David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 21 (4):393-432 (2012)
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)|
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
Noam Chomsky (1995). The Minimalist Program. The Mit Press.
Peter Gardenfors (2004). Conceptual Spaces as a Framework for Knowledge Representation. Mind and Matter 2 (2):9-27.
Peter Hagoort (2005). On Broca, Brain, and Binding: A New Framework. Trends in Cognitive Sciences 9 (9):416-423.
John Hale (2006). Uncertainty About the Rest of the Sentence. Cognitive Science 30 (4):643-672.
Citations of this work BETA
No citations found.
Similar books and articles
Paul Smolensky (1990). Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems. Artificial Intelligence 46:159-216.
Cedric Boeckx (2008). Understanding Minimalist Syntax: Lessons From Locality in Long-Distance Dependencies. Blackwell Pub..
Dirk P. Janssen (1999). The Place of Analogy in Minimalist Morphology and the Irregularity of Regular Forms. Behavioral and Brain Sciences 22 (6):1025-1026.
Mati Pentus (1997). Product-Free Lambek Calculus and Context-Free Grammars. Journal of Symbolic Logic 62 (2):648-660.
Daniel Feinstein & Shuly Wintner (2008). Highly Constrained Unification Grammars. Journal of Logic, Language and Information 17 (3):345-381.
Barbara Dziemidowicz-Gryz (2007). On Learnability of Restricted Classes of Categorial Grammars. Studia Logica 85 (2):153 - 169.
Željko Bošković & Howard Lasnik (eds.) (2007). Minimalist Syntax: The Essential Readings. Blackwell Pub..
Christian Retoré & Sylvain Salvati (2010). A Faithful Representation of Non-Associative Lambek Grammars in Abstract Categorial Grammars. Journal of Logic, Language and Information 19 (2):185-200.
John E. Hummel (2000). Localism as a First Step Toward Symbolic Representation. Behavioral and Brain Sciences 23 (4):480-481.
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.
Denis Bouchard (1995). The Semantics of Syntax: A Minimalist Approach to Grammar. University of Chicago Press.
Eric Dietrich & A. Markman (2003). Discrete Thoughts: Why Cognition Must Use Discrete Representations. Mind and Language 18 (1):95-119.
Added to index2012-09-11
Total downloads5 ( #234,600 of 1,099,911 )
Recent downloads (6 months)1 ( #303,846 of 1,099,911 )
How can I increase my downloads?