A Frobenius Algebraic Analysis for Parasitic Gaps
This work addresses a specific problem in computational linguistics for researchers in formal semantics and syntax, offering an incremental improvement by reformulating existing analyses with a lexical focus.
The paper tackles the interpretation of parasitic gaps in natural language by proposing a lexical approach that confines semantic duplication to the lexicon, using Lambek calculus with structural control modalities and a compositional translation to vector spaces with Frobenius algebras. It analyzes two types of parasitic gaps—in adjuncts as generalized coordination and in arguments via lexical polymorphism—without relying on syntactic copying.
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.