The Classical Sentential Calculus

Abstract

This chapter is concerned with the research of the Warsaw School into the classical, that is two-valued, sentential calculus. I begin by presenting Łukasiewicz’s parenthesis-free symbolism and some structural criteria concerning the construction of logical systems. In Section 2 I present the axiomatic versions of the functionally complete (i.e., containing all twenty monadic and dyadic sentential connectives) sentential calculus. In Section 3 reference is made to the so-called partial sentential calculi, i.e., those in which only some sentential connectives (e.g., implication) occur. Section 4 is dedicated to the sentential calculus with variable connectives. Section 5 discusses Jaśkowski’s system of natural deduction, and Section 6, the metalogic of the sentential calculus. The chapter concludes with a section containing supplementary information.