The Classical Sentential Calculus

  • Jan Wolenski
Part of the Synthese Library book series (SYLI, volume 198)


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.


Deductive System Axiom System Natural Deduction Chapter Versus Primitive Concept 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Jan Wolenski
    • 1
  1. 1.The Jagiellonian UniversityKrakówPoland

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