Jacob Collard


2022

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Extracting Mathematical Concepts from Text
Jacob Collard | Valeria de Paiva | Brendan Fong | Eswaran Subrahmanian
Proceedings of the Eighth Workshop on Noisy User-generated Text (W-NUT 2022)

We investigate different systems for extracting mathematical entities from English texts in the mathematical field of category theory as a first step for constructing a mathematical knowledge graph. We consider four different term extractors and compare their results. This small experiment showcases some of the issues with the construction and evaluation of terms extracted from noisy domain text. We also make available two open corpora in research mathematics, in particular in category theory: a small corpus of 755 abstracts from the journal TAC (3188 sentences), and a larger corpus from the nLab community wiki (15,000 sentences)

2020

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Unsupervised Formal Grammar Induction with Confidence
Jacob Collard
Proceedings of the Society for Computation in Linguistics 2020

2018

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Finite State Reasoning for Presupposition Satisfaction
Jacob Collard
Proceedings of the First International Workshop on Language Cognition and Computational Models

Sentences with presuppositions are often treated as uninterpretable or unvalued (neither true nor false) if their presuppositions are not satisfied. However, there is an open question as to how this satisfaction is calculated. In some cases, determining whether a presupposition is satisfied is not a trivial task (or even a decidable one), yet native speakers are able to quickly and confidently identify instances of presupposition failure. I propose that this can be accounted for with a form of possible world semantics that encapsulates some reasoning abilities, but is limited in its computational power, thus circumventing the need to solve computationally difficult problems. This can be modeled using a variant of the framework of finite state semantics proposed by Rooth (2017). A few modifications to this system are necessary, including its extension into a three-valued logic to account for presupposition. Within this framework, the logic necessary to calculate presupposition satisfaction is readily available, but there is no risk of needing exceptional computational power. This correctly predicts that certain presuppositions will not be calculated intuitively, while others can be easily evaluated.