A Frobenius Algebraic Analysis for Parasitic Gaps

TL;DR

This paper presents a novel algebraic framework using Frobenius algebras within Lambek calculus to analyze parasitic gaps in natural language, focusing on lexical polymorphism and structural control.

Contribution

It introduces a Frobenius algebraic approach to model parasitic gaps without syntactic copying, extending Lambek calculus with structural control modalities.

Findings

Models parasitic gaps as lexical polymorphism

Uses Frobenius algebras to interpret semantic content

Provides a compositional translation to vector space semantics

Abstract

The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon. Parasitic gaps in adjuncts are analysed as forms of generalized coordination with a polymorphic type schema for the head of the adjunct phrase. For parasitic gaps affecting arguments of the same predicate, the polymorphism is associated with the lexical item that introduces the primary gap. Our analysis is formulated in terms of Lambek calculus extended with structural control modalities. A compositional translation relates syntactic types and derivations to the interpreting compact closed category of finite dimensional vector spaces and linear maps with Frobenius algebras over it. When interpreted over the necessary semantic spaces, the Frobenius algebras provide the tools to model the proposed instances of lexical polymorphism.