Journal of Logic and Computation, Volume 9, Issue 2, pp. 181-195: Abstract.
Some probability logics with new types of probability operators
Z Ognjanovic1 and M Raskovic2
1Matematicki institut, Kneza Mihaila 35, 11000 Beograd, Yugoslavia. E-mail: email@example.com, 2Prirodno-matematicki fakultet, R Domanovica 12, 34000 Kragujevac, Yugoslavia. E-mail: firstname.lastname@example.org
We introduce new types of probability operators of the form QF, where F is a recursive rational subset of [0,1]. A formula QF[agr] is satisfied in a probability model if the measure of the set of worlds that satisfy [agr] is in F. The new operators are suitable for describing events in discrete sample spaces. We provide sound and complete axiomatic systems for a number of probability logics augmented with the QF-operators. We show that the new operators are not definable in languages of probability logics that have been used so far. We study decidability of the presented logics. We describe a relation of 'being more expressive' between the new probability logics.
Key words: Probability logic, completeness, decidability.