Studia Logica 95 (3):355-378 (2010)

Authors
Katalin Bimbo
University of Alberta
Abstract
We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the theorems of Fol that are needed in the proof. Using the insights gained from the proof, we show that there are four binary operators that each can serve as the only undefined logical constant for Fol . Finally, we show that from every n -ary connective that yields a functionally complete singleton set of connectives two Schönfinkel-type operators are definable, and all the latter are so definable.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-010-9265-3
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References found in this work BETA

The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.
Principia Mathematica.Morris R. Cohen - 1912 - Philosophical Review 21 (1):87.

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Combinatory Logic.Katalin Bimbó - 2009 - Stanford Encyclopedia of Philosophy.

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