On reduction systems equivalent to the Lambek calculus with the empty string
type: Item
instance of: scholarly article
title: On reduction systems equivalent to the Lambek calculus with the empty string
zbMATH Open document ID: 1013.03015
DOI: 10.1023/A:1016382907414
author: Wojciech Zielonka
published in: Studia Logica
publication date: 2002-08-21T00:00:00Z
review text: This is one of the author's papers concerning the axiomatizability of the Lambek Calculus. The main result of the paper is the theorem saying that the product-free Lambek calculus with the empty string is not axiomatizable if Lambek's cut rule is the only admitted rule of inference. The proof of the theorem is technically rather complicated. It uses the cut-rule axiomatized calculus \(C\) and its special subsystems \(C_{n}\), \(C_{n}^{R}\), \(C_{n}^{r}\) introduced in order to simplify the proof. This reduction calculus, being the union of the chain \((C_{n})\), is equivalent to the Lambek Calculus with the empty string. The difficulties appearing in the solution of the problem described in the paper are connected with the type raising elimination.
reviewed by: Mirosława Kołowska-Gawiejnowicz
Mathematics Subject Classification ID: 03B47
zbMATH DE Number: 1785607
zbMATH Keywords: Lambek calculus
zbMATH Keywords: cut rule
zbMATH Keywords: axiomatizability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1785607