  Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a
compositional model of meaning for distributional semantics, in which each word
in a sentence has a meaning vector and the distributional meaning of the
sentence is a function of the tensor products of the word vectors. Abstractly
speaking, this function is the morphism corresponding to the grammatical
structure of the sentence in the category of finite dimensional vector spaces.
In this paper, we provide a concrete method for implementing this linear
meaning map, by constructing a corpus-based vector space for the type of
sentence. Our construction method is based on structured vector spaces whereby
meaning vectors of all sentences, regardless of their grammatical structure,
live in the same vector space. Our proposed sentence space is the tensor
product of two noun spaces, in which the basis vectors are pairs of words each
augmented with a grammatical role. This enables us to compare meanings of
sentences by simply taking the inner product of their vectors.
