CMU DESIGN GOALS Kevin T Kelly Hanti Lin

CMU DESIGN GOALS { Kevin T. Kelly , Hanti Lin } Carnegie Mellon University CMU Responsiveness

Qualitative Reasoning that Tracks Conditioning

Qualitative Reasoning that Tracks Conditioning

Qualitative Reasoning that Tracks Conditioning stic i l i b ing a b Pro dition con

Qualitative Reasoning that Tracks Conditioning stic i l i b ing a b Pro dition con Ac cep tan ce

Qualitative Reasoning that Tracks Conditioning stic i l i b ing a b Pro dition con Ac cep tan ce al n o iti ion s o p is Pro ef rev i bel

Qualitative Reasoning that Tracks Conditioning stic i l i b ing a b Pro dition con Ac cep tan ce al n o iti ion s o p is Pro ef rev i bel

Qualitative Reasoning that Tracks Conditioning stic i l i b ing a b Pro dition con Ac = Ac cep tan ce al n o iti ion s o p is Pro ef rev i bel Conditioning + acceptance = acceptance + revision

Pre-established Harmony tic s i l i ab ing b o Pr ion t i d con Ac ce pta nce al n io ion t i os evis p o r Pr lief be

Cheap Bayes With Harmony tic s i l i ab ing b o Pr ion t i d con Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

When You Need Bayes… Help! Bayes! tic s i l i ab ing b o Pr ion t i d con Invest? Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

Call Him Then e nc o y nl o n itio d Con Invest? Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

Call Him Then Thanks. I’ll take it from here e nc o y nl o n itio d Con Invest? TV? Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

Expensive Bayes Without Harmony g in n o i it nd o c d te a e ep Invest? TV? R Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

Cheap Bayes with Harmony e nc o y nl o n itio d Con Invest? TV? Eat breakfast? Tie shoes? Ac ce pta nce Get out of bed?

LMU Design Principle: Steadiness LMU Steadiness = “Just conjoin the new data with your old propositions if the two are consistent” E B

AGM is Steady A B C

AGM is Steady A C

Non-steady Revision Rule Yoav Shoham A B C

Non-steady Revision Rule Yoav Shoham A C

Non-steady Revision Rule Yoav Shoham A C

Some Shared Design Principles LMU CMU

Consistency Inconsistency is accepted nowhere.

Non-skepticism Every atom A is accepted over some open neighborhood.

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

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

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

Sensible Rules Sensible = all four properties. Av. B C C C

Both are Sensible! CMU LMU A A Av. C Av. B T B Bv. C Av. B T C B Bv. C C

Incompatibility Theorem No sensible acceptance rule is both steady and tracks conditioning. Sorry. You can’t have both. consumer designer

A New Paradox of Acceptance A p(. |A v B) A p Av. B B C

A New Paradox of Acceptance A Accept A. p(. |A v B) A Learn its consequence A v B. If you track, you retract A! p Av. B B C

“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? 0. 9 A 0. 8 Av. C Av. B T B Bv. C C

Another New Paradox of Acceptance A p B

Another New Paradox of Acceptance A p p(. |B) B B

Another New Paradox of Acceptance A A p B p(. | B)

Another New Paradox of Acceptance A 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. A p T p(. |B) B B p(. | 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 R sensible R tracks conditioning Implies CMU rule + avoidance of the 2 new paradoxes.

Gettier Without False Lemmas Nobody Gettier case Nogot Somebody Havit = the Truth

CMU Rule Represents it Nobody Nogot Somebody Havit = the Truth

CMU Rule is Unsteady! Nobody “Somebody” is retracted but not refuted. Nogot Somebody Havit

Gettier/Unsteadiness Zones Nobody Nogot Somebody Havit

Shoham Revision vs. AGM Revision Nobody Nogot Havit

Shoham Revision vs. AGM Revision Nobody Nogot Havit “Re-examine your reasons” Nobody Nogot Havit “Trust what you accepted”

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

Some Clear Cases A B C

Interpolation A B C

What About Here? A B C

Probability Lives in the Unit Cube 111 110 101 011 100 010 001 000

Classical Logic Lives on the Corners 111 110 101 011 100 010 001 000

But What if Logic Filled the Cube? 111 110 101 011 100 010 001 000

Classical Negation 111 110 101 011 100 010 001 000

Partial Negation 111 110 101 011 100 010 001 000

Geologic Close classical logic under Partial negation

Geological Entailment Logical 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 Theorem The 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 R avoids both new paradoxes R represents no-false-lemma Gettier cases R unique geo-logical representation

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