  Let L be some extension of classical propositional logic. The non-iterated
probabilistic logic over L, is the logic PL that is defined by adding
non-nested probabilistic operators in the language of L. For example in PL we
can express a statement like "the probability of truthfulness of A is at 0.3"
where A is a formula of L. The iterated probabilistic logic over L is the logic
PPL, where the probabilistic operators may be iterated (nested). For example,
in PPL we can express a statement like "this coin is counterfeit with
probability 0.6". In this paper we investigate the influence of probabilistic
operators in the complexity of satisfiability in PL and PPL. We obtain
complexity bounds, for the aforementioned satisfiability problem, which are
parameterized in the complexity of satisfiability of conjunctions of positive
and negative formulas that have neither a probabilistic nor a classical
operator as a top-connective. As an application of our results we obtain tight
complexity bounds for the satisfiability problem in PL and PPL when L is
classical propositional logic or justification logic.
