A Monotonicity Calculus and Its Completeness
By Thomas F. Icard III, Larry Moss, William Tune. 2017
12 citations recorded by the source corpus.
One of the prominent mathematical features of natural language is the prevalence of “upward” and “downward” inferences involving determiners and other functional expressions. These inferences are associated with negative and positive polarity positions in syntax, and they also feature in computer implementations of textual entailment. Formal treatments of these phenomena began in the 1980’s and have been refined and expanded in the last 10 years. This paper takes a large step in the area by extending typed lambda calculus to the ordered setting . Not only does this provide a formal tool for reasoning about upward and downward inferences in natu-ral language, it also applies to the analysis of monotonicity arguments in mathematics more generally.
Subfields: Computational Linguistics & Semantics, Philosophy
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- Kaj Bostrom
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- Swarat Chaudhuri
- Greg Durrett
- Uri Alon
- Sam Wiseman
- Antonia Creswell
- Alexander M. Rush
Citations in the corpus
- Natural Language Deduction through Search over Statement Compositions (2022, methodology): “Explicitly using the monotonicity calculus (Icard et al., 2017) and natural logic to generate contrastive examples for semisynthetic mid-training is a promising future direction that could help to address the monotonicity issues encountered by our step deduction model, as discussed in Section 5.”