| 研究実績の概要 |
R. A. Martin (PI) conducted extensive joint research on the physics of language with overseas collaborators J. Uriagereka (U. Maryland), M. Jarret (Perimeter Inst.), R. Orus (Johannes Gutenberg U.), and A. Gallego (Autonomous U. Barcelona). The most notable result was the discovery of the Chomsky-Pauli group (CPG) containing the 2x2 matrices in the Pauli group, as well as objects of the same sort but with mixed 1 and i values. The latter objects, we argue, correspond to Chomsky type lexical categories, making the Fundamental Assumption that the conceptually orthogonal N and V categorial features correspond to the numerically orthogonal 1 and i units, respectively. We argue that the other matrices in the CPG correspond to lexical projections and functional categories/projections. The resulting 32 matrices form a group for matrix multiplication, which we have demonstrated can be used to model the process of First Merge (the merger of of a head and its complement), including well-known but ill-understood restrictions on possible combinations. We also explored merge introducing specifiers, which we take to involve tensor products of the 2x2 matrices, in turn resulting in a new group for matrix multiplication with 256 4x4 matrices, which preserves many of the symmetries found in the GPG. Since specifiers may themselves have specifiers, this mechanism doesn’t just double the dimension of the matrices, but dimensionality explodes. This led us to propose a compression solution, which in effect predicts the class of possible matrices that can be specifiers in human language.
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