Cmu design goals
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CMU Design Goals. { Kevin T. Kelly , Hanti Lin } Carnegie Mellon University. CMU. Responsive-ness. Qualitative Reasoning that Tracks Conditioning. Qualitative Reasoning that Tracks Conditioning. Qualitative Reasoning that Tracks Conditioning. Probabilistic conditioning.

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CMU Design Goals

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Cmu design goals

CMU Design Goals

{ Kevin T. Kelly ,Hanti Lin }

Carnegie Mellon University

CMU

Responsive-ness


Qualitative reasoning that tracks conditioning

Qualitative Reasoning that Tracks Conditioning


Qualitative reasoning that tracks conditioning1

Qualitative Reasoning that Tracks Conditioning


Qualitative reasoning that tracks conditioning2

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning


Qualitative reasoning that tracks conditioning3

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Acceptance


Qualitative reasoning that tracks conditioning4

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Acceptance

Propositional

belief revision


Qualitative reasoning that tracks conditioning5

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Acceptance

Acceptance

Propositional

belief revision


Qualitative reasoning that tracks conditioning6

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Acceptance

=

Acceptance

Propositional

belief revision

Conditioning + acceptance = acceptance + revision


Pre established harmony

Pre-established Harmony

Probabilistic

conditioning

Propositional

belief revision

Acceptance


Cheap bayes with harmony

Cheap Bayes With Harmony

Probabilistic

conditioning

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


When you need bayes

When You Need Bayes…

Help!

Bayes!

Probabilistic

conditioning

Invest?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


Call him then

Call Him Then

Condition only once

Invest?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


Call him then1

Call Him Then

Thanks.

I’ll take it from here

Condition only once

Invest?

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


Expensive bayes without harmony

Expensive Bayes Without Harmony

Invest?

Repeated conditioning

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


Cheap bayes with harmony1

Cheap Bayes with Harmony

Condition only once

Invest?

TV?

Eat breakfast?

Tie shoes?

Get out of bed?

Acceptance


Lmu design principle steadiness

LMU Design Principle: Steadiness

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

LMU

E

B


Agm is steady

AGM is Steady

A

B C


Agm is steady1

AGM is Steady

A

C


Non steady revision rule

Non-steady Revision Rule

  • YoavShoham

A

B

C


Non steady revision rule1

Non-steady Revision Rule

  • YoavShoham

A

C


Non steady revision rule2

Non-steady Revision Rule

  • YoavShoham

A

C


Some shared design principles

Some Shared Design Principles

LMU

CMU


Consistency

Consistency

Inconsistency is accepted nowhere.


Non skepticism

Non-skepticism

Every atom Ais accepted over some open neighborhood.


Non opinionation

Non-Opinionation

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

  • A v B


Corner monotonicity

Corner-monotonicity

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

C


Corner monotonicity1

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


Sensible rules

Sensible Rules

Sensible = all four properties.

  • A v B

C

C

C

C

C


Both are sensible

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


Incompatibility theorem

Incompatibility Theorem

  • No sensibleacceptance rule is both steadyand tracks conditioning.

Sorry. You can’t have both.

designer

consumer


A new paradox of acceptance

A New Paradox of Acceptance

A

p(.|A v B)

A

p

A v B

B

C


A new paradox of acceptance1

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


Cautious monotonicity hypothetico deductive monotonicity

“Cautious” Monotonicity= Hypothetico-Deductive Monotonicity

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


A better idea

A Better Idea?

0.9

A

0.8

A v C

A v B

T

B

C

B v C


Another new paradox of acceptance

Another New Paradox of Acceptance

A

p

B


Another new paradox of acceptance1

Another New Paradox of Acceptance

A

p

p(.|B)

B

B


Another new paradox of acceptance2

Another New Paradox of Acceptance

A

A

p(.|B)

p

B


Another new paradox of acceptance3

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


Case reasoning

Case Reasoning

Accept a hypothesis, if you will accept it

no matter whether E is learned or E is learned.


Theorem

Theorem

  • The CMU rule + Shoham revision (non-steady) satisfies:

  •  sensible

  •  tracks conditioning

  •  avoids both new paradoxes


Partial converse

Partial Converse

  •  Shoham revision

  • sensible

  • tracks conditioning

  • Implies

  • CMU rule + avoidance of the 2 new paradoxes.


Gettier without false lemmas

Gettier Without False Lemmas

Nobody

Gettier case

Havit

= the Truth

Somebody

Nogot


Cmu rule represents it

CMU Rule Represents it

Nobody

Havit

= the Truth

Somebody

Nogot


Cmu rule is unsteady

CMU Rule is Unsteady!

Nobody

“Somebody”

is retracted but

not refuted.

Havit

Somebody

Nogot


Gettier unsteadiness zones

Gettier/Unsteadiness Zones

Nobody

Havit

Somebody

Nogot


Shoham revision vs agm revision

Shoham Revision vs. AGM Revision

Nobody

Nogot

Havit

Nobody

Nogot

Havit


Shoham revision vs agm revision1

Shoham Revision vs. AGM Revision

Nobody

“Re-examine your reasons”

Nogot

Havit

Nobody

“Trust what you accepted”

Nogot

Havit


Structure preservation

Structure Preservation

Geometry

Logic

(0, 1, 0)

Acpt

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

B

A

C

(0, 0, 1)

(1, 0, 0)


Some clear cases

Some Clear Cases

A

B

C


Interpolation

Interpolation

A

B

C


What about here

What About Here?

A

B

C


Probability lives in the unit cube

Probability Lives in the Unit Cube

111

110

101

011

010

001

100

000


Classical logic lives on the corners

Classical Logic Lives on the Corners

111

110

101

011

010

001

100

000


But what if logic filled the cube

But What if Logic Filled the Cube?

111

110

101

011

010

001

100

000


Classical negation

Classical Negation

111

110

101

011

010

001

100

000


Partial negation

Partial Negation

111

110

101

011

010

001

100

000


Geologic

Geologic

Close classical logic under

Partial negation


Geological entailment

Geological Entailment

Logical Closure =

Sub-crystals


Probability is a surface in geologic

Probability is a Surface in Geologic


Classical principle of indifference

Classical Principle of Indifference


Principle of indifference completed

Principle of Indifference Completed


Probalogic projection of geologic

Probalogic = Projection of Geologic


Probalogic as geologic in perspective

Probalogic as Geologic in Perspective


Probalogic as geologic in perspective1

Probalogic as Geologic in Perspective


Projection of geological consequences

Projection of Geological Consequences


Probalogic

= Probalogic


Acceptance should preserve logical structure

Acceptance Should Preserve Logical Structure

Acpt


Representation theorem

Representation Theorem

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

Acpt


Feature checklist for the cmu rule

Feature Checklist for the CMU Rule

  • The CMU rule + Shoham revision satisfies

  •  sensible

  •  tracks conditioning

  • avoids both new paradoxes

  • represents no-false-lemma Gettier cases

  • unique geo-logical representation


Thank you

THANK YOU!

  • 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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