Geometric representations for minimalist grammars

Details Geometric representations for minimalist grammars Geometric representations for minimalist grammars

2011-01-26

arxiv.org/abs/1101.5076v5

Computer Science

Computation and Language

43 pages, 4 figures

Scientific paper

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.

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