A Frobenius Algebraic Analysis for Parasitic Gaps

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.Comment: SemSpace 2019, to appear in Journal of Applied Logic

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

A Compositional Vector Space Model of Ellipsis and Anaphora.

PhD ThesisThis thesis discusses research in compositional distributional semantics: if words are defined by their use in language and represented as high-dimensional vectors reflecting their co-occurrence behaviour in textual corpora, how should words be composed to produce a similar numerical representation for sentences, paragraphs and documents? Neural methods learn a task-dependent composition by generalising over large datasets, whereas type-driven approaches stipulate that composition is given by a functional view on words, leaving open the question of what those functions should do, concretely. We take on the type-driven approach to compositional distributional semantics and focus on the categorical framework of Coecke, Grefenstette, and Sadrzadeh [CGS13], which models composition as an interpretation of syntactic structures as linear maps on vector spaces using the language of category theory, as well as the two-step approach of Muskens and Sadrzadeh [MS16], where syntactic structures map to lambda logical forms that are instantiated by a concrete composition model. We develop the theory behind these approaches to cover phenomena not dealt with in previous work, evaluate the models in sentence-level tasks, and implement a tensor learning method that generalises to arbitrary sentences. This thesis reports three main contributions. The first, theoretical in nature, discusses the ability of categorical and lambda-based models of compositional distributional semantics to model ellipsis, anaphora, and parasitic gaps; phenomena that challenge the linearity of previous compositional models. Secondly, we perform an evaluation study on verb phrase ellipsis where we introduce three novel sentence evaluation datasets and compare algebraic, neural, and tensor-based composition models to show that models that resolve ellipsis achieve higher correlation with humans. Finally, we generalise the skipgram model [Mik+13] to a tensor-based setting and implement it for transitive verbs, showing that neural methods to learn tensor representations for words can outperform previous tensor-based methods on compositional tasks