Journal of Logic and Computation, Volume 9, Issue 2, pp. 181195: Abstract.
Some probability logics with new types of probability operatorsZ Ognjanovic^{1} and M Raskovic^{2} ^{1}Matematicki institut, Kneza Mihaila 35, 11000 Beograd, Yugoslavia. Email: zorano@mi.sanu.ac.yu, ^{2}Prirodnomatematicki fakultet, R Domanovica 12, 34000 Kragujevac, Yugoslavia. Email: miodragr@mi.sanu.ac.yu
We introduce new types of probability operators of the form Q_{F}, where F is a recursive rational subset of [0,1]. A formula Q_{F}[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 Q_{F}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.
