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

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Presentation on theme: "{ Kevin T. Kelly, Hanti Lin } Carnegie Mellon University Responsive -ness CMU."— Presentation transcript:

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

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4 Probabilistic conditioning

5 Probabilistic conditioning Acceptance

6 Probabilistic conditioning Acceptance Propositional belief revision

7 Probabilistic conditioning Acceptance Propositional belief revision Acceptance

8 Probabilistic conditioning Acceptance Propositional belief revision Acceptance = Conditioning + acceptance = acceptance + revision

9 Acceptance Propositional belief revision Probabilistic conditioning

10 Acceptance Tie shoes? Probabilistic conditioning Eat breakfast? Get out of bed?

11 Acceptance Probabilistic conditioning Help! Bayes! Invest? Tie shoes? Eat breakfast? Get out of bed?

12 Acceptance Condition only once Tie shoes? Eat breakfast? Get out of bed? Invest?

13 Acceptance Thanks. Ill take it from here Tie shoes? Eat breakfast? Get out of bed? Invest? Condition only once TV?

14 Acceptance Repeated conditioning Tie shoes? Eat breakfast? Get out of bed? Invest? TV?

15 Acceptance Tie shoes? Eat breakfast? Get out of bed? Invest? Condition only once TV?

16 Steadiness = Just conjoin the new data with your old propositions if the two are consistent E B LMU

17 B C A

18 C A

19 A BC Yoav Shoham

20 A C

21 AC

22 LMU CMU

23 Inconsistency is accepted nowhere.

24 Every atom A is accepted over some open neighborhood.

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

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

27 C C C C C

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

29 A v C A C B v C T B A v B A v C A C B v C T B A v B LMUCMU

30 No sensible acceptance rule is both steady and tracks conditioning. consumer designer Sorry. You cant have both.

31 A BC A A v B p p(.|A v B)

32 A BC A A v B p p(.|A v B) Accept A. Learn its consequence A v B. If you track, you retract A!

33 If you accept a hypothesis, dont retract it when you learn what it entails (i.e. predicts).

34 A v B A v C A B C B v C T

35 p A B

36 A B B p p(.|B)

37 A B A p

38 A B A B T p You will accept A v B no matter whether B or B is learned. But if you track, you dont accept A v B.

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

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

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

42 Nogot Nobody Somebody Gettier case Havit = the Truth

43 Havit = the Truth Nogot Nobody Somebody

44 Havit Nogot Nobody Somebody is retracted but not refuted.

45 Havit Nogot Nobody Somebody

46 Havit NogotHavit Nobody Nogot Nobody

47 Trust what you accepted Re-examine your reasons Havit NogotHavit Nobody Nogot Nobody

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

49 A BC

50 A BC

51 A BC

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57 Close classical logic under Partial negation

58 Logical Closure = Sub-crystals

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67 Acpt

68 The CMU rule is the only rule that preserves logical structure (entailment, disjunction and consistent conjunction). Acpt

69 The CMU rule + Shoham revision satisfies sensible tracks conditioning avoids both new paradoxes represents no-false-lemma Gettier cases unique geo-logical representation

70 The CMU rule + Shoham revision satisfies sensible tracks conditioning avoids both new paradoxes represents no-false-lemma Gettier cases unique geo-logical representation


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