An Orthonormal Basis for Entailment

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Entailment is a logical relationship in which the truth of a proposition implies the truth of another proposition. The ability to detect entailment has applications in IR, QA, and many other areas. This study uses the vector space model to explore the relationship between cohesion and entailment. A Latent Semantic Analysis space is used to measure cohesion between propositions using vector similarity. We present perhaps the first vector space model of entailment. The critical element of the model is the orthonormal basis, which we propose is a geometric construction for inference.