Repository | Book | Chapter
(2009) Towards mathematical philosophy, Dordrecht, Springer.
Weak implicational logics related to the Lambek calculus
Gentzen versus Hilbert formalisms
Wojciech Zielonka
pp. 201-212
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
DOI: 10.1007/978-1-4020-9084-4_10
Full citation:
Zielonka, W. (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, pp. 201-212.
This document is unfortunately not available for download at the moment.