A logic for reasoning about probabilities

6 January 2003

conference paper
Published by Institute of Electrical and Electronics Engineers (IEEE)

p. 410-421
https://doi.org/10.1109/lics.1988.5138

Abstract

A language for reasoning about probability is considered that allows statements such as 'the probability of E/sub 1/ is less than 1/3' and 'the probability of E/sub 1/ is at least twice the probability of E/sub 2/', where E/sub 1/ and E/sub 2/ are arbitrary events. The case is treated in which all events are measurable (i.e. represent measurable sets), as well as the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) N. Nilson's (1986) probabilistic logic, while the general (nonmeasurable) case corresponds precisely to replacing probability functions by Dempster-Shafer belief functions. In both cases, an elegant complete axiomization is provided, and it is shown that the problem of deciding satisfiability is NP-complete.

Keywords

This publication has 0 references indexed in Scilit: