Semantic Vector Models and Functional Models for Pregroup Grammars

Abstract
We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns.
Keywords Compositional semantics  Quantum logic  Pregroup grammars  Semantic vector models  Symmetric compact closed categories  Two-sorted functional first order logic
Categories (categorize this paper)
DOI 10.1007/s10849-011-9132-2
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,188
Through your library
References found in this work BETA
The Mathematics of Sentence Structure.Joachim Lambek - 1968 - Journal of Symbolic Logic 33 (4):627-628.
The Emergence of Syntactic Structure.Marcus Kracht - 2007 - Linguistics and Philosophy 30 (1):47 - 95.
Toward Discourse Representation Via Pregroup Grammars.Anne Preller - 2007 - Journal of Logic, Language and Information 16 (2):173-194.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Toward Discourse Representation Via Pregroup Grammars.Anne Preller - 2007 - Journal of Logic, Language and Information 16 (2):173-194.
Pregroup Grammars and Chomsky's Earliest Examples.J. Lambek - 2008 - Journal of Logic, Language and Information 17 (2):141-160.
Chunks, Bindings, STAR, and Holographic Reduced Representations.Tony A. Plate - 1998 - Behavioral and Brain Sciences 21 (6):844-845.
Geometric Representations for Minimalist Grammars.Peter Beim Graben & Sabrina Gerth - 2012 - Journal of Logic, Language and Information 21 (4):393-432.
Guards, Bounds, and Generalized Semantics.Johan van Benthem - 2005 - Journal of Logic, Language and Information 14 (3):263-279.

Monthly downloads

Added to index

2011-10-18

Total downloads

42 ( #120,527 of 2,153,858 )

Recent downloads (6 months)

1 ( #398,274 of 2,153,858 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums