Distributive Full Nonassociative Lambek Calculus with S4-Modalities Is Context-Free

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7351)


We study Nonassociative Lambek Calculus with additives, satisfying the distributive law and S4-modalities. We prove that the categorial grammars based on it, also enriched with assumptions, generate context-free languages. This extends earlier results of Buszkowski [4] for NL (Nonassociative Lambek Calculus), Buszkowski and Farulewski [6] for DNFL (Distributive Full Nonassociative Lambek Calculus) and Plummer [19], [20] for NLS4 (Nonassociative Lambek Calculus with S4-modalities) without assumptions.


Distributive Lattice Mathematical Linguistics Additional Axiom Categorial Grammar Derivable Sequent 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhe Lin
    • 1
    • 2
  1. 1.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouChina
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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