Henkin semantics for reasoning with natural language

Michael Hahn, University of Tübingen, Germany
Frank Richter, University of Frankfurt, Germany


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.

The paper is accompanied by the source code (cf. SUPP. FILES) of the grammar and reasoning architecture described in the paper.


Henkin semantics; reasoning; reducing higher-order reasoning to first-order reasoning

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DOI: http://dx.doi.org/10.15398/jlm.v3i2.113

ISSN of the paper edition: 2299-856X