Displacement Calculus

TL;DR

The paper introduces the displacement calculus, a generalized logic extending Lambek calculus to handle discontinuous dependencies in natural language, maintaining key proof-theoretic properties and enabling linguistic applications.

Contribution

It presents the displacement calculus as a novel extension of Lambek calculus that incorporates discontinuity while preserving proof-theoretic properties.

Findings

Proves Cut-elimination and subformula property

Establishes decidability of the calculus

Demonstrates linguistic applications of the calculus

Abstract

The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability