A Learnable Representation for Syntax Using Residuated Lattices

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We propose a representation for natural language syntax based on the theory of residuated lattices: in particular on the Galois lattice between contexts and substrings, which we call the syntactic concept lattice. The natural representation derived from this is a richly structured context sensitive formalism that can be learned using a generalisation of distributional learning. In this paper we define the basic algebraic properties of the syntactic concept lattice, together with a representation derived from this lattice and discuss the generative power of the formalism. We establish some basic results which show that these representations, because they are defined language theoretically, can be inferred from information about the set of grammatical strings of the language. We also discuss the relation to other grammatical formalisms notably categorial grammar and context free grammars. We claim that this lattice based formalism is plausibly both learnable from evidence about the grammatical strings of a language and may be powerful enough to represent natural languages, and thus presents a potential solution to the central problem of theoretical linguistics.
Original languageEnglish
Title of host publicationFormal Grammar
Subtitle of host publication14th International Conference, FG 2009, Bordeaux, France, July 25-26, 2009, Revised Selected Papers
EditorsPhilippe Groote, Markus Egg, Laura Kallmeyer
PublisherSpringer Berlin Heidelberg
Number of pages16
ISBN (Electronic)978-3-642-20169-1
ISBN (Print)978-3-642-20168-4
Publication statusPublished - 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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