Symmetries in Natural Language Syntax and Semantics: The Lambek-Grishin Calculus

@inproceedings{Moortgat2007SymmetriesIN,
  title={Symmetries in Natural Language Syntax and Semantics: The Lambek-Grishin Calculus},
  author={Michael Moortgat},
  booktitle={WoLLIC},
  year={2007}
}
In this paper, we explore the Lambek-Grishin calculus LG: a symmetric version of categorial grammar based on the generalizations of Lambek calculus studied in Grishin [1]. The vocabulary of LG complements the Lambek product and its left and right residuals with a dual family of type-forming operations: coproduct, left and right difference. The two families interact by means of structure-preserving distributivity principles. We present an axiomatization of LG in the style of Curry’s combinatory… CONTINUE READING

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