Probability as a modal operator: the possibilities of its combination with other modalities

In this work we examine some of the possibilities of combining a simple probability operator with other modal operators, in particular with a belief operator. We will examine the semantics of two possible situations for expressing probabilistic belief or the lack of it, a simple subjective probability operator (SPO) versus the composition of a belief operator, plus an objective modal operator (BOP). We will study their interpretations in two probabilistic semantics: a relational Kripkean one and a variation of neighbourhood semantics, showing that the latter is able to represent the lack of probabilistic belief more directly, just with the SPO, whereas relational semantics needs the combination of BOP probability to represent lack of belief.