Geometrical morphology
This work addresses a theoretical problem in linguistics by providing a novel geometric framework for understanding morphology, which is incremental as it builds on existing discrete-continuous relationships.
The paper tackles the problem of modeling inflectional morphology by representing grammatical feature values as corners of a hypercube and selecting morphemes based on geometric proximity, proposing that the chosen morpheme maximizes the inner product with the target feature vector.
We explore inflectional morphology as an example of the relationship of the discrete and the continuous in linguistics. The grammar requests a form of a lexeme by specifying a set of feature values, which corresponds to a corner M of a hypercube in feature value space. The morphology responds to that request by providing a morpheme, or a set of morphemes, whose vector sum is geometrically closest to the corner M. In short, the chosen morpheme $μ$ is the morpheme (or set of morphemes) that maximizes the inner product of $μ$ and M.