In view of Kathy's comment:
"However, it's worth noting that Phil Dawid, Vladimir Vovk, and Glenn
Shafer have been working on an alternate formulation of probability
("prequential games"), based on agents engaged in sequential games.
(Shafer and Vovk just published a book which they announced on this
list.)"
in response to Kevin's earlier comment:
"The product and sum rules of probability theory give us the proof theory of
our logic. Set-theoretic probability theory gives us the model theory for our
logic."
it is worth noting that prequential games may be viewed as a game-theoretic
semantics (model theory), in the sense of logician Jaako Hintikka (although his
ideas may be traced to the work of C. S. Peirce a century ago). In this
approach, a statement in some logical language is assigned the value "true" if
a particular player in an associated game has a winning strategy, and "false"
otherwise. Game-semantics have recently found application in theoretical
computer science, as a semantics for computer programming languages. (Work by
e.g. Abramsky, McCusker, Hyland, Schalk.) The approach has also recently been
applied (unwittingly) to model and predict financial markets; see the web-pages
of David Lamper at Oxford University:
http://www.maths.ox.ac.uk/~lamper/index2.html
Regarding alternative semantics for probability, UAI list members may
be interested in a nice recent book by philosopher Donald Gillies
(although it does not discuss prequential games semantics):
D. Gillies (2000): "Philosophical Theories of Probability". London, UK:
Routledge.
This compares and contrasts logical, subjectivist, frequentist and propensity
theories of probability in an accessible and historically-minded fashion.
After comparing these, Gillies argues for an eclectic approach, in particular
for a subjectivist philosophy of probability in the social sciences and
a non-subjectivist philosophy in the natural sciences.
- -- Peter
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Peter McBurney
Agent Applications, Research and Technology (Agent ART) Group
Department of Computer Science
University of Liverpool
Liverpool L69 7ZF
U.K.
Tel: + 44 151 794 6768
Email: P.J.McBurney@csc.liv.ac.uk
Web page: www.csc.liv.ac.uk/~peter/
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