaborative Intelligence Spaces (CISpaces) Acknowledgement This handout include material from a number of collaborators including Alice Toniolo and Timothy J. Norman. Main reference: [Ton+15].5 6.1 Introduction Problem • Intelligence analysis is critical for making well-informed decisions • Complexities in current military operations increase the amount of information available to intelligence analysts10 CISpaces (Collaborative Intelligence Spaces) • A toolkit developed to support collaborative intelligence analysis • CISpaces aims to improve situational understanding of evolving sit- uations 6.2 Intelligence Analysis15 Deﬁnition 50 ([DCD11]). The directed and coordinated acquisition and analysis of information to assess capabilities, intent and opportunities for exploitation by leaders at all levels. ♠ Fig. 6.1 summarises the Pirolli and Card Model [PC05]. Table 6.1 illustrates the problems of individual analysis and how col-20 laborative analysis can improve it. Cardiff University, 2016 Page 43
- 56. CISpaces • Intelligence Analysis External Data Sources Presentation Search and Filter Schematize Build Case Tell Story Reevaluate Search for support Search for evidence Search for information FORAGING LOOP SENSE-MAKING LOOP Structure Effort inf Shoebox Ev Ev EvEv Ev Ev Ev Ev Ev Ev Ev Evidence File Hyp1 Hyp2 Hypotheses Pirolli & Card Model Figure 6.1: The Pirolli & Card Model [PC05] Individual analysis Collaborative analysis • Scattered Information & Noise • Hard to make connections • Missing Information • Cognitive biases • Missing Expertise • More effective and reliable • Brings together different expertise, resources • Prevent biases Table 6.1: Individual vs. Collaborative Analysis Cardiff University, 2016 Page 44
- 57. CISpaces • Intelligence Analysis Harbour Kish Farm KISH River Water pipe Aqueduct KISHSHIRE Kish Hall Hotel Illness among young and elderly people in Kishshire caused by bacteria Unidentified illness is affecting the local livestock in Kishshire, the rural area of Kish Figure 6.2: Initial information assigned to Joe PEOPLE and LIVESTOCK illness Water TEST shows a BACTERIA in the water supply Answer to POI: "GER-MAN" seen in Kish Explosion in KISH Hall Hotel TIME Tests on people/livestock POI for suspicious people Figure 6.3: Further events happening in Kish Example of Intelligence Analysis Process Goal: discover potential threats in Kish Analysts: Joe, Miles and Ella What Joe knows is summarised by Figs. 6.2 and 6.3 Main critical points and possible conclusions during the analysis:5 • Causes of water contamination → waterborne/non-waterborne bacteria; • POI responsible for water contamination; • Causes of hotel explosion. Cardiff University, 2016 Page 45
- 58. CISpaces • Reasoning with Evidence 6.3 Reasoning with Evidence • Identify what to believe happened from the claims constructed upon information (the sensemaking process); • Derive conclusions from data aggregated from explicitly requested information (the crowdsourcing process);5 • Assess what is credible according to the history of data manipula- tion (the provenance reasoning process). 6.4 Arguments for Sensemaking Formal Linkage for Semantics Computation A CISpace graph, WAT, can be transformed into a corresponding ASPIC-10 based argumentation theory. An edge in CISpaces is represented textu- ally as →, an info/claim node is written pi and a link node is referred to as type where type = {Pro,Con}. Then, [p1,...,pn → Pro → pφ] indicates that the Pro-link has p1,..., pn as incoming nodes and an outgoing node pφ.15 Deﬁnition 51. A WAT is a tuple 〈K, AS〉 such that AS= 〈L ,¯,R〉 is con- structed as follows: • L is a propositional logic language, and a node corresponds to a proposition p ∈ L . The WAT set of propositions is Lw. • The set R is formed by rules ri ∈ R corresponding to Pro links20 between nodes such that: [p1,..., pn → Pro → pφ] is converted to ri : p1,..., pn ⇒ pφ • The contrariness function between elements is deﬁned as: i) if [p1 → Con → p2] and [p2 → Con → p1], p1 and p2 are contradictory; ii) [p1 → Con → p2] and p1 is the only premise of the Con link, then p125 is a contrary of p2; iii) if [p1, p3 → Con → p2] then a rule is added such that p1 and p3 form an argument with conclusion ph against p2, ri : p1, p3 ⇒ ph and ph is a contrary of p2. ♠ Deﬁnition 52. K is composed of propositions pi, K = {pj, pi,...}, such that: i) let a set of rules r1,...,rn ∈ R indicate a cycle30 such that for all pi that are consequents of a rule r exists r containing pi as antecedent, then pi ∈ K if pi is an info-node; ii) otherwise, pi ∈ K if pi is not consequent of any rule r ∈ R. ♠ Cardiff University, 2016 Page 46
- 59. CISpaces • Arguments for Sensemaking An Example of Argumentation Schemes for Intelligence Analysis Intelligence analysis broadly consists of three components: Activities (Act) including actions performed by actors, and events happening in the world; Entities (Et) including actors as individuals or groups, and objects5 such as resources; and Facts (Ft) including statements about the state of the world regarding entities and activities. A hypothesis in intelligence analysis is composed of activities and events that show how the situation has evolved. The argument from cause to ef- fect (ArgCE) forms the basis of these hypotheses. The scheme, adapted10 from [WRM08], is: Argument from cause to effect Premises: • Typically, if C (either a fact Fti or an ac- tivity Acti) occurs, then E (either a fact Fti or an activity Acti) will occur • In this case, C occurs Conclusions: In this case E will occur Critical questions: CQCE1 Is there evidence for C to occur? CQCE1 Is there a general rule for C causing E ? CQCE3 Is the relationship between C and E causal? CQCE4 Are there any exceptions to the causal rule that prevent the effect E from occur- ring? CQCE5 Has C happened before E ? CQCE6 Is there any other C that caused E ? Formally: rCE : rule(R,C ,E ),occur(C ),before(C ,E ), ruletype(R,causal),noexceptions(R) ⇒ occur(E )15 Cardiff University, 2016 Page 47
- 60. CISpaces • Arguments for Provenance WasInformedBy Used WasGeneratedBy WasAssociatedWith ActedOnBehalfOf WasAttributedTo WasDerivedFrom Entity Actor Activity Figure 6.4: PROV Data Model [MM13] Lab Water Testing wasGeneratedBy Used wasAssociatedWith pjID:Bacteria contaminates local water Water Sample Generate Requirement Water monitoring Requirement wasDerivedFrom Used wasGeneratedBy wasInformedBy Monitoring of water supply used water contamination report Report generation Used wasGeneratedBy wasAssociatedWith wasDerivedFrom ?a1Pattern Pg Goal NGO lab assistant NGO Chemical Lab PrimarySource Time2014-11-13T08-16-45Z Time2014-11-12T10-14-40Z Time2014-11-14T05-14-10Z ?a2 ?p ?ag LEGEND p-Agent p-Entity p-Activity Node Older p-elements Newer Figure 6.5: Provenance of Joe’s information 6.5 Arguments for Provenance Provenance can be used to annotate how, where, when and by whom some information was produced [MM13]. Figure 6.4 depicts the core model for representing provenance, and Figure 6.5 shows an example of provenance for the pieces of information for analyst Joe w.r.t. the water contamination5 problem in Kish. Patterns representing relevant provenance information that may war- rant the credibility of a datum can be integrated into the analysis by ap- plying the argument scheme for provenance (ArgPV) [Ton+14]: Cardiff University, 2016 Page 48
- 61. CISpaces • Arguments for Provenance Argument Scheme for Provenance Premises: • Given pj about activity Acti, entity Eti, or fact Fti (ppv1) • GP(pj) includes pattern Pm of p-entities Apv, p-activities Ppv, p-agents Agpv in- volved in producing pj (ppv2) • GP(pj) infers that information pj is true (ppv3) Conclusions: Acti/Eti/Fti in pj may plausibly be true (ppvcn) Critical questions: CQPV1 Is pj consistent with other information? CQPV2 Is pj supported by evidence? CQPV3 Does GP(pj) contain p-elements that lead us not to believe pj? CQPV4 Is there any other p-element that should have been included in GP(pj) to infer that pj is credible? Cardiff University, 2016 Page 49
- 62. 7 Natural Language Interfaces 7.1 Experiments with Humans: Scenarios [CTO14] Scenario 1.B The weather forecasting service of the broadcasting com- pany AAA says that it will rain tomorrow. Meanwhile, the5 forecast service of the broadcasting company BBB says that it will be cloudy tomorrow but that it will not rain. It is also well known that the forecasting service of BBB is more accu- rate than the one of AAA. Γ1.B = 〈S1.B,D1.B〉, where:10 S1.B D1.B s1 : ⇒ sAAA s2 : ⇒ sBBB r1 : sAAA ∧ ∼ exAAA ⇒ rain r2 : sBBB ∧ ∼ exBBB ⇒ ¬ rain r3 : ∼ exaccuracy ⇒ r1 r2 Γ1.B gives rise to the following set of arguments: A1.B = {a1 = 〈s1,r1〉,a2 = 〈s2,r2〉,a3 = 〈r3〉}, where a2 A1.B-defeats a1. Therefore the set of justiﬁed arguments (which is also the unique stable extensions) is {a2,a3}. Scenario 1.E15 The weather forecasting service of the broadcasting com- pany AAA says that it will rain tomorrow. Meanwhile, the forecast service of the broadcasting company BBB says that it will be cloudy tomorrow but that it will not rain. It is also well known that the forecasting service of BBB is more accu-20 rate than the one of AAA. However, yesterday the trustwor- thy newspaper CCC published an article which said that BBB has cut the resources for its weather forecasting service in the past months, thus making it less reliable than in the past. Γ1.E = 〈S1.E,D1.E〉, where S1.E = S1.B ∪{s3 :⇒ sCCC}, and D1.E = D1.B ∪25 {r4 : sCCC ∧ ∼ exCCC ⇒ cut, r5 : cut ∧ ∼ excut ⇒ exaccuracy}. Γ1.E gives rise to the following set of arguments A1.E = A1.B ∪ {a4 = 〈s3,r4,r5〉}. a4 is the unique justiﬁed argument, while the defensible ex- tensions (which are also stable) are {a1,a4}, {a2,a4}. Cardiff University, 2016 Page 50
- 63. Natural Language Interfaces • Experiments with Hu- mans: Scenarios [CTO14] Scenario 2.B In a TV debate, the politician AAA argues that if Region X becomes independent then X’s citizens will be poorer than now. Subsequently, ﬁnancial expert Dr. BBB presents a doc- ument; which scientiﬁcally shows that Region X will not be5 worse off ﬁnancially if it becomes independent. Γ2.B = 〈S2.B,D2.B〉, where: S2.B D2.B s1 : ⇒ sAAA s2 : ⇒ sBBB s3 : ⇒ sdoc r1 : sAAA ∧ ∼ exAAA ⇒ poorer r2 : sBBB ∧ sdoc ∧ ∼ exBBB ∧ ∼ exdoc ⇒ ¬ poorer r3 : ∼ exexpert ⇒ r1 r2 Γ2.B gives rise to the following set of arguments A2.B = {a1 = 〈s1,r1〉,a2 = 〈s2,s3,r2〉,a3 = 〈r3〉}, where a2 A2.B-defeats a1. Therefore the set of justi-10 ﬁed arguments is {a2,a3}. Scenario 2.E In a TV debate, the politician AAA argues that if Region X becomes independent then X’s citizens will be poorer than now. Subsequently, ﬁnancial expert Dr. BBB presents a doc-15 ument; which scientiﬁcally shows that Region X will not be worse off ﬁnancially if it becomes independent. After that, the moderator of the debate reminds BBB of more recent research by several important economists that disputes the claims in that document.20 Γ2.E = 〈S2.E,D2.E〉, where S2.E = S2.B ∪{s4 :⇒ sresearch, s5 : sresearch ⇒ ¬sdoc}, and D2.E = D2.B. Γ2.E gives rise to the following set of arguments A2.E = A2.B ∪ {a4 = 〈s4,s5〉}. Therefore, there are two stable extensions which are also the defensible extensions: {a1,a3,a4} and {a2,a3}.25 Scenario 3.B You are planning to buy a second-hand car, and you go to a dealership with BBB, a mechanic whom has been recom- mended you by a friend. The salesperson AAA shows you a car and says that it needs very little work done to it. BBB30 says it will require quite a lot of work, because in the past he had to ﬁx several issues in a car of the same model. Cardiff University, 2016 Page 51
- 64. Natural Language Interfaces • Experiments with Hu- mans: Scenarios [CTO14] Γ3.B = 〈S3.B,D3.B〉, where: S3.B D3.B s1 : ⇒ sAAA s2 : ⇒ sBBB r1 : sAAA ∧ ∼ exAAA ⇒ ¬ work r2 : sBBB ∧ ∼ exBBB ⇒ work r3 : ∼ exprof essional ⇒ r1 r2 Γ3.B gives rise to the following set of arguments A3.B = {a1 = 〈s1,r1〉,a2 = 〈s2,s3,r2〉,a3 = 〈r3〉}, where a2 A3.B-defeats a1. Therefore the set of justi- ﬁed arguments (which is also the unique stable extensions) is {a2,a3}.5 Scenario 3.E You are planning to buy a second-hand car, and you go to a dealership with BBB, a mechanic whom has been recom- mended you by a friend. The salesperson AAA shows you a car and says that it needs very little work done to it. BBB10 says it will require quite a lot of work, because in the past he had to ﬁx several issues in a car of the same model. While you are at the dealership, your friend calls you to tell you that he knows (beyond a shadow of a doubt) that BBB made unneces- sary repairs to his car last month.15 Γ3.E = 〈S3.E,D3.E〉, where S3.E = S3.B ∪ {s3 :⇒ sf riend}, and D3.E = D4.B ∪{r4 : sf riend ∧ ∼ exf riend ⇒ unnecc_work, r5 : unnec_work ∧ ∼ exunnec_work ⇒ exprof essional}. Γ3.E gives rise to the following set of arguments A3.E = A2.E ∪ {a4 = 〈s3,r4,r5〉}. Similarly to Scenario 1.E, a4 is the only justiﬁed argument20 and there are two stable extensions: {a1,a4}, and {a2,a4}. Scenario 4.B After several dates, you would like to start a serious rela- tionship with J but you turn to ask two close friends of yours, AAA and BBB, for advice. You have known BBB for longer25 than you have known AAA. AAA tells you that J is lovely and you should go ahead, while BBB suggests that you should be very cautious because J might have a hidden agenda. Γ4.B = 〈S4.B,D4.B〉, where S4.B D4.E s1 : ⇒ sAAA s2 : ⇒ sBBB r1 : sAAA ∧ ∼ exAAA ⇒ go r2 : sBBB ∧ ∼ exBBB ⇒ ¬ go r3 : ∼ exbest_f riend ⇒ r1 r2 30 Cardiff University, 2016 Page 52
- 65. Natural Language Interfaces • Experiments with Hu- mans: Scenarios [CTO14] Γ4.B gives rise to the following set of arguments A4.B = {a1 = 〈s1,r1〉,a2 = 〈s2,s3,r2〉,a3 = 〈r3〉}, where a2 A4.B-defeats a1. Therefore the set of justi- ﬁed arguments (which is also the unique stable extensions) is {a2,a3}. Scenario 4.E After several dates, you would like to start a serious rela-5 tionship with J. but you turn to ask two friends of yours, AAA and BBB, for advice. You have known BBB for longer than you have known AAA. AAA tells you that J is lovely and you should go ahead, while BBB suggests that you should be very cautious because J might have a hidden agenda. After some10 weeks, CCC, who is also a close friend of BBB, tells you that BBB has been into you for years; BBB is too shy to tell you about their feelings about you, but are still possessive of you. Γ4.E = 〈S4.E,D4.E〉, where S4.E = S4.B ∪{s3 :⇒ sCCC}, and D4.E = D4.B ∪ {r4 : sCCC ∧ ∼ exCCC ⇒ possessive, r5 : possessive ∧ ∼ expossessive ⇒15 ¬ r1 r2}. Γ4.E gives rise to the following set of arguments A4.E = A4.B ∪ {a4 = 〈s3,r4,r5〉}, with no justiﬁed arguments. The stable extensions are: {a1,a4},{a2,a3},{a2,a4}. Results 0 15 30 45 60 PA PB PU % Distribution of acceptability of actors’ positions Base cases Extended cases Figure 7.1: Distribution of the ﬁnal conclusion PA/PB/PU, comparing base cases with extended cases, in percent. Cardiff University, 2016 Page 53
- 66. Natural Language Interfaces • Experiments with Hu- mans: Scenarios [CTO14] Base Cases Extended Cases PA PB PU PA PB PU 1, weather 5.0 50.0 45.0 15.8 21.1 63.2 2, politics 5.3 63.2 31.6 21.1 10.5 68.4 3, buying car 0.0 68.2 31.8 23.8 23.8 52.4 4, romance 12.5 68.8 18.8 48.0 36.0 16.0 Table 7.1: Distribution of the ﬁnal conclusion PA/PB/PU in percent, for each scenarios. Shading denotes the most likely conclusions. 0 15 30 45 60 U1 U2 U3 % Distributions of motivations for PU (scenarios 1.B and 3.B) 1.B 3.B Figure 7.2: Distribution across three categories of justiﬁcation (U1: lack of information, U2: domain speciﬁc reasons; U3: other) for agreement with the PU position in scenarios 1.B and 3.B. Cardiff University, 2016 Page 54
- 67. Natural Language Interfaces • Lessons From Argu- ment Mining: [BR11] Base cases Extended cases RB † Md∗ B RE † Md∗ E C.D.‡ Relevance 1, weather 110.38 6.00 82.92 4.00 46.60 2, politics 107.45 6.00 69.45 4.00 47.19 3, buying car 118.05 6.50 67.45 4.00 44.38 4, romance 48.34 2.00 44.40 2.00 46.57 Agreement 1, weather 116.38 6.00 87.18 4.00 46.60 2, politics 103.34 6.00 65.05 4.00 47.19 3, buying car 121.93 6.50 64.33 4.00 44.38 4, romance 44.94 2.00 44.20 2.00 46.57 (a) Scenario 3.B Scenario 4.B R3.B † Md∗ 3.B R4.B † Md∗ 4.B C.D.‡ Relevance 118.05 6.50 48.34 2.00 47.79 Agreement 121.93 6.50 44.94 2.00 47.79 (b) Table 7.2: Post-hoc analysis regarding relevance and agreement: pairwise comparison base-extended cases (a); and between 1.B and 4.B (b). Sta- tistically signiﬁcant cases (i.e. when |Rx − Ry| > C.D) are highlighted in grey. † Mean rank as computed with the Kruskal-Wallis test ∗ Median ‡ Critical Difference, as computed in [SC88] cited by [Fie09] with α = 0.05. 7.2 Lessons From Argument Mining: [BR11] Bob says: Lower taxes stimulate the economy Bob says: The government will inevitably lower the tax rate. Wilma says: Why? Challenging Substantiating Asserting Asserting Challenging Lower taxes stimulate the economy An application of the argument scheme for Argument from Positive Consequences The government will inevitably lower the tax rate. Arguing Bob is credible Bob is credible Cardiff University, 2016 Page 55
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