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Weak implicational logics related to the Lambek calculus
Gentzen versus Hilbert formalisms
pp. 201-212
Abstract
It has been proved by the author that the product-free Lambek calculus with the empty string in its associative (L 0) and non-associative (NL 0) variant is not finitely Gentzen-style axiomatizable if the only rule of inference is the cut rule. We give here rather detailed outlines of the proofs for both L 0 and NL 0. In the last section, Hilbert-style axiomatics for the corresponding weak implicational calculi are given.
Publication details
Published in:
Makinson David, Malinowski Jacek, Wansing Heinrich (2009) Towards mathematical philosophy: papers from the Studia logica conference Trends in logic IV. Dordrecht, Springer.
Pages: 201-212
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DOI: 10.1007/978-1-4020-9084-4_10
Full citation:
Zielonka Wojciech (2009) „Weak implicational logics related to the Lambek calculus: Gentzen versus Hilbert formalisms“, In: D. Makinson, J. Malinowski & H. Wansing (eds.), Towards mathematical philosophy, Dordrecht, Springer, 201–212.