Cerutti--Introduction to Argumentation (seminar @ University of Aberdeen)

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Cerutti--Introduction to Argumentation (seminar @ University of Aberdeen)

  1. 1. Introduction to ArgumentationTheoryFederico CeruttiDL LunchTuesday 18thDecember, 2012c 2012 Federico Cerutti <f.cerutti@abdn.ac.uk>
  2. 2. Non Monotonic LogicsClassical logic is monotonic: whenever a sentence A is a logicalconsequence of a set of sentences T (T A), then A is also aconsequence of an arbitrary superset of T;Commonsense reasoning is dierent: we often draw plausibleconclusions based on the assumption that the world is normaland as expected;This is farm from being irrational: it is the best we can do insituations in which we have only incomplete information;It can happen that our normality assumptions turn out to bewrong: in this case we may have to revise our conclusions.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 2
  3. 3. Answer Set Programming: the Tweety Examplef l i e s (X) :− bird (X) , not abnormal (X) .abnormal (X) :− penguin (X) .bird (X) :− penguin (X) .bird ( tweety ) .penguin ( tux ) .Resulting Answer Sets:{penguin ( tux ) , f l i e s ( tweety ) , bird ( tweety ) ,bird ( tux ) , abnormal ( tux )}f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 3
  4. 4. Answer Set Programming: the Nixon DiamondUsually, Quakers are pacistUsually, Republicans are not pacistRichard Nixon is both a Quaker and a Republicanquaker ( nixon ) .republican ( nixon ) .p a c i f i s t (X) :− quaker (X) , not −p a c i f i s t (X) .−p a c i f i s t (X) :− republican (X) , not p a c i f i s t (X) .Resulting Answer Sets:{quaker ( nixon ) , republican ( nixon ) , p a c i f i s t ( nixon )}{quaker ( nixon ) , republican ( nixon ) , −p a c i f i s t ( nixon )}f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 4
  5. 5. Argumentation: an Informal Example (Courtesyof M. Giacomin)The reasonThe conclusionWe are justified in believing that we should run LHC We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  6. 6. Argumentation: an Informal Example (Courtesyof M. Giacomin)The reasonThe conclusionWe are justified in believing that we should run LHC We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodIn Argumentation (and in real life as well):- reasons are not necessary “conclusive”(they don’t logically entail conclusions)- arguments and conclusions can be “retracted”in front of new information, i.e. counterargumentsBUTf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  7. 7. Argumentation: an Informal Example (Courtesyof M. Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badNow we are justified in believing that we should not run LHC f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  8. 8. Argumentation: an Informal Example (Courtesyof M. Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationNow we are again justified in believing that we should run LHC f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  9. 9. Argumentation: an Informal Example (Courtesyof M. Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationHawking radiationdoes not existDr Azzeccagarbuglisays soNow we are again justified in believing that we should not run LHC f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  10. 10. Argumentation: an Informal Example (Courtesyof M. Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationHawking radiationdoes not existDr Azzeccagarbuglisays soDr Azzeccagarbugliis not expert in physicsHe is a lawyerNow we are again justifiedin believing that we shouldrun LHC f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 5
  11. 11. What is Argumentation?[Prakken, 2011] Argumentation is the process of supportingclaims with grounds and defending them against attack.[van Eemeren et al., 1996] Argumentation is a verbal and socialactivity of reason aimed at increasing (or decreasing) theacceptability of a controversial standpoint for the listener orreader, by putting forward a constellation of propositionsintended to justify (or refute) the standpoint before a rationaljudge.A framework for practical and uncertain reasoning able to copewith partial and inconsistent knowledge.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 6
  12. 12. The Elements of an Argumentation System[Prakken and Vreeswijk, 2001]1 The denition of an argument (possibly including an underlyinglogical language + a notion of logical consequence)2 The notion of attack and defeat (successful attack) betweenarguments;3 An argumentation semantics selecting acceptable (justied)argumentsf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 7
  13. 13. Classical logic and argumentation[Besnard and Hunter, 2008]Let ∆ be set of formulae in classical logic.An argument is a pair Φ, α such that:1 Φ ⊥2 Φ α3 Φ is a minimal subset of ∆ satisfying 2.A defeater for Φ, α is an argument Ψ, β such thatβ ¬(φ1 ∧ . . . ∧ φn) for some {φ1, . . . , φn} ⊆ ΦA rebuttal for Φ, α is an argument Ψ, β where β ¬αAn undercut for Φ, α is an argument Ψ, ¬(φ1 ∧ . . . ∧ φn) where{φ1, . . . , φn} ⊆ Ψf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 8
  14. 14. Arguments and Attacks: Argument Schemes[Walton, 1996]An argument scheme is a reasoning pattern giving us thepresumption in favour of its conclusion.A critical question is a question that can be posed by an opponentin order to undermine the validity of the stated argument.There are several argument schemes in literature.Expert testimonyPremise 1: E is expert on DPremise 2: E says PPremise 3: P is in DConclusion: P is the caseCritical questions:1 Is E biased?2 Is P consistent with what other experts say?3 Is P consistent with known evidence?f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 9
  15. 15. Abstract argumentation: Nixon DiamondAn abstract argumentation framework AF is a tuple A, R , where Ais a set of argument (whose origin and structure is not specied), andR ⊆ A × A is a set of attack (or defeat) relations.AFN = AN , RN , where AN = {A1, A2}, RN = { A1, A2 , A2, A1 },andA1: since Nixon is a quaker, then he is also a pacist;A2: since Nixon is a republican, he is not a pacist.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 10
  16. 16. Nixon: from Prolog to Arguments (the Dungsway)AR = {(K, k)|∃C ∈ Gp : head(C) = k, and body(C) =K} ∪ {({¬k}, ¬k)|k is a ground atom}(K, h) attacks (K , h ) i h∗ ∈ Kf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 11
  17. 17. Nixon: from Prolog to Arguments (the Dungsway)A1 ({¬quaker(nixon)}, ¬quaker(nixon))A2 ({¬republican(nixon)}, republican(nixon))A3 ({}, quaker(nixon))A4 ({}, republican(nixon))A5 ({pacifist(nixon), quaker(nixon)}, pacifist(nixon))A6 ({¬pacifist(nixon), republican(nixon)}, ¬pacifist(nixon))A7 ({¬pacifist(nixon)}, ¬pacifist(nixon))A5 A6A3 A1 A4 A2A7f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 11
  18. 18. Tweety: from Prolog to Arguments (the Dungsway)A1 ({¬penguin(tux)}, ¬penguin(tux))A2 ({}, penguin(tux))A3 ({¬bird(tux)}, ¬bird(tux))A4 ({¬bird(tweety)}, ¬bird(tweety))A5 ({}, bird(tweety))A6 ({¬penguin(tweety)}, ¬penguin(tweety))A7 ({¬abnormal(tux)}, ¬abnormal(tux))A8 ({¬abnormal(tweety)}, ¬abnormal(tweety))A9 ({¬flies(tux)}, ¬flies(tux))A10 ({¬flies(tweety)}, ¬flies(tweety))A11 ({penguin(tweety)}, bird(tweety))A12 ({penguin(tweety)}, abnormal(tweety))A13 ({bird(tweety), ¬abnormal(tweety)}, flies(tweety))A14 ({penguin(tux)}, bird(tux))A15 ({penguin(tux)}, abnormal(tux))A16 ({bird(tux), ¬abnormal(tux)}, flies(tux))f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 12
  19. 19. Tweety: from Prolog to Arguments (the Dungsway)A5 A4A13A6 A11A12 A8A10A2 A1A14 A3A15 A7A16 A9f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 12
  20. 20. Argumentation Semantics (Courtesy of M.Giacomin)Argument evaluation: given an argumentation framework, determine thejustication state (defeat status) of arguments. In particular, whatargument emerge undefeated from the conict, i.e. are acceptable?• Specification of a method for argument evaluation, or ofcriteria to determine, given a set of arguments, their “defeat status”Argumentation FrameworkSemanticsDefeat statusDefeat statusUndefeatedDefeatedProvisionally Defeatedf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 13
  21. 21. Extension-based Semantics (Courtesy of M.Giacomin)Set of extensions ℰS(AF)Argumentation framework AFSemantics SDefeat/Justification Statusf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 14
  22. 22. Complete Semantics (Courtesy of M. Giacomin)Acceptabilityα acceptable w.r.t. (“defended by”) S• all attackers of α are attacked by SAdmissible set S• conflict-free• every element acceptable w.r.t. S(defends all of its elements)αSIFalso includes allacceptable elementsw.r.t. itselfCompleteextensionComplete semanticsAll traditional semanticsselect complete extensionsf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 15
  23. 23. Labelling Approach [Caminada and Gabbay, 2009](Courtesy of M. Caminada)argument labels: in, out, undecAn argument is iniff all its defeaters are outAn argument is outiff it has a defeater that is inf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 16
  24. 24. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  25. 25. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  26. 26. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  27. 27. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  28. 28. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  29. 29. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  30. 30. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  31. 31. Labelling Approach: Examples (Courtesy of M.Caminada)ABCA BDCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 17
  32. 32. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  33. 33. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  34. 34. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  35. 35. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  36. 36. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  37. 37. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  38. 38. Labelling Approach: Examples (Courtesy of M.Caminada)DBAA BCf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 18
  39. 39. Semantics and Labelling (Courtesy of M.Caminada)restriction on Dung-stylecompl. labeling semanticsno restrictions complete semanticsempty undec stable semanticsmaximal in preferred semanticsmaximal out preferred semanticsmaximal undec grounded semanticsminimal in grounded semanticsminimal out grounded semanticsminimal undec semi-stable semanticsf.cerutti@abdn.ac.uk Tuesday 18th December, 2012 19
  40. 40. Nixon: LabellingsA5 A6A3 A1 A4 A2A7quaker(nixon), republican(nixon), pacifist(nixon)f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 20
  41. 41. Nixon: LabellingsA5 A6A3 A1 A4 A2A7quaker(nixon), republican(nixon), ¬pacifist(nixon)f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 20
  42. 42. Nixon: LabellingsA5 A6A3 A1 A4 A2A7quaker(nixon), republican(nixon)f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 20
  43. 43. Tweety: LabellingsA5 A4A13A6 A11A12 A8A10A2 A1A14 A3A15 A7A16 A9bird(tweety), ¬penguin(tweety), ¬abnormal(tweety), flies(tweety)penguin(tux), bird(tux), abnormal(tux), ¬flies(tux)f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 21
  44. 44. ConclusionsArgumentation as a way for encompassing common sensereasoningArgumentation as a way for encompassing non-monotonicreasoningArgumentation as a way for encompassing defeasible reasoningFundamental elements:Structure of arguments;Structure of attacks (notion of defeat);Way for determining the outcome of the reasoning(semantics/labellings).f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 22
  45. 45. References I[Alechina, 2011] Alechina, N. (2011).Knowledge representation and reasoning 2011-2012: G53KRR course slides.http://www.cs.nott.ac.uk/~nza/G53KRR/.[Berners-Lee and Fischetti, 2000] Berners-Lee, T. and Fischetti, M. (2000).Weaving the Web.HarperBusiness.[Besnard and Hunter, 2008] Besnard, P. and Hunter, A. (2008).Elements of Argumentation.The MIT Press.[Black et al., 2009] Black, E., Hunter, A., and Pan., J. Z. (2009).An Argument-based Approach to Using Multiple Ontologies.In the Proc. of the 3rd International Conference on Scalable Uncertainty Management (SUM2009).[Bondarenko et al., 1993] Bondarenko, A., Toni, F., and Kowalski, R. (1993).An assumption-based framework for non-monotonic reasoning.In Nerode, A. and Pereira, L., editors, Proceedings Second International Workshop on LogicProgramming and Non-Monotonic Reasoning. MIT Press.[Brachman and Levesque, 2004a] Brachman, R. and Levesque, H. (2004a).Knowledge Representation and Reasoning.Elsevier.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 23
  46. 46. References II[Brachman and Levesque, 2004b] Brachman, R. and Levesque, H. (2004b).Knowledge representation and reasoning: Overhead slides.http://www.cs.toronto.edu/~hector/PublicKRSlides.pdf.[Caminada and Gabbay, 2009] Caminada, M. and Gabbay, D. M. (2009).A logical account of formal argumentation.Studia Logica, 93(2-3):109145.[Dung, 1995] Dung, P. M. (1995).On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logicprogramming, and n-person games.Articial Intelligence, 77(2):321357.[Flouris et al., 2006] Flouris, G., Huang, Z., Pan, J. Z., Plexousakis, D., and Wache, H. (2006).Inconsistencies, negations and changes in ontologies.In 21st AAAI Conf., pages 12951300.[Gaertner and Toni, 2008] Gaertner, D. and Toni, F. (2008).Hybrid argumentation and its properties.In Proceedings of COMMA 2008.[Herman, 2011] Herman, I. (2011).Introduction to the semantic web.http://www.w3.org/2011/Talks/0606-SemTech-Tut-IH/Talk.pdf.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 24
  47. 47. References III[Horrocks and Sattler, 2002] Horrocks, I. and Sattler, U. (2002).Description logics - basics, applications, and more (tutorial at ecai-2002).http://www.cs.man.ac.uk/~horrocks/Slides/ecai-handout.pdf.[McCune, 2010] McCune, W. (20052010).Prover9 and mace4.http://www.cs.unm.edu/~mccune/prover9/.[Prakken, 2011] Prakken, H. (2011).An overview of formal models of argumentation and their application in philosophy.Studies in Logic, 4:6586.[Prakken and Vreeswijk, 2001] Prakken, H. and Vreeswijk, G. A. W. (2001).Logics for defeasible argumentation.In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, Second Edition.Kluwer Academic Publishers, Dordrecht.[Reiter, 1980] Reiter, R. (1980).A logic for default reasoning.Articial Intelligence, 13(1-2):81 132.[van Eemeren et al., 1996] van Eemeren, F. H., Grootendorst, R., Johnson, R. H., Plantin, C., Walton,D. N., Willard, C. A., Woods, J., and Zarefsky, D. (1996).Fundamentals of Argumentation Theory. A Handbook of Historical Backgrounds andContemporary Developments.Lawrence Erlbaum Associates.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 25
  48. 48. References IV[van Harmelen et al., 2007] van Harmelen, F., van Harmelen, F., Lifschitz, V., and Porter, B. (2007).Handbook of Knowledge Representation.Elsevier Science, San Diego, USA.[W3C, 2012] W3C (2012).Rdf tutorial.http://www.w3schools.com/rdf/default.asp.[Walton, 1996] Walton, D. N. (1996).Argumentation Schemes for Presumptive Reasoning.Lawrence Erlbaum Associates.f.cerutti@abdn.ac.uk Tuesday 18th December, 2012 26

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