Internal Wiring of Cartesian Verbs and Prepositions
This work addresses a specific bottleneck in computational linguistics for researchers in semantics, but it is incremental as it extends prior methods to a new class of words.
The paper tackled the problem of representing transitive verbs in categorical compositional distributional semantics by introducing 'internal wiring' for Cartesian verbs, reducing their meaning space from a ternary tensor to a unary one, with some experimental evidence provided.
Categorical compositional distributional semantics (CCDS) allows one to compute the meaning of phrases and sentences from the meaning of their constituent words. A type-structure carried over from the traditional categorial model of grammar a la Lambek becomes a 'wire-structure' that mediates the interaction of word meanings. However, CCDS has a much richer logical structure than plain categorical semantics in that certain words can also be given an 'internal wiring' that either provides their entire meaning or reduces the size their meaning space. Previous examples of internal wiring include relative pronouns and intersective adjectives. Here we establish the same for a large class of well-behaved transitive verbs to which we refer as Cartesian verbs, and reduce the meaning space from a ternary tensor to a unary one. Some experimental evidence is also provided.