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Enhancing Qualitative Reasoning Through Probabilistic Conditioning at CMU

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70 diapositives · 839 Views · Jul 29, 2014

This research explores the integration of qualitative reasoning and probabilistic conditioning, focusing on acceptance and belief revision frameworks. By investigating various design principles, the study aims to identify strategies that ensure consistency while circumventing paradoxes in probabilistic reasoning. Key themes include the application of LMU design principles to qualitative reasoning, examining how acceptance can be structured to maintain both steady beliefs and track conditioning. This work ultimately seeks to provide frameworks that can enhance decision-making processes in uncertain environments.

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  1. CMU Design Goals { Kevin T. Kelly ,Hanti Lin } Carnegie Mellon University CMU Responsive-ness

  2. Qualitative Reasoning that Tracks Conditioning

  3. Qualitative Reasoning that Tracks Conditioning

  4. Qualitative Reasoning that Tracks Conditioning Probabilistic conditioning

  5. Qualitative Reasoning that Tracks Conditioning Probabilistic conditioning Acceptance

  6. Qualitative Reasoning that Tracks Conditioning Probabilistic conditioning Acceptance Propositional belief revision

  7. Qualitative Reasoning that Tracks Conditioning Probabilistic conditioning Acceptance Acceptance Propositional belief revision

  8. Qualitative Reasoning that Tracks Conditioning Probabilistic conditioning Acceptance = Acceptance Propositional belief revision Conditioning + acceptance = acceptance + revision

  9. Pre-established Harmony Probabilistic conditioning Propositional belief revision Acceptance

  10. Cheap Bayes With Harmony Probabilistic conditioning Eat breakfast? Tie shoes? Get out of bed? Acceptance

  11. When You Need Bayes… Help! Bayes! Probabilistic conditioning Invest? Eat breakfast? Tie shoes? Get out of bed? Acceptance

  12. Call Him Then Condition only once Invest? Eat breakfast? Tie shoes? Get out of bed? Acceptance

  13. Call Him Then Thanks. I’ll take it from here Condition only once Invest? TV? Eat breakfast? Tie shoes? Get out of bed? Acceptance

  14. Expensive Bayes Without Harmony Invest? Repeated conditioning TV? Eat breakfast? Tie shoes? Get out of bed? Acceptance

  15. Cheap Bayes with Harmony Condition only once Invest? TV? Eat breakfast? Tie shoes? Get out of bed? Acceptance

  16. LMU Design Principle: Steadiness • Steadiness = “Just conjoin the new data with your old propositions if the two are consistent” LMU E B

  17. AGM is Steady A B C

  18. AGM is Steady A C

  19. Non-steady Revision Rule • YoavShoham A B C

  20. Non-steady Revision Rule • YoavShoham A C

  21. Non-steady Revision Rule • YoavShoham A C

  22. Some Shared Design Principles LMU CMU

  23. Consistency Inconsistency is accepted nowhere.

  24. Non-skepticism Every atom Ais accepted over some open neighborhood.

  25. Non-Opinionation There is an open neighborhood over which you accept a non-atom and nothing stronger. • A v B

  26. Corner-monotonicity If an atom is accepted, it continues to be accepted along the straight line to the corresponding corner. C

  27. Corner-monotonicity If an atom is accepted, it continues to be accepted along the straight line to the corresponding corner. C C C C C

  28. Sensible Rules Sensible = all four properties. • A v B C C C C C

  29. Both are Sensible! CMU LMU A A A v C A v C A v B A v B T T B B C C B v C B v C

  30. Incompatibility Theorem • No sensibleacceptance rule is both steadyand tracks conditioning. Sorry. You can’t have both. designer consumer

  31. A New Paradox of Acceptance A p(.|A v B) A p A v B B C

  32. A New Paradox of Acceptance A Accept A. Learn its consequenceA v B. If you track, you retractA! p(.|A v B) A p A v B B C

  33. “Cautious” Monotonicity= Hypothetico-Deductive Monotonicity If you accept a hypothesis, don’t retract it when you learn what it entails(i.e. predicts).

  34. A Better Idea? 0.9 A 0.8 A v C A v B T B C B v C

  35. Another New Paradox of Acceptance A p B

  36. Another New Paradox of Acceptance A p p(.|B) B B

  37. Another New Paradox of Acceptance A A p(.|B) p B

  38. Another New Paradox of Acceptance A You will acceptA v Bno matterwhether B or B is learned. But if you track, you don’t accept A v B. A p(.|B) p T p(.|B) B B

  39. Case Reasoning Accept a hypothesis, if you will accept it no matter whether E is learned or E is learned.

  40. Theorem • The CMU rule + Shoham revision (non-steady) satisfies: •  sensible •  tracks conditioning •  avoids both new paradoxes

  41. Partial Converse •  Shoham revision • sensible • tracks conditioning • Implies • CMU rule + avoidance of the 2 new paradoxes.

  42. Gettier Without False Lemmas Nobody Gettier case Havit = the Truth Somebody Nogot

  43. CMU Rule Represents it Nobody Havit = the Truth Somebody Nogot

  44. CMU Rule is Unsteady! Nobody “Somebody” is retracted but not refuted. Havit Somebody Nogot

  45. Gettier/Unsteadiness Zones Nobody Havit Somebody Nogot

  46. Shoham Revision vs. AGM Revision Nobody Nogot Havit Nobody Nogot Havit

  47. Shoham Revision vs. AGM Revision Nobody “Re-examine your reasons” Nogot Havit Nobody “Trust what you accepted” Nogot Havit

  48. Structure Preservation Geometry Logic (0, 1, 0) Acpt (1/3, 1/3, 1/3) B A C (0, 0, 1) (1, 0, 0)

  49. Some Clear Cases A B C

  50. Interpolation A B C