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The Classical Sentential Calculus

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

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.

Keywords

Deductive System Axiom System Natural Deduction Chapter Versus Primitive Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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