CMU DESIGN GOALS

{ Kevin T. Kelly , Hanti Lin }Carnegie Mellon University

Responsive-ness

CMU

Qualitative Reasoning that Tracks Conditioning

Qualitative Reasoning that Tracks Conditioning

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

Acceptance

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

AcceptancePropositional

belief revision

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

AcceptancePropositional

belief revision

Acceptance

Qualitative Reasoning that Tracks Conditioning

Probabilistic

conditioning

AcceptancePropositional

belief revision

Acceptance=

Conditioning + acceptance = acceptance + revision

Pre-established Harmony

Acceptance

Propositional

belief revisio

n

Probabilistic

conditioning

Cheap Bayes With Harmony

Acceptance

Tie shoes?

Probabilistic

conditioning

Eat breakfast?

Get out of bed?

When You Need Bayes…

Acceptance

Probabilistic

conditioning

Help! Bayes!

Invest?

Tie shoes?

Eat breakfast?

Get out of bed?

Call Him Then

Acceptance

Condition only once

Tie shoes?

Eat breakfast?

Get out of bed?

Invest?

Call Him Then

Acceptance

Thanks.I’ll take it from here

Tie shoes?

Eat breakfast?

Get out of bed?

Invest?Condition only once

TV?

Expensive Bayes Without Harmony

Acceptance

Repeated conditioning

Tie shoes?

Eat breakfast?

Get out of bed?

Invest?

TV?

Cheap Bayes with Harmony

Acceptance

Tie shoes?

Eat breakfast?

Get out of bed?

Invest?Condition only once

TV?

LMU Design Principle: Steadiness

Steadiness = “Just conjoin the new data with

your old propositions if the two are consistent”

EB

LMU

AGM is Steady

B C

A

AGM is Steady

C

A

Non-steady Revision Rule

A

B C

Yoav Shoham

Non-steady Revision Rule

A

C

Yoav Shoham

Non-steady Revision Rule

A C

Yoav Shoham

Some Shared Design Principles

LMU

CMU

Consistency

Inconsistency is accepted nowhere.

Non-skepticism

Every atom A is accepted over some open neighborhood.

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

A v B

Corner-monotonicity

C

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

C

CC

C

C

Corner-monotonicity

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

Sensible Rules

Sensible = all four properties.

C

CC

C

C

A v B

Both are Sensible!

A v C

A

CB v C

T

B

A v B A v C

A

CB v C

T

B

A v B

LMU CMU

Incompatibility Theorem

No sensible acceptance rule is both steady and tracks conditioning.

consumer designer

Sorry. You can’t have both.

A New Paradox of AcceptanceA

B C

A

A v B

p

p(.|A v B)

A New Paradox of AcceptanceA

B C

A

A v B

p

p(.|A v B)

Accept A.

Learn its consequence A v B.

If you track, you retract A!

“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 v B A v C

A

B CB v C

T

0.8

0.9

Another New Paradox of Acceptance

p

A

B

Another New Paradox of AcceptanceA

B

B

p

p(.|B)

Another New Paradox of AcceptanceA

B

A

p

p(.|B)

Another New Paradox of AcceptanceA

B

A

B

T

p

p(.|B)

p(.|B)

You will accept A v B no matter whether B or B is learned.

But if you track, you don’t accept A v B.

Case Reasoning

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

Theorem

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

sensible tracks conditioning avoids both new paradoxes

Partial Converse

Shoham revision sensible tracks conditioningImpliesCMU rule + avoidance of the 2 new paradoxes.

Gettier Without False Lemmas

Nogot

Nobody

Somebody

Gettier case

Havit= the Truth

CMU Rule Represents it

Havit= the Truth

Nogot

Nobody

Somebody

CMU Rule is Unsteady!

HavitNogot

Nobody

Somebody

“Somebody”is retracted but not refuted.

Gettier/Unsteadiness Zones

HavitNogot

Nobody

Somebody

Shoham Revision vs. AGM Revision

Havit

Nogot Havit

Nobody

Nogot

Nobody

Shoham Revision vs. AGM Revision

“Trust what you accepted”

“Re-examine your reasons”Havit

Nogot Havit

Nobody

Nogot

Nobody

Structure Preservation

(0, 1, 0)

(0, 0, 1)(1, 0, 0)

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

LogicGeometry

A CB

Acpt

Some Clear CasesA

B C

InterpolationA

B C

What About Here?A

B C

Probability Lives in the Unit Cube111

100 010 001

000

011110 101

Classical Logic Lives on the Corners111

100 010 001

000

011110 101

But What if Logic Filled the Cube?111

100 010 001

000

011110 101

Classical Negation111

100 010 001

000

011110 101

Partial Negation111

100 001

000

011110

010

101

GeologicClose classical logic underPartial negation

Geological EntailmentLogical Closure =Sub-crystals

Probability is a Surface in Geologic

Classical Principle of Indifference

Principle of Indifference Completed

Probalogic = Projection of Geologic

Probalogic as Geologic in Perspective

Probalogic as Geologic in Perspective

Projection of Geological Consequences

= Probalogic

Acceptance Should Preserve Logical Structure

Acpt

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

Acpt

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!

The CMU rule + Shoham revision satisfies

sensible tracks conditioning avoids both new paradoxes represents no-false-lemma Gettier cases unique geo-logical representation