Complexity of Grammar Induction for Quantum Types

Complexity of Grammar Induction for Quantum Types

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information fl...

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Main Author: Antonin Delpeuch
Format: Article
Language:English
Published: Open Publishing Association 2014-12-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1404.3925v2
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spelling doaj-43f7e0ff6cb4404d95239ff9d8bee9cd2020-11-24T23:20:37ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802014-12-01172Proc. QPL 201423624810.4204/EPTCS.172.16:19Complexity of Grammar Induction for Quantum TypesAntonin Delpeuch0 École Normale Supérieure, Paris Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.http://arxiv.org/pdf/1404.3925v2
collection DOAJ
language English
format Article
sources DOAJ
author Antonin Delpeuch
spellingShingle Antonin Delpeuch
Complexity of Grammar Induction for Quantum Types
Electronic Proceedings in Theoretical Computer Science
author_facet Antonin Delpeuch
author_sort Antonin Delpeuch
title Complexity of Grammar Induction for Quantum Types
title_short Complexity of Grammar Induction for Quantum Types
title_full Complexity of Grammar Induction for Quantum Types
title_fullStr Complexity of Grammar Induction for Quantum Types
title_full_unstemmed Complexity of Grammar Induction for Quantum Types
title_sort complexity of grammar induction for quantum types
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2014-12-01
description Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.
url http://arxiv.org/pdf/1404.3925v2
work_keys_str_mv AT antonindelpeuch complexityofgrammarinductionforquantumtypes
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