Title: SEQUENT CALCULUS FOR CLASSICAL LOGIC PROBABILIZED

Abstract: Gentzen’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas that appeared in logic of the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized in the sequent calculus, we introduce the notion of ‘probabilized sequent’ $\Gamma\vdash_a^b\Delta$ with the intended meaning that “the probability of truthfulness of $\Gamma\vdash\Delta$ belongs to the interval $[a,b]$”. This method makes it possible to define a system of derivations based on ‘axioms’ of the form $\Gamma_i\vdash_{a_i}^{b_i}\Delta_i$, obtained as a result of empirical research, and then infer conclusions of the form $\Gamma\vdash_a^b\Delta$. We discuss the consistency, define the models, and prove the soundness and completeness for the defined probabilized sequent calculus.