Compositional distributional semantics is a subfield of Computational Linguistics which investigates methods for representing the meanings of phrases and sentences.In this paper, we explore implementations of a framework based on Combinatory Categorial Grammar (CCG), in which words with certain grammatical types have meanings represented by multilinear maps (i.e.multi-dimensional arrays, or tensors).An obstacle to full implementation of the framework is the size of these tensors.We examine the performance of lower dimensional approximations of transitive verb tensors on a sentence plausibility/selectional preference task.We find that the matrices perform as well as, and sometimes even better than, full tensors, allowing a reduction in the number of parameters needed to model the framework.