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Graded Entailment for Compositional Distributional Semantics | | Desislava Bankova
; Bob Coecke
; Martha Lewis
; Daniel Marsden
; | | Date: |
19 Jan 2016 | | Abstract: | The categorical compositional distributional model of natural language
provides a conceptually motivated procedure to compute the meaning of
sentences, given grammatical structure and the meanings of its words. This
approach has outperformed other models in mainstream empirical language
processing tasks. However, until now it has lacked the crucial feature of
lexical entailment -- as do other distributional models of meaning.
In this paper we solve the problem of entailment for categorical
compositional distributional semantics. Taking advantage of the abstract
categorical framework allows us to vary our choice of model. This enables the
introduction of a notion of entailment, exploiting ideas from the categorical
semantics of partial knowledge in quantum computation.
The new model of language uses density matrices, on which we introduce a
novel robust graded order capturing the entailment strength between concepts.
This graded measure emerges from a general framework for approximate
entailment, induced by any commutative monoid. Quantum logic embeds in our
graded order.
Our main theorem shows that entailment strength lifts compositionally to the
sentence level, giving a lower bound on sentence entailment. We describe the
essential properties of graded entailment such as continuity, and provide a
procedure for calculating entailment strength. | | Source: | arXiv, 1601.4908 | | Services: | Forum | Review | PDF | Favorites | |
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