Lambek Grammars as Second-Order Abstract Categorial Grammars

Oleg Kiselyov, Yuya Hoshino

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We demonstrate that for all practical purposes, Lambek Grammars (LG) are strongly equivalent to Context-Free Grammars (CFG) and hence to second-order Abstract Categorial Grammars (ACG). To be precise, for any Lambek Grammar LG there exists a second-order ACG with a second-order lexicon such that: the set of LG derivations (with a bound on the ‘nesting’ of introduction rules) is the abstract language of the ACG, and the set of yields of those derivations is its object language. Furthermore, the LG lexicon is represented in the abstract ACG signature with no duplications. The fixed, and small, bound on the nesting of introduction rules seems adequate for natural languages. One may therefore say that ACGs are not merely just as expressive as LG, but strongly equivalent. The key is the algebraic description of Lambek Grammar derivations, and the avoidance of the Curry-Howard correspondence with lambda calculus.

Original languageEnglish
Title of host publicationNew Frontiers in Artificial Intelligence - JSAI-isAI International Workshops, JURISIN, AI-Biz, LENLS, Kansei-AI, 2019, Revised Selected Papers
EditorsMaki Sakamoto, Naoaki Okazaki, Koji Mineshima, Ken Satoh
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783030587895
Publication statusPublished - 2020
Event11th JSAI International Symposium on Artificial Intelligence, JSAI-isAI 2019 - Yokohama, Japan
Duration: 2019 Nov 102019 Nov 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12331 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th JSAI International Symposium on Artificial Intelligence, JSAI-isAI 2019


  • ACG
  • Context-free grammar
  • Lamkek grammar
  • Pentus construction


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