Abstract
Formalizing “meaning as context” mathematically leads to a new, algebraic theory of meaning, in which composition is bilinear and associative. These properties are shared by other methods that have been proposed in the literature, including the tensor product, vector addition, point-wise multiplication, and matrix multiplication. Entailment can be represented by a vector lattice ordering, inspired by a strengthened form of the distributional hypothesis, and a degree of entailment is defined in the form of a conditional probability. Approaches to the task of recognizing textual entailment, including the use of subsequence matching, lexical entailment probability, and latent Dirichlet allocation, can be described within our framework.
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