Categories with Complements
Bibliographic Data
| ID | 22134277 |
|---|---|
| Authors | Juan Uriagereka (0000-0001-9194-3626, University of Maryland, College Park, corresponding author) |
| Year | 2022 |
| Volume | 7 |
| Issue | 5 |
| Pages | 102 |
| Publication date | 2022-09-15 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Philosophies (JOURNAL) |
| Journal identifiers | ISSN: 2409-9287 • E-ISSN: 2409-9287 |
| Publisher | MDPI AG (PUBLISHER • IT) |
| DOI | 10.3390/philosophies7050102 |
| OpenAlex | W4296097479 |
| Language | EN |
| References cited | 15 |
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
Algebra over a field · Diagonal · Eigenvalues and eigenvectors · Hermitian matrix · Linguistics · Noun · Physics · Pure mathematics · Vector space · Advanced Algebra and Logic · Computer Science · DNA and Biological Computing · Mathematics · Philosophy · semigroups and automata theory · Artificial Intelligence
| Highly cited | No |
|---|