Henkin Semantics for Reasoning with Natural Language (bibtex)
by Michael Hahn, Frank Richter
Abstract:
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.
Reference:
Henkin Semantics for Reasoning with Natural Language (Michael Hahn, Frank Richter), In Journal of Language Modeling, volume 3, 2015.
Bibtex Entry:
@Article{hahn_henkin_2015,
  author = {Hahn, Michael and Richter, Frank},
  title = {Henkin {Semantics} for {Reasoning} with {Natural} {Language}},
  journal = {Journal of Language Modeling},
  year = {2015},
  volume = {3},
  number = {2},
  pages = {513--568},
  URL = {http://jlm.ipipan.waw.pl/index.php/JLM/article/view/113},
  github = {https://github.com/m-hahn/henkin},
  abstract = {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.}
}
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