Geometric Representations for Minimalist Grammars

Abstract
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations
Keywords Geometric cognition  Vector symbolic architectures  Tensor product representations  Minimalist grammars  Harmony theory
Categories (categorize this paper)
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
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,365
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

View all 10 references

Citations of this work BETA

No citations found.

Similar books and articles
Daniel Feinstein & Shuly Wintner (2008). Highly Constrained Unification Grammars. Journal of Logic, Language and Information 17 (3):345-381.
Philip Ehrlich (1986). The Absolute Arithmetic and Geometric Continua. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:237 - 246.
Andoni Ibarra & Thomas Mormann (1997). Theories as Representations. Poznan Studies in the Philosophy of the Sciences and the Humanities 61:39 - 87.
Analytics

Monthly downloads

Added to index

2012-09-11

Total downloads

4 ( #198,718 of 1,089,100 )

Recent downloads (6 months)

1 ( #69,982 of 1,089,100 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.