caa a22 4500 475800133 CHVBK 20180406123735.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1023/A:1008309805070 doi (NATIONALLICENCE)springer-10.1023/A:1008309805070 Zielonka Wojciech Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, 60-769, Poznań, Poland aut Cut-Rule Axiomatization of the Syntactic Calculus NL0 [Elektronische Daten] [Wojciech Zielonka] An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L 0 andNL 0 was partially solved, viz., for formulas withoutleft (or, equivalently, right) division and an (infinite) cut-ruleaxiomatics for the whole of L 0 has been given. Thepresent paper yields an analogous axiomatics forNL 0. Like in the author's previous work, the notionof rank of an axiom is introduced which, although inessentialfor the results given below, may be useful for the expectednonfinite-axiomatizability proof. Kluwer Academic Publishers, 2000 axiomatizability nationallicence cut rule nationallicence Lambek calculus nationallicence Journal of Logic, Language and Information Kluwer Academic Publishers 9/3(2000-07-01), 339-352 0925-8531 9:3<339 2000 9 10849 https://doi.org/10.1023/A:1008309805070 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008309805070 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zielonka Wojciech Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, 60-769, Poznań, Poland aut NATIONALLICENCE 773 0- Journal of Logic, Language and Information Kluwer Academic Publishers 9/3(2000-07-01), 339-352 0925-8531 9:3<339 2000 9 10849 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 475800133 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer