Categories with Complements
| dc.contributor.author | Uriagereka, Juan | |
| dc.date.accessioned | 2023-10-19T19:47:14Z | |
| dc.date.available | 2023-10-19T19:47:14Z | |
| dc.date.issued | 2022-09-15 | |
| dc.description.abstract | Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features into ±1, ±i scalars that allow for the construction of a vector space, this paper studies the possibility of organizing said features into 2 × 2 square matrices. In the system proposed to explore “head-complement” relations, operating on nouns yields a measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical categories. Functional/grammatical categories in the system deploy the same features, albeit organized differently in the matrix diagonal and off-diagonal. The algebraic result is a group with well-defined mathematical properties, which properly includes the Pauli group of standard use in quantum computation. In the system, the presumed difference between categories and interactions—here, in a context of the head-complement sort—reduces to whether the magnitude of the matrix eigenvalue is 1 or not, in the latter instance inducing asymmetric interactions. | |
| dc.description.uri | https://doi.org/10.3390/philosophies7050102 | |
| dc.identifier | https://doi.org/10.13016/dspace/xdjv-fyz1 | |
| dc.identifier.citation | Uriagereka, J. Categories with Complements. Philosophies 2022, 7, 102. | |
| dc.identifier.uri | http://hdl.handle.net/1903/31086 | |
| dc.language.iso | en_US | |
| dc.publisher | MDPI | |
| dc.relation.isAvailableAt | College of Arts & Humanities | en_us |
| dc.relation.isAvailableAt | Linguistics | en_us |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_us |
| dc.relation.isAvailableAt | University of Maryland (College Park, MD) | en_us |
| dc.subject | lexical categories | |
| dc.subject | functional categories | |
| dc.subject | (external) merge | |
| dc.subject | matrix syntax | |
| dc.subject | Pauli group | |
| dc.title | Categories with Complements | |
| dc.type | Article | |
| local.equitableAccessSubmission | No |