Introduction to ABSTRACT ARGUMENTATION

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1 Introduction to ABSTRACT ARGUMENTATION Massimiliano Giacomin DII - Dipartimento di Ingegneria dell Informazione Università degli Studi di Brescia (Italy)

2 What s abstract argumentation? DEFINITION OF ARGUMENT STATUS DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE (and consequence) 2

3 What s abstract argumentation? DEFINITION OF ARGUMENT STATUS Abstract argumentation focuses on this level DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE (and consequence) 3

4 DUNG S MODEL (1995)

5 Argumentation framework AF = <A, > Attack relation Arguments A: set of arguments - Their origin and structure is left unspecified : a binary relation of attack, i.e. AxA - Its origin is left unspecified Graphical representation as a directed graph [defeat graph] 5

6 A weather example A1: It s raining, since Smith says so A2: It s not raining, since Bob says so A3: Bob is not reliable, since he is drunk A1 A2 A3 6

7 Vaccination example Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important There is a study supporting correlation Vaccines don t cause autism Paper by A. Wakefield et al., Lancet 1998 All scientific studies concluded vaccines don t cause it That paper is fraudolent Results not reproduced; conflicts of interest 7

8 Argumentation framework: the task ARGUMENT EVALUATION: GIVEN AN ARGUMENTATION FRAMEWORK, DETERMINE THE JUSTIFICATION STATE (ALSO CALLED DEFEAT STATUS) OF ARGUMENTS, IN PARTICULAR: WHAT ARGUMENTS EMERGE UNDEFEATED FROM THE CONFLICT, I.E. ARE ACCEPTABLE? 8

9 Argumentation semantics Specification of a method/criteria for argument evaluation, i.e. to determine, given a set of arguments, their defeat status Semantics Argumentation Framework Defeat status Undefeated Defeat status Defeated Provisionally Defeated 9

10 (Extension-based) semantics Semantics S Argumentation framework AF Set of extensions E S (AF) 10

11 From extensions to defeat status Set of extensions E S (AF) Defeat/Justification Status A common definition (Skeptically) justified argument: belongs to all of the extensions Unjustified argument: does not - Credulously justified: belongs to at least one extension - Indefensible: does not belong to any extension 11

12 A REVIEW OF MOST COMMON ARGUMENTATION SEMANTICS - GROUNDED SEMANTICS - STABLE SEMANTICS - PREFERRED SEMANTICS

13 Unique-status vs. multiple-status semantics Unique-Status Semantics Unique extension: empty set and directly unjustified Multiple-Status Semantics and unjustified 13

14 The Grounded Semantics: a unique status approach - INITIAL ARGUMENTS: ASSIGNED UNDEFEATED - ARGUMENTS THEY ATTACK: ASSIGNED DEFEATED - REMOVAL OF ALL THESE ARGUMENTS NO initial arguments There are initial arguments - REMAINING ARGUMENTS: PROVISIONALLY DEFEATED Grounded extension: includes the set of undefeated arguments 14

15 The Grounded Semantics: a unique status approach - INITIAL ARGUMENTS: ASSIGNED UNDEFEATED - ARGUMENTS THEY ATTACK: ASSIGNED DEFEATED - REMOVAL OF ALL THESE ARGUMENTS NO initial arguments There are initial arguments - REMAINING ARGUMENTS: PROVISIONALLY DEFEATED Grounded extension: includes the set of undefeated arguments 15

16 The Grounded Semantics: a unique status approach - INITIAL ARGUMENTS: ASSIGNED UNDEFEATED - ARGUMENTS THEY ATTACK: ASSIGNED DEFEATED - REMOVAL OF ALL THESE ARGUMENTS NO initial arguments There are initial arguments - REMAINING ARGUMENTS: PROVISIONALLY DEFEATED Grounded extension: includes the set of undefeated arguments 16

17 The Grounded Semantics: a unique status approach - INITIAL ARGUMENTS: ASSIGNED UNDEFEATED - ARGUMENTS THEY ATTACK: ASSIGNED DEFEATED - REMOVAL OF ALL THESE ARGUMENTS NO initial arguments There are initial arguments - REMAINING ARGUMENTS: PROVISIONALLY DEFEATED Grounded extension: includes the set of undefeated arguments 17

18 The Grounded Semantics: a unique status approach - INITIAL ARGUMENTS: ASSIGNED UNDEFEATED - ARGUMENTS THEY ATTACK: ASSIGNED DEFEATED - REMOVAL OF ALL THESE ARGUMENTS NO initial arguments There are initial arguments - REMAINING ARGUMENTS: PROVISIONALLY DEFEATED Grounded extension: includes the set of undefeated arguments 18

19 Grounded semantics: example γ AF Example of instantiation: : it will be dry in London since there will be sunshine according to BBC γ: it will be wet in London since there will be rain according to CNN : according to previous experiences, BCC forecasts are unreliable 19

20 Grounded semantics: example γ AF Example of instantiation: : it will be dry in London since there will be sunshine according to BBC γ: it will be wet in London since there will be rain according to CNN : according to previous experiences, BCC forecasts are unreliable 20

21 Grounded semantics: example γ AF Example of instantiation: : it will be dry in London since there will be sunshine according to BBC γ: it will be wet in London since there will be rain according to CNN : according to previous experiences, BCC forecasts are unreliable 21

22 Grounded semantics: example γ AF GE(AF) = {, γ} Example of instantiation: : it will be dry in London since there will be sunshine according to BBC γ: it will be wet in London since there will be rain according to CNN : according to previous experiences, BCC forecasts are unreliable 22

23 Grounded semantics: example γ AF GE(AF) = { } Example of instantiation: : it will be dry in London since there will be sunshine according to BBC γ: it will be wet in London since there will be rain according to CNN : according to previous experiences, BCC forecasts are unreliable : these experiences are too old 23

24 Floating arguments: a problem for grounded semantics γ δ according to Grounded Semantics But here a more discriminative behavior may be desirable: γ δ 24

25 Floating Arguments Example (by H. Prakken) A B A = Frederic Michaud is French since he has a French name B = Frederic Michaud is Dutch since he is a marathon skater C = F.M. likes the EU since he is European (assuming he is not Dutch or French) D = F.M. does not like the EU since he looks like a person who does not like the EU C D 25

26 University adaptation (by M. Giacomin) A = John will watch TV this evening since there is the football match B = John will go to a party this evening since there is a university students party C = John will study Computer Organization and Design this evening since the exam is not very far away, unless he has to go out or watch TV D = John will not study this evening, since usually students do not study in the evening A C D B 26

27 How to manage floating arguments? γ δ - Assume IN: then γ is OUT and δ IN - Assume IN: then γ is OUT and δ IN Let us consider multiple status semantics! 27

28 Stable Semantics Stable extension = conflict-free set attacking all outside arguments for any and in the set, it is not the case that THE CASE OF FLOATING ARGUMENTS γ δ γ δ E ST (AF) = { {, δ}, {, δ} } δ is justified 28

29 Odd-length cycles: a problem for stable semantics No stable extension exists! γ E ST (AF) = ø which is different w.r.t. E S (AF) = {ø} An unsatisfactory patch Stable extensions = - conflict-free sets attacking all outside arguments, if there is one - {ø}, otherwise 29

30 Stable Semantics: an unsatisfactory patch Stable extensions = - conflict-free sets attacking all outside arguments, if there is one - {ø}, otherwise 1 3 γ 2 E ST (AF) = {ø } NOT justified!!! 30

31 Example 2 3 γ 1 : Today John is not drunk since it s a week that there are no parties γ: Today John is drunk since he always get drunk in a University party 1: John says that Smith is unreliable 2: Smith says that Rob is unreliable 3: Rob says that John is unreliable 31

32 Preferred semantics Admissible set S b - conflict-free - every argument a in S is defended by S: > if b attacks a, then (an element of) S attacks b a S Intuition: a coherent point of view able to respond to all critiques - e.g. the empty set (abstaining from any decision) is always admissible Preferred semantics [P.M. Dung, 95] Preferred extension: maximal (under ) admissible set 32

33 Examples Non admissible sets γ δ γ δ γ δ Admissible but non maximal sets γ δ γ δ so, what are the preferred extensions? 33

34 Preferred semantics and floating arguments γ δ γ γ δ δ E PR (AF) = E ST (AF) = { {, δ}, {, δ} } DEFEAT STATUS γ δ (δ is justified) 34

35 Preferred semantics and odd-length cycles 1 E PR (AF) = {{}} 3 E ST (AF) = ø γ 2 E GE (AF) = {{}} Preferred semantics handles odd-length cycles better than stable semantics (as the grounded semantics) Preferred semantics handles the case of floating arguments better than grounded semantics (as stable semantics) 35

36 S T A Traditional semantics [Dung 1995] B LE GROUNDED SEMANTICS: UNIQUE STATUS, THE MOST SKEPTICAL! P R EF E R R E D 36

37 Alternative equivalent definitions based on complete extensions Complete extension Admissible set which includes ALL arguments it defends Complete semantics-based definitions GROUNDED EXTENSION THE LEAST COMPLETE EXTENSION PREFERRED EXTENSION MAXIMAL COMPLETE EXTENSION STABLE EXTENSION COMPLETE EXTENSION ATTACKING ALL OUTSIDE ARGUMENTS 37

38 Examples Chain γ Admissible sets: ø, {}, {, γ} Only one complete extension: E CO (AF) = {{, γ}} Nixon Diamond All admissible sets are complete E CO (AF) = { ø, {}, {} } 38

39 Alternative equivalent definitions based on labellings Extensions Labellings UND UND IN OUT OUT IN LABEL OF AN ARGUMENT - IN = belongs to the extension - OUT = attacked by the extension - UNDEC= does not belong to + not attacked by the extension 39

40 Labelling-based semantics definitions (1) Complete labelling - each argument labelled IN is legally IN (all its attackers are OUT) - each argument labelled OUT is legally OUT (there is an attacker IN) - each argument labelled UNDEC is legally UNDEC (there is an attacker UNDEC and no attacker is IN) Example UND UND IN OUT OUT IN 40

41 Labelling-based semantics definitions (2) Grounded labelling - the complete labelling minimizing the set of IN arguments, or - the complete labelling minimizing the set of OUT arguments, or - the complete labelling maximizing the set of UNDEC arguments Preferred labelling - a complete labelling maximizing the set of IN arguments, or - a complete labelling maximizing the set of OUT arguments, or Stable labelling - a complete labelling without arguments labelled UNDEC 41

42 Labelling-based semantics: examples (1) Nixon Diamond UND UND IN OUT OUT IN COMPLETE AND GROUNDED NOT PREFERRED NOR STABLE COMPLETE PREFERRED AND STABLE 42

43 Labelling-based semantics: examples (2) Floating arguments γ δ γ δ γ δ COMPLETE, GROUNDED NOT PREFERRED COMPLETE PREFERRED STABLE 43

44 AN APPLICATION EXAMPLE A. Hunter, M. Williams, Aggregating evidence about the positive and negative effects of treatments, Artificial Intelligence in Medicine 56 (2012)

45 Meta analysis of clinical trials (1) Left Right Outcome indicator Value Net Sig Type e 01 BB NT Visual field prog 0.77 > No MA e 02 BB NT Change in IOP 2.88 > Yes MA e 03 BB NT Respiratory prob 3.06 < No MA e 04 BB NT Cardio prob 9.17 < No MA e 05 PG BB Change in IOP 1.32 > Yes MA e 06 PG BB Acceptable IOP 1.54 > Yes MA e 07 PG BB Respiratory prob 0.59 > Yes MA e 08 PG BB Cardio prob 0.87 > No MA e 09 PG BB Allergy prob 1.25 < No MA e 10 PG BB Hyperaemia 3.59 < Yes MA e 11 PG SY Change in IOP 2.21 > Yes MA e 12 PG SY Allergic prob 0.03 > Yes MA e 13 PG SY Hyperaemia 1.01 < No MA e 14 CA NT Convert to COAG 0.77 > No MA e 15 CA NT Visual field prog 0.69 > No MA e 16 CA NT IOP > 35 mmhg 0.08 > Yes MA e 17 CA BB Hyperaemia 6.42 < No MA e 18 SY BB Visual field prog 0.92 > No MA e 19 SY BB Change in IOP 0.25 > No MA e 20 SY BB Allergic prob < Yes MA e 21 SY BB Drowsiness 1.21 < No MA from NICE glaucoma guidelines - change in IOP: negative if left arm superior wrt right arm - acceptable IOP: greater than 1 if left arm superior - others (undesirable): lower than 1 if left arm is superior 45

46 Meta analysis of clinical trials (2) Generation of inductive arguments (X, ε) X Evidence ε: τ 1 >τ 2 τ 1 τ 2 τ 1 <τ 2 Example Left Right Outcome indicator Value Net Sig Type e 1 ACE CCB Mortality 1.04 < No MA e 2 ACE CCB Stroke 1.15 < Yes MA e 3 ACE CCB Heart failure 0.84 > Yes MA e 4 ACE CCB Diabetes 0.85 > Yes MA {e 3 }, ACE > CCB {e 4 }, ACE > CCB {e 3,e 4 }, ACE > CCB {e 1 }, ACE < CCB {e 2 }, ACE < CCB {e 1,e 2 }, ACE < CCB 46

47 Meta analysis of clinical trials (3) Inductive argument graph ve argument graph constructed according to Definition 10. e 82,e 83 },CP >NC e 81,e 84 },CP <NC e 82 },CP >NC e 81 },CP <NC e 83 },CP >NC e 84 },CP <NC A i attacks A j iff - they have conflicting conclusions - Benefits(A j ) are NOT strictly preferred wrt Benefits(A i ) Benefits: normalized results (winner point of view) 47

48 Meta analysis of clinical trials (4) User defined preference between benefits Reflexivity Benefits(A i ) Benefits(A i ) Transitivity Benefits(A i ) Benefits(A j ) and Benefits(A j ) Benefits(A k ) implies Benefits(A i ) Benefits(A k ) Monotonicity Support(A i ) Support(A j ) implies Benefits(A j ) Benefits(A i ) Weakening Support(A ) Support(A ) and Benefits(A ) Benefits(A ) Example preference relation. {(oc, 0.99), (preg, 0.05)} {(bc, 0.96), (th, 0.98)} {(oc, 0.99)} {(bc, 0.96)} {(preg, 0.05)} {(th, 0.98)} 48

49 Meta analysis of clinical trials (5) Introduction of meta-arguments Against the quality of the evidence used in the inductive arguments Examples: - the evidence contains flawed Randomized Clinical Trials - the evidence contains results that are not statistically significant - the evidence is for trials that are for a very narrow patient class - the evidence has outcomes that are not consistent Not Statistically Significant e 18 },SY >BB e 19 },SY >BB e 18,e 19 },SY >BB e 20 },SY <BB e 21 },SY <BB e 20,e 21 },SY <BB 49

50 Meta analysis of clinical trials (6) The final result: superiority graph Prostaglandin Analogue (PG) Beta-blocker (BB) Sympathomimetic (SY) No Treatment (NT) Carbonic Anhydraise Inhibitor (CA) (a) Superiority graph for the glaucoma case study. 50

51 SOME EXTENSIONS OF DUNG S MODEL Value-based argumentation frameworks Argumentation frameworks with attacks to attacks

52 Epistemic vs Practical reasoning γ EPISTEMIC REASONING: reasoning about what to believe : it will be dry in London (there will be sunshine according to BBC) γ: it will be wet in London (there will be rain according to CNN) skeptical acceptance appropriate (both arguments undecided) PRACTICAL REASONING: reasoning about what to do : give aspirin (to prevent blood clotting) γ: give chlopidrogel (to prevent blood clotting) credulous acceptance more appropriate (choose one argument!) 52

53 Value-based argumentation frameworks (1) VAF = <A,, V, val, P> [Bench-Capon, 2003] V 1 V 2 Audience a: total ordering > a a b c between values Arguments promote social values An attack 1 2 succeeds only if it is not the case that val( 2 ) > a val( 1 ) A specific audience expresses a total preference order between values - Audience 1: V1>V2 - Audience 2: V2>V1 53

54 Value-based argumentation frameworks (2) VAF = <A,, V, val, P> [Bench-Capon, 2003] V 1 V 2 Audience a: total orderings between values a b c EXAMPLE (Modgil 2010) a: give aspirin (to prevent blood clotting) b: give chlopidrogel (to prevent blood clotting) c: chlopidrogel is prohibitively expensive V1: improving the (specific) patient s health V2: cost (save money for all patients) 54

55 Value-based argumentation frameworks (3) Audience V1 (patient s health)>v2 (cost) V 1 V 2 Aspirin and Chlopidrogel equally preferable a b c (choose a preferred extension) Audience V2 (cost)>v1 (patient s health) V 1 V 2 (Less expensive) Aspirin is the unique option a b c 55

56 Modelling attacks to attacks (1) Representing preferences between arguments at the argument level possibility of arguing about (and reasoning with) preferences B A A: BBC forecast sunshine dry in London B: CNN forecast rain wet in London C: I feel BBC as more trustworthy than CNN C C expresses the preference of A wrt B it must attack the attack from B to A NB: C does not attack B, in fact - if A was not the case, B should be accepted (and C is still believed) - the same if an independent argument D attacks A (e.g. BBC did not really forecast sunshine) 56

57 Modelling attacks to attacks (2) EXAMPLE CONTINUED B A A: BBC forecast sunshine dry in London B: CNN forecast rain wet in London C: I feel BBC as more trustworthy than CNN C : statistically CNN more accurate than BBC C C [C and C express contradictory conclusions they attack each other] 57

58 Modelling attacks to attacks (3) EXAMPLE CONTINUED B A A: BBC forecast sunshine dry in London B: CNN forecast rain wet in London C: I feel BBC as more trustworthy than CNN C : statistically CNN more accurate than BBC C C [C and C express contradictory conclusions they attack each other] D D: statistics is more reliable than feeling! 58

59 Modelling VAFs with attacks to attacks (1) BACK TO THE EXAMPLE A1: V 1 >V 2 A2: V 2 >V 1 V 2 >V 1 V 1 >V 2 A Β (V 1 ) (V 1 ) C (V 2 ) 59

60 Modelling VAFs with attacks to attacks (2) FIRST EXTENSION (AUDIENCE) A1: V 1 >V 2 A2: V 2 >V 1 V 2 >V 1 V 1 >V 2 A Β (V 1 ) (V 1 ) C (V 2 ) 60

61 Modelling VAFs with attacks to attacks (3) SECOND EXTENSION (AUDIENCE) A1: V 1 >V 2 A2: V 2 >V 1 V 2 >V 1 V 1 >V 2 A Β (V 1 ) (V 1 ) C (V 2 ) 61

Repairing Preference-Based Argumentation Frameworks

Repairing Preference-Based Argumentation Frameworks Leila Amgoud IRIT CNRS 118, route de Narbonne 31062, Toulouse Cedex 09 amgoud@irit.fr Srdjan Vesic IRIT CNRS 118, route de Narbonne 31062, Toulouse Cedex