An algebraic approach to multiple context-free grammars

Alexander Clark, Ryo Yoshinaka

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

2 Citations (Scopus)


We define an algebraic structure, Paired Complete Idempotent Semirings (pcis), which are appropriate for defining a denotational semantics for multiple context-free grammars of dimension 2 (2-mcfg). We demonstrate that homomorphisms of this structure will induce well-behaved morphisms of the grammar, and generalize the syntactic concept lattice from context-free grammars to the 2-mcfg case. We show that this lattice is the unique minimal structure that will interpret the grammar faithfully and that therefore 2-mcfgs without mergeable nonterminals will have nonterminals that correspond to elements of this structure.

Original languageEnglish
Title of host publicationLogical Aspects of Computational Linguistics - 8th International Conference, LACL 2014, Proceedings
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783662437414
Publication statusPublished - 2014

Publication series

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


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