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Some uses of higher-order logic in computational linguistics
Open accessAbstract
Consideration of the question of meaning in the framework of linguistics often requires an allusion to sets and other higher-order notions. The traditional approach to representing and reasoning about meaning in a computational setting has been to use knowledge representation systems that are either based on first-order logic or that use mechanisms whose formal justifications are to be provided after the fact. In this paper we shall consider the use of a higher-order logic for this task. We first present a version of definite clauses (positive Horn clauses) that is based on this logic. Predicate and function variables may occur in such clauses and the terms in the language are the typed λ-terms. Such term structures have a richness that may be exploited in representing meanings. We also describe a higher-order logic programming language, called λProlog, which represents programs as higher-order definite clauses and interprets them using a depth-first interpreter. A virtue of this language is that it is possible to write programs in it that integrate syntactic and semantic analyses into one computational paradigm. This is to be contrasted with the more common practice of using two entirely different computation paradigms, such as DCGs or ATNs for parsing and frames or semantic nets for semantic processing. We illustrate such an integration in this language by considering a simple example, and we claim that its use makes the task of providing formal justifications for the computations specified much more direct.
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“However, FOL is not expressive enough to han-dle problems requiring higher-order logics (Miller and Nadathur, 1986;Higginbotham, 1998).”
From LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers (2023) · cites this paper as Miller and Nadathur, 1986
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Metadata
- Authors
- Miller, D. A., & Nadathur, G.
- Affiliations
- University of Pennsylvania (US)
- Venue
- Proceedings of the 24th annual meeting on Association for Computational Linguistics -
- Published
- 1986
- Pages
- 247-256
- ISSN
- 0736-587X (ISSN-L)
- OpenAlex
- W2119749753
- Cited by
- 58
- References
- 14
- Citations by year
- 2023: 1 · 2021: 2 · 2019: 1 · 2017: 3 · 2016: 1
- FWCI
- 3.49
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the conference - Association for Computational Linguistics. Meeting (publishedVersion)
- OLAC - Open Language Archives Community (submittedVersion)
- Americanae (AECID Library) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Social Sciences › Arts and Humanities › Language and Linguistics › Syntax, Semantics, Linguistic Variation
- Physical Sciences › Computer Science › Artificial Intelligence › Natural Language Processing Techniques
- Keywords
- higher-order logic, meaning representation, definite clauses, Horn clauses, lambda calculus, λProlog, higher-order logic programming, knowledge representation, formal semantics
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