Static and Dynamic Vector Semantics for Lambda Calculus Models of Natural Language

TL;DR

This paper integrates vector-based and truth-conditional models of language within lambda calculus frameworks, introducing static and dynamic vector semantics to better capture meaning and entailment in natural language.

Contribution

It develops a novel vector semantics approach combining static and dynamic models within simply typed lambda calculus for natural language understanding.

Findings

Dynamic vector semantics can model entailment between corpus and sentences.

Static vector semantics use familiar techniques from truth-conditional models.

Examples demonstrate the application of the dynamic model to entailment.

Abstract

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim's context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and we provide examples.