Some probability logics with new types of probability operators. (English) Zbl 0941.03022

Ognjanović, Zoran; Rašković, Miodrag

J. Log. Comput. 9, No. 2, 181-195 (1999).

Summary: We introduce new types of probability operators of the form \(Q_F\), where \(F\) is a recursive rational subset of \([0,1]\). A formula \(Q_F \alpha\) is satisfied in a probability model if the measure of the set of worlds that satisfy \(\alpha\) 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.

MSC:

03B48

Probability and inductive logic

Keywords:

probabilistic reasoning; completeness; probability operators; probability model; events in discrete sample spaces; probability logics; decidability