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(1989) Logic and philosophy in the Lvov—Warsaw school, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-94-009-2581-6_5
Full citation:
Woleński, J. (1989). The classical sentential calculus, in Logic and philosophy in the Lvov—Warsaw school, Dordrecht, Springer, pp. 97-118.
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