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Explaining Answer Sets in Argumentative Terms Claudia Schulz - PowerPoint PPT Presentation

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Explaining Answer Sets in Argumentative Terms Claudia Schulz Imperial College London, UK 24th February, 2015 patient is shortsighted patient is shortsighted glasses? laser surgery? contact lenses? intraocular lenses? patient is

  1. ABA-Based Answer Set Justifications - an overview translate Logic Program ABA framework compute derive answer sets stable extensions 𝑇 𝐹 𝑚 ∈ 𝑇

  2. ABA-Based Answer Set Justifications - an overview translate Logic Program ABA framework compute derive answer sets stable extensions 𝑇 𝐹 construct 𝑚 ∈ 𝑇 … ⊢ 𝑚 ∈ 𝐹

  3. ABA-Based Answer Set Justifications - an overview translate Logic Program ABA framework compute derive answer sets stable extensions 𝑇 𝐹 construct 𝑚 ∈ 𝑇 … ⊢ 𝑚 ∈ 𝐹 construct explains Attack Tree

  4. ABA-Based Answer Set Justifications - an overview translate Logic Program ABA framework compute derive answer sets stable extensions 𝑇 𝐹 construct 𝑚 ∈ 𝑇 … ⊢ 𝑚 ∈ 𝐹 construct explains Attack Tree construct LABAS Justification

  5. ABA-Based Answer Set Justifications - an overview translate Logic Program ABA framework compute derive answer sets stable extensions 𝑇 𝐹 construct 𝑚 ∉ 𝑇 … ⊢ 𝑚 ∉ 𝐹 construct explains Attack Tree construct LABAS Justification

  6. Attack Trees

  7. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a

  8. Attack Trees

  9. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a

  10. Attack Trees

  11. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d

  12. Attack Trees

  13. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + 14 : ( ∅ , { e } ) ⊢ e

  14. Attack Trees

  15. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a

  16. Attack Trees A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  17. laser surgery! Answer Set Programming (ASP) intraocular lenses!

  18. Why is laser surgery not part of the solution? Answer Set: { shortSighted , afraidToTouchEyes , student , likesSports , tightOnMoney , correctiveLens , caresAboutPracticality , intraocularLens }

  19. Why is laser surgery not part of the solution? Answer Set: { shortSighted , afraidToTouchEyes , student , likesSports , tightOnMoney , correctiveLens , caresAboutPracticality , intraocularLens } A 1 − : ( { shortSighted } , { not tightOnMoney , not correctiveLens } ) ⊢ laserSurgery A 2+ : ( { student } , { not richParents } ) ⊢ tightOnMoney

  20. Why is intraocular lens part of the solution? Answer Set: { shortSighted , afraidToTouchEyes , student , likesSports , tightOnMoney , correctiveLens , caresAboutPracticality , intraocularLens }

  21. Why is intraocular lens part of the solution? Answer Set: { shortSighted , afraidToTouchEyes , student , likesSports , tightOnMoney , correctiveLens , caresAboutPracticality , intraocularLens } A 3+ : ( { shortSighted } , { not laserSurgery , not glasses , not contactLens } ) ⊢ intraocularLens A 1 − : ( . . . ) ⊢ laserSurgery A − 4 : ( . . . , not afraidToTouchEyes , . . . ) ⊢ contactLens A 2+ : ( . . . ) ⊢ tightOnMoney A + 5 : ( { afraidToTouchEyes } , ∅ ) ⊢ afraidToTouchEyes A − 6 : ( . . . , not caresAboutPracticality , . . . ) ⊢ glasses A + 7 : ( { likesSports } , ∅ ) ⊢ caresAboutPracticality

  22. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  23. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9

  24. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  25. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm

  26. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  27. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11

  28. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  29. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + not c + not d + asm asm

  30. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  31. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + not c + not d + asm asm − c − A 12

  32. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  33. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + not c + not d + asm asm − c − A 12 − not e − asm

  34. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  35. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + not c + not d + asm asm − c − A 12 − not e − asm + e + fact

  36. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  37. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + not c + not d + asm asm − − c − d − A 12 A 13 − not e − asm + e + fact

  38. Labelled ABA-Based Answer Set (LABAS) Justifications A − 9 : ( { not ¬ a } , ∅ ) ⊢ a A + 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d A + A + 14 : ( ∅ , { e } ) ⊢ e 11 : ( { not c , not d } , ∅ ) ⊢ ¬ a A − A − 12 : ( { not e } , ∅ ) ⊢ c 13 : ( { not ¬ a } , ∅ ) ⊢ d . . . A + 14 : ( ∅ , { e } ) ⊢ e

  39. Labelled ABA-Based Answer Set (LABAS) Justifications a − A 9 − not ¬ a − asm + ¬ a + A 11 + + − not c + not d + asm asm − − c − d − A 12 A 13 − not e − asm + e + fact

  40. laser surgery! Answer Set Programming (ASP) intraocular lenses!

  41. Why is laser surgery not part of the solution? Attack Tree A 1 − : ( { shortSighted } , { not tightOnMoney , not correctiveLens } ) ⊢ laserSurgery A 2+ : ( { student } , { not richParents } ) ⊢ tightOnMoney

  42. Why is laser surgery not part of the solution? Attack Tree A 1 − : ( { shortSighted } , { not tightOnMoney , not correctiveLens } ) ⊢ laserSurgery A 2+ : ( { student } , { not richParents } ) ⊢ tightOnMoney ABA-Based Answer Set (ABAS) Justification laserSurgery − A 1 − not tightOnMoney − asm + tightOnMoney + A 2 + + student + not richParents + asm fact

  43. Why is intraocular lens part of the solution? Attack Tree A 3+ : ( { shortSighted } , { not laserSurgery , not glasses , not contactLens } ) ⊢ intraocularLens A 1 − : ( . . . ) ⊢ laserSurgery A − 4 : ( . . . , not afraidToTouchEyes , . . . ) ⊢ contactLens A 2+ : ( . . . ) ⊢ tightOnMoney A + 5 : ( { afraidToTouchEyes } , ∅ ) ⊢ afraidToTouchEyes A − 6 : ( . . . , not caresAboutPracticality , . . . ) ⊢ glasses A + 7 : ( { likesSports } , ∅ ) ⊢ caresAboutPracticality

  44. Why is intraocular lens part of the solution? ABA-Based Answer Set (ABAS) Justification intraocularLens + A 3 + + + + shortSighted + not contactLens + fact not laserSurgery + not glasses + asm asm asm − − − laserSurgery − contactLens − glasses − A 4 A 1 A 6 − − − not afraidToTouchEyes − not tightOnMoney − not caresAboutPracticality − asm asm asm + + + afraidToTouchEyes + tightOnMoney + caresAboutPracticality + fact A 2 + A 7 + + student + not richParents + fact likesSports + asm fact

  45. Other justificiation approaches LABAS Justification Off-line Justification (Pontelli, Son, Elkhatib) b + A 1 + + not a + e + asm fact − + a − A 2 − not b − asm

  46. Other justificiation approaches LABAS Justification Off-line Justification (Pontelli, Son, Elkhatib) a − A 2 − not b − asm + − b + A 1 + + not a + e + asm fact

  47. Conclusion Answer Set Programming (ASP) + ABA-Based Answer Set Justification =

  48. Conclusion Answer Set Programming (ASP) + ABA-Based Answer Set Justification = laser surgery! intraocular lenses!

  49. Future Work So far: restricted do consistent logic programs

  50. Future Work So far: restricted do consistent logic programs ◮ find source of inconsistency in a logic program ◮ debug the logic program ⇒ more existing literature

  51. IMPERIAL COLLEGE COMPUTER Computational Checking Model and Verication • Systems of Machine Theory • Engineering Software • Intelligence Articial • Learning Logic nd iccsw.doc.ac.uk visit workshop, the about more out To • Databases • Graphics Computer • Languages Programming and • STUDENT WORKSHOP 2015 • Tool papers describing the design, functionality and applicability of a software tool London, United Kingdom 24-25 September 2015 following: Areas of interest cover all elds of research in computer science, including (but not limited to) the • Papers that synthesise the state of the art in a particular topic of computer science • A survey track featuring • Technical papers focused on current topics in computer science To • A traditional track featuring The workshop offers: will be hosted by the Department of Computing at Imperial College London. review papers and take part in the event. It is a workshop organised by students for students. The workshop specic research areas, we encourage doctoral students from all disciplines in computer science to submit, for doctoral students in computing. While most conferences and workshops in academia solely cater for The fth Imperial College Computing Student Workshop (ICCSW) aims to provide an international forum iccsw@imperial.ac.uk contact Communications international forum for doctoral students in and Networks • Systems Computer • computing. Show us, and everybody else. ICCSW is an workshop Have something interesting in development? email: please questions, any with organisers In associa�on with:

  52. Explaining Answer Sets in Argumentative Terms Questions?!

  53. ASP Semantics Why not simply display the derivation? The answer set of P ( AS ( P )), is the smallest set S ⊆ Lit P s.t.: 1. for any clause l 0 ← l 1 , . . . , l m in P : if l 1 , . . . , l m ∈ S then l 0 ∈ S 2. S = Lit P if S contains complementary literals a and ¬ a . ⇒ For P without NAF literals For P with NAF literals S is an answer set of P if it is the answer set of the reduct P S , i.e. if S = AS ( P S ).

  54. ASP Semantics It all depends on the reduct... For P possibly with NAF literals and for any S ⊆ Lit P The reduct P S is obtained from P by deleting: 1. all clauses with not l in their bodies where l ∈ S 2. all NAF literals in the remaining clauses.

  55. ASP Semantics It all depends on the reduct... For P possibly with NAF literals and for any S ⊆ Lit P The reduct P S is obtained from P by deleting: 1. all clauses with not l in their bodies where l ∈ S 2. all NAF literals in the remaining clauses. Example a ← not ¬ a ← ¬ a , not c , not e a ¬ a ← not c , not d ← c not e d ← not ¬ a ← e

  56. ASP Semantics It all depends on the reduct... For P possibly with NAF literals and for any S ⊆ Lit P The reduct P S is obtained from P by deleting: 1. all clauses with not l in their bodies where l ∈ S 2. all NAF literals in the remaining clauses. Example a ← not ¬ a ← ¬ a , not c , not e a ¬ a ← not c , not d e ∈ S ← c not e d ← not ¬ a ← e

  57. ASP Semantics It all depends on the reduct... For P possibly with NAF literals and for any S ⊆ Lit P The reduct P S is obtained from P by deleting: 1. all clauses with not l in their bodies where l ∈ S 2. all NAF literals in the remaining clauses. Example a ← not ¬ a ← ¬ a , not c , not e a ¬ a ← not c , not d e ∈ S ← c not e d ← not ¬ a ← e

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