Graded Entailment for Compositional Distributional Semantics

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 recently 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.

References in corpus (3)

• The Frobenius anatomy of word meanings I: subject and object relative pronouns
• Sentence Entailment in Compositional Distributional Semantics
• Compositional Distributional Semantics with Compact Closed Categories and Frobenius Algebras

Cited by in corpus (16)

• QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer
• Quantum Algorithms for Compositional Natural Language Processing
• A CCG-Based Version of the DisCoCat Framework
• Siamese recurrent networks learn first-order logic reasoning and exhibit zero-shot compositional generalization
• Interacting Conceptual Spaces
• Meaning updating of density matrices
• Distributional Inclusion Hypothesis for Tensor-based Composition
• Dual Density Operators and Natural Language Meaning
• Ordering information on distributions
• Translating and Evolving: Towards a Model of Language Change in DisCoCat
• Entailment Relations on Distributions
• Higher-order CPM Constructions
• At the Interface of Algebra and Statistics
• Compositional Distributional Cognition
• Density Matrices with Metric for Derivational Ambiguity
• Double Dilation $\ne$ Double Mixing