McPheat, Lachlan;
(2024)
Categorical Vector Space Semantics of Anaphora and Ellipsis.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Anaphora and ellipsis are well-studied kinds of reference in natural language and are used to create semantic links between parts of expressions of arbitrary lengths. Lambek calculus has been used to model grammar of natural languages, and modal extensions of Lambek calculus have been used to model discontinuity and movement-phenomena as well as some kinds of anaphora and ellipsis. A novel modal extension of Lambek calculus is shown to model a wide range of anaphora and ellipsis, providing a proof-theoretic distinction between anaphora and ellipsis. This new logic is proven to be cut-free and its derivation problem decidable. The new logic is interpreted as a monoidal biclosed category with additional structures, known as its categorical semantics. The categorical semantics provides a string diagrammatic calculus, giving an intuitive representation of the derivations of the logic. From the categorical semantics, a structure-preserving functor into the category of finite dimensional vector spaces defines a vector space semantics, built using Fock spaces and projections. The vector space semantics provides a compositional-distributional model of meaning which can model not only grammar, like its predecessor, but now also anaphora and ellipsis, allowing for compositional-distributional analysis beyond sentence-length. A compositional-distributional semantics of donkey sentences is derived in terms of another functor, this time from the categorical semantics into the category of sets and relations. The vector space semantics is validated empirically on similarity and disambiguation experiments, and is shown to improve on conventional language models.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Categorical Vector Space Semantics of Anaphora and Ellipsis |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10194729 |
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