Henkin semantics for reasoning with natural language
- The frequency of intensional and non-first-order definable operators in natural languages constitutes a challenge for automated reasoning with the kind of logical translations that are deemed adequate by formal semanticists. Whereas linguists employ expressive higher-order logics in their theories of meaning, the most successful logical reasoning strategies with natural language to date rely on sophisticated first-order theorem provers and model builders. In order to bridge the fundamental mathematical gap between linguistic theory and computational practice, we present a general translation from a higher-order logic frequently employed in the linguistics literature, two-sorted Type Theory, to first-order logic under Henkin semantics. We investigate alternative formulations of the translation, discuss their properties, and evaluate the availability of linguistically relevant inferences with standard theorem provers in a test suite of inference problems stated in English. The results of the experiment indicate that translation from higher-order logic to first-order logic under Henkin semantics is a promising strategy for automated reasoning with natural languages.
Author: | Michael Hahn, Frank RichterORCiDGND |
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URN: | urn:nbn:de:hebis:30:3-438412 |
DOI: | https://doi.org/10.15398/jlm.v3i2.113 |
ISSN: | 2299-8470 |
ISSN: | 2299-856X |
Parent Title (English): | Journal of language modelling |
Publisher: | Instytut Podstaw Informatyki (Warszawa) |
Place of publication: | Warszawa |
Document Type: | Article |
Language: | English |
Date of Publication (online): | 2017/09/04 |
Year of first Publication: | 2015 |
Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
Release Date: | 2017/09/04 |
Tag: | Henkin semantics; reasoning; reducing higher-order reasoning to first-order reasoning |
Volume: | 3 |
Issue: | 2 |
Page Number: | 56 |
First Page: | 513 |
Last Page: | 568 |
Note: | This work is licensed under the Creative Commons Attribution 3.0 Unported License. http://creativecommons.org/licenses/by/3.0/ |
HeBIS-PPN: | 423895273 |
Institutes: | Neuere Philologien / Neuere Philologien |
Dewey Decimal Classification: | 4 Sprache / 41 Linguistik / 410 Linguistik |
Sammlungen: | Universitätspublikationen |
Licence (German): | Creative Commons - Namensnennung 3.0 |