Lambek Grammars as Second-Order Abstract Categorial Grammars

Oleg Kiselyov, Yuya Hoshino

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトルNew Frontiers in Artificial Intelligence - JSAI-isAI International Workshops, JURISIN, AI-Biz, LENLS, Kansei-AI, 2019, Revised Selected Papers
編集者Maki Sakamoto, Naoaki Okazaki, Koji Mineshima, Ken Satoh
出版社Springer Science and Business Media Deutschland GmbH
ページ231-243
ページ数13
ISBN(印刷版)9783030587895
DOI
出版ステータスPublished - 2020
イベント11th JSAI International Symposium on Artificial Intelligence, JSAI-isAI 2019 - Yokohama, Japan
継続期間: 2019 11 102019 11 12

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12331 LNAI
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference11th JSAI International Symposium on Artificial Intelligence, JSAI-isAI 2019
国/地域Japan
CityYokohama
Period19/11/1019/11/12

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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