This short paper presents the basic definitions for a ‘probabilistic’ propositional logic generated by extending superintuitionistic logic by the addition of two types of ‘probability’ operators, \(\pi^r\), \(\pi_r\) (for \(r\) in subset \(S\) of real numbers). Rules of formation and deduction are given for the logic after which a Kripke type semantics is presented based on frame \(\langle W, R, p^*, p_*\rangle\), where \(W\) as usual is a set of ‘worlds’ and \(R\) an ‘accessibility’ relation on \(W\), while the \(p^*\), \(p_*\) are defined as probabilistic measures meeting conditions designed to give meaning to the logical ‘probability’ operators. The paper ends with a completeness and soundness theorem.