Studia Logica 49 (4):515 - 522 (1990)

Axiomatics which do not employ rules of inference other than the cut rule are given for commutative product-free Lambek calculus in two variants: with and without the empty string. Unlike the former variant, the latter one turns out not to be finitely axiomatizable in that way.
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DOI 10.1007/BF00370162
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References found in this work BETA

Untersuchungen über das logische Schließen. I.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 35:176–210.
Untersuchungen über das logische Schließen. II.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 39:405–431.
Axiomatizability of Ajdukiewicz-Lambek Calculus by Means of Cancellation Schemes.Wojciech Zielonka - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (13-14):215-224.
The Logic of Types.Wojciech Buszkowski - 1987 - In Jan T. J. Srzednicki (ed.), Initiatives in Logic. M. Nijhoff. pp. 180--206.

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Cut-Rule Axiomatization of the Syntactic Calculus NL.Wojciech Zielonka - 2000 - Journal of Logic, Language and Information 9 (3):339-352.

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