  Within classical propositional logic, assigning probabilities to formulas is
shown to be equivalent to assigning probabilities to valuations. A novel notion
of probabilistic entailment enjoying desirable properties of logical
consequence is proposed and shown to collapse into the classical entailment
when the language is left unchanged. Motivated by this result, a decidable
conservative enrichment of propositional logic is proposed by giving the
appropriate semantics to a new language construct that allows the constraining
of the probability of a formula. A sound and weakly complete axiomatization is
provided using the decidability of the theory of real closed ordered fields.
