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CMU Design Goals

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CMU Design Goals

{ Kevin T. Kelly ,Hanti Lin }

Carnegie Mellon University

CMU

Responsive-ness

Probabilistic

conditioning

Probabilistic

conditioning

Acceptance

Probabilistic

conditioning

Acceptance

Propositional

belief revision

Probabilistic

conditioning

Acceptance

Acceptance

Propositional

belief revision

Probabilistic

conditioning

Acceptance

=

Acceptance

Propositional

belief revision

Conditioning + acceptance = acceptance + revision

Probabilistic

conditioning

Propositional

belief revision

Acceptance

Probabilistic

conditioning

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

Help!

Bayes!

Probabilistic

conditioning

Invest?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

Condition only once

Invest?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

Thanks.

I’ll take it from here

Condition only once

Invest?

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

Invest?

Repeated conditioning

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

Condition only once

Invest?

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance

- Steadiness = “Just conjoin the new data with your old propositions if the two are consistent”

LMU

E

B

A

B C

A

C

- YoavShoham

A

B

C

- YoavShoham

A

C

- YoavShoham

A

C

LMU

CMU

Inconsistency is accepted nowhere.

Every atom Ais accepted over some open neighborhood.

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

- A v B

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

C

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

C

C

C

C

C

Sensible = all four properties.

- A v B

C

C

C

C

C

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

- No sensibleacceptance rule is both steadyand tracks conditioning.

Sorry. You can’t have both.

designer

consumer

A

p(.|A v B)

A

p

A v B

B

C

A

Accept A.

Learn its consequenceA v B.

If you track, you retractA!

p(.|A v B)

A

p

A v B

B

C

If you accept a hypothesis, don’t retract it when you learn what it entails(i.e. predicts).

0.9

A

0.8

A v C

A v B

T

B

C

B v C

A

p

B

A

p

p(.|B)

B

B

A

A

p(.|B)

p

B

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

Accept a hypothesis, if you will accept it

no matter whether E is learned or E is learned.

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

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

Nobody

Gettier case

Havit

= the Truth

Somebody

Nogot

Nobody

Havit

= the Truth

Somebody

Nogot

Nobody

“Somebody”

is retracted but

not refuted.

Havit

Somebody

Nogot

Nobody

Havit

Somebody

Nogot

Nobody

Nogot

Havit

Nobody

Nogot

Havit

Nobody

“Re-examine your reasons”

Nogot

Havit

Nobody

“Trust what you accepted”

Nogot

Havit

Geometry

Logic

(0, 1, 0)

Acpt

(1/3, 1/3, 1/3)

B

A

C

(0, 0, 1)

(1, 0, 0)

A

B

C

A

B

C

A

B

C

111

110

101

011

010

001

100

000

111

110

101

011

010

001

100

000

111

110

101

011

010

001

100

000

111

110

101

011

010

001

100

000

111

110

101

011

010

001

100

000

Close classical logic under

Partial negation

Logical Closure =

Sub-crystals

Acpt

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

Acpt

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

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