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

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Probabilistic conditioning

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Probabilistic conditioning Acceptance

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Probabilistic conditioning Acceptance Propositional belief revision

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Probabilistic conditioning Acceptance Propositional belief revision Acceptance

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

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Acceptance Propositional belief revision Probabilistic conditioning

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

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

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

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

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

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

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

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B C A

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C A

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A BC Yoav Shoham

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A C

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AC

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LMU CMU

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Inconsistency is accepted nowhere.

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Every atom A is accepted over some open neighborhood.

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

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

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C C C C C

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

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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

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

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

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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!

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

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

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p A B

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A B B p p(.|B)

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A B A p

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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.

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

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

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

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Nogot Nobody Somebody Gettier case Havit = the Truth

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Havit = the Truth Nogot Nobody Somebody

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Havit Nogot Nobody Somebody is retracted but not refuted.

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Havit Nogot Nobody Somebody

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Havit NogotHavit Nobody Nogot Nobody

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

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

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A BC

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A BC

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A BC

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Close classical logic under Partial negation

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Logical Closure = Sub-crystals

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Acpt

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

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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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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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