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The Doxastic engineering of acceptance rules. { Kevin T. Kelly , Hanti Lin } Carnegie Mellon University. This work was supported by a generous grant by the Templeton Foundation. Two Models of Belief. Propositions. B. A. C. Two Models of Belief. Propositions. Probabilities. - PowerPoint PPT Presentation
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THE DOXASTIC ENGINEERING OF ACCEPTANCE RULES
{ Kevin T. Kelly , Hanti Lin }Carnegie Mellon University
This work was supported by a generous grant by the Templeton Foundation.
Two Models of Belief
Propositions
A CB
Two Models of Belief
(0, 1, 0)
(0, 0, 1)(1, 0, 0)
(1/3, 1/3, 1/3)
PropositionsProbabilities
A CB
How Do They Relate?
(0, 1, 0)
(0, 0, 1)(1, 0, 0)
(1/3, 1/3, 1/3)
PropositionsProbabilities
A CB
?
Acceptance
(0, 1, 0)
(0, 0, 1)(1, 0, 0)
(1/3, 1/3, 1/3)
PropositionsProbabilities
A CB
Acpt
Acceptance as Inference
You condition on whatever you accept (Kyburg, Levi, etc.)
Very serious business! Does it ever happen?
“It’s not Sunday, so let’s buy beer at the super market”.
You would never bet your life against nothing that what you say to yourself in routine planning are true.
Acceptance as Apt Representation
The geometry of probabilities is much richer than the lattice of propositions.
Aim: represent Bayesian credences as aptly as possible with propositions.
Acceptance as Apt Representation
The geometry of probabilities is much richer than the lattice of propositions.
Aim: represent Bayesian credences as aptly as possible with propositions.
A
B
C
Acpt B
Acceptance as Apt Representation
The geometry of probabilities is much richer than the lattice of propositions.
Aim: represent Bayesian credences as aptly as possible with propositions.
B CAcpt B v C
A
Familiar Puzzle for Acceptance
Suppose you accept propositions more probable than 1/2.
Consider a 3 ticket lottery. For each ticket, you accept that it loses. That entails that every ticket loses. (Kyburg)
-B -C-A1/2
Thresholds as Logic
High probability is like truth value 1.
B
CA
1
Thresholds as Geometry(0, 1, 0)
(0, 0, 1)(1, 0, 0)
(1/3, 1/3, 1/3)
Thresholds as GeometryA
B C
p(A) = 0.8
Thresholds as GeometryA
B C
A v B
p(A v B) = 0.8
Thresholds as GeometryA
B C
A v B A v C
Thresholds as GeometryA
B C
A v B A v C
AClosure under conjunction
Thresholds as Geometry
A v B A v C
A
B CB v C
Thresholds as Geometry
A v B A v C
A
B CB v C
T
The Lottery Paradox
A v B A v C
A
B CB v C
T2/3
t
The Lottery Paradox
A v B A v C
A
B v C
T
B C
2/3t
The Lottery Paradox
A v B A v C
A
B v CB C
T 2/3
t
Two Solutions
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
(Levi 1996)
Two Solutions
A v C
B v C
T
A v B A v C
A
CB v C
T
B
A v B
LMU CMU
A
CB
(Levi 1996)
Two Solutions
A v C
B v C
T
A
CB
LMU CMU
A
CB
A v B
(Levi 1996)
Why Cars Look Different
That’s junk!I want a smoother ride!I want tighter handling!
consumer designer
Why Cars Look Different
consumer designer
Grow up.We can optimize one or the other but not both.
Why Cars Look Different
consumer designerresponsive
Grow up.We can optimize one or the other but not both.
steady
LMU
CMU
Why Cars Look Different
= Change what you accept only when it is logically refuted.
responsive
steady
LMU
CMU= Track probabilistic conditioning exactly.
End of Roundtable Segment 1
Steadiness
Responsive-ness
responsive
steady
LMU
CMU
