Logical foundations for hybrid type-logical grammars

• URL: http://arxiv.org/abs/2009.10387v1
• Date: Tue, 22 Sep 2020 08:26:14 GMT
• Title: Logical foundations for hybrid type-logical grammars
• Authors: Richard Moot (TEXTE, LIRMM, CNRS), Symon Stevens-Guille
• Abstract summary: This paper explores proof-theoretic aspects of hybrid type-logical grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property. We present both a sequent and a proof net calculus for hybrid type-logical grammars.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to a non-associative version and a multimodal version incorporating structural rules and unary modes.

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