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FIRST INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Ghent, Belgium

30 June - 2 July 1999

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** ELECTRONIC PROCEEDINGS **

## Nic Wilson

# A Logic of Extended Probability

** Abstract **

This paper shows how the logic of gambles corresponding to
Peter Walley's system of Imprecise Probability can be extended
to allow gambles involving infinitesimal values and infinite values.
This logic can then be used for reasoning with infinitesimal
probabilities alongside conventional reasoning with linear constraints
on probabilities. The proof theory is shown to be sound and complete
for finite input sets.

** Keywords. ** Imprecise Probability, Probabilistic Logic, infinitesimals, order of magnitude probabilistic reasoning.

The paper is available in the following formats:

** Authors addresses: **

School of Computing

and Mathematical Sciences

Oxford Brookes University

Gipsy Lane, Headington, Oxford,

OX3 0BP, U.K.

** E-mail addresses: **

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