Introducing a Calculus of Effects and Handlers for Natural Language Semantics

TL;DR

This paper introduces a new calculus for natural language semantics that uses effect handlers to modularly combine different semantic phenomena, extending lambda calculus with formal guarantees.

Contribution

It presents an extended simply-typed lambda calculus leveraging effect handlers to model multiple semantic effects in a compositional and modular manner.

Findings

The calculus maintains key formal properties of lambda calculus.

It enables modular semantics for complex linguistic phenomena.

Demonstrates the approach on a small semantic fragment.

Abstract

In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena.