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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

CMU Design Goals

{ Kevin T. Kelly ,Hanti Lin }

Carnegie Mellon University

CMU

Responsive-ness

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

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 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)

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

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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