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Abstracts.2020.NLSemantics

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Nachi edited this page Mar 16, 2021 · 5 revisions

Type Theory and Natural Language Semantics

by Warrick Macmillan

Abstract

I will give an overview of natural language (NL) semantics, from the vantage of Modern Type Theories (MTT). This will be a survey of semantics developed in the tradition of Montague, and then further refined by Sundholm & Ranta by applying Martin-Löf's Type Theory to treat NL quantifiers as dependent types. I will trace some of the historical development with explicit constructions from the classic and modern view, focusing on more recent work by Chatzikyriakidis, Luo, and more. One particular emphasis will target common nouns: whereas classically they are treated as propositions, the contemporary account treats them as types. The type common noun is really a universe, and therefore allows for a use of subtyping for making simpler ontological distinctions. Additionally, I will conclude with some live coding which may include GF, Agda, and Coq, time permitting. Although much of this work is more expository and a recapitulation of others' work, I will include a more personal view on how I view it in the context of the NL–PL distinction.

Resources

Reading & References

The talk is meant to be a segway to any of these more complete materials:

  1. D. R. Dowty, R. Wall, and S. Peters. 1981. Introduction to Montague Semantics. Springer. Note: This is a general, complete overview of Montague semantics while the original papers are incredibly dense.

  2. Unknown. 2014. Montague's approach to semantics. NASSLLI 2014. Note: These are some nice slides with examples.

  3. A. Ranta. 1995. Type-Theoretical Grammar. ISBN: 9780198538578. Oxford University Press.

  4. J.-P. Bernardy and S. Chatzikyriakidis. 2017. A Type-Theoretical System for the FraCaS Test Suite: Grammatical Framework Meets Coq. IWCS 2017.

  5. S. Chatzikyriakidis and Z. Luo. 2016. Proof Assistants for Natural Language Semantics. LACL 2016.

  6. S. Chatzikyriakidis and Z. Luo. 2017. Introduction: Modern Perspectives in Type Theoretical Semantics. Springer.

  7. Z. Luo. 2019. MTT-Semantics is Model-Theoretic as well as Proof-Theoretic.

  8. S. Chatzikyriakidis and Z. Luo. 2019. From Montague Semantics to MTT-Semantics: A Meaningful Comparison. ESSLLI 2019.

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