# A Frobenius Algebraic Analysis for Parasitic Gaps

arXiv: https://arxiv.org/abs/2005.05639 · HTML: https://mlsanity.com/paper/2005.05639/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2020.

## Built on by (most cited first, 3 of 3)

- [A Quantum Natural Language Processing Approach to Pronoun Resolution](https://mlsanity.com/paper/2208.05393/) (2022)
- [Structural Ambiguity and its Disambiguation in Language Model Based Parsers: the Case of Dutch Clause Relativization](https://mlsanity.com/paper/2305.14917/) (2023)
- [Lambek pregroups are Frobenius spiders in preorders](https://mlsanity.com/paper/2105.03038/) (2021)

## Abstract (arXiv)

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.