Download presentation

Presentation is loading. Please wait.

Published byMateo Grooms Modified over 4 years ago

1
{ Kevin T. Kelly, Hanti Lin } Carnegie Mellon University This work was supported by a generous grant by the Templeton Foundation.

2
Propositions A C B

3
(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B

4
(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B ? ?

5
(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B Acpt

6
You condition on whatever you accept (Kyburg, Levi, etc.) Very serious business! Does it ever happen? Its not Sunday, so lets 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.

7
The geometry of probabilities is much richer than the lattice of propositions. Aim: represent Bayesian credences as aptly as possible with propositions.

8
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

9
The geometry of probabilities is much richer than the lattice of propositions. Aim: represent Bayesian credences as aptly as possible with propositions. B C Acpt B v C A

10
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-A 1/2

11
High probability is like truth value 1. B CA 1

12
(0, 1, 0) (0, 0, 1)(1, 0, 0) (1/3, 1/3, 1/3)

13
A BC p(A) = 0.8

14
A BC A v B p(A v B) = 0.8

15
A BC A v B A v C

16
A BC A v B A v C A Closure under conjunction

17
A v B A v C A BCB v C

18
A v B A v C A BCB v C T

19
A v B A v C A BCB v C T 2/3 t

20
A v B A v C A B v C T BC 2/3 t

21
A v B A v C A B v CBC T 2/3 t

22
A v C A C B v C T B A v B A v C A C B v C T B A v B LMUCMU (Levi 1996)

23
A v C B v C T A v B A v C A CB v C T B A v B LMUCMU A CB (Levi 1996)

24
A v C B v C T A CB LMUCMU A CB A v B (Levi 1996)

25
Thats junk! I want a smoother ride! I want tighter handling! consumer designer

26
consumer designer Grow up. We can optimize one or the other but not both.

27
consumer designer responsive Grow up. We can optimize one or the other but not both. steady LMU CMU

28
= Change what you accept only when it is logically refuted. responsive steady LMU CMU = Track probabilistic conditioning exactly.

29
Steadiness Responsive -ness responsive steady LMU CMU

Similar presentations

OK

Chapter 10 Probability. Gambling ethics Should you gamble? There are many ways people gamble … whether they play the Lotto, bet at the racetrack or buy.

Chapter 10 Probability. Gambling ethics Should you gamble? There are many ways people gamble … whether they play the Lotto, bet at the racetrack or buy.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on nepal culture Ppt on global marketing management Ppt on you can win lyrics Keynote opening ppt on ipad Ppt on tourism in rajasthan Can keynote read ppt on iphone Ppt on agriculture for class 8 Ppt on sikkim culture and tradition Ppt on different types of computer languages Ppt on current account deficit usa