Distributional Formal Semantics

TL;DR

This paper introduces a novel Distributional Formal Semantics framework that combines formal and distributional approaches, enabling probabilistic, compositional, and incremental semantic representations that capture core semantic phenomena.

Contribution

It presents a unified probabilistic, compositional semantic model integrating distributional and formal semantics, with an incremental neural network-based derivation process.

Findings

Probabilistic, compositional semantic representations capturing quantification and entailment.

Incremental semantic construction modeling negation, presupposition, and anaphoricity.

Theoretical integration of distributional and formal semantics with neural network implementation.

Abstract

Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with distributional meaning representations, thereby introducing the notion of semantic similarity into formal semantics, or to define distributional systems that aim to incorporate formal notions such as entailment and compositionality. However, given the fundamentally different 'representational currency' underlying formal and distributional approaches - models of the world versus linguistic co-occurrence - their unification has proven extremely difficult. Here, we define a Distributional Formal Semantics that integrates distributionality into a formal semantic system on the level of formal models. This approach offers probabilistic, distributed meaning representations that are also inherently compositional, and that naturally capture fundamental semantic notions such as quantification and entailment. Furthermore, we show how the probabilistic nature of these representations allows for probabilistic inference, and how the information-theoretic notion of "information" (measured in terms of Entropy and Surprisal) naturally follows from it. Finally, we illustrate how meaning representations can be derived incrementally from linguistic input using a recurrent neural network model, and how the resultant incremental semantic construction procedure intuitively captures key semantic phenomena, including negation, presupposition, and anaphoricity.