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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DOI 10.1007/s10849-021-09348-5
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References found in this work BETA

The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Proofs and Types.Jean-Yves Girard - 1989 - Cambridge University Press.
Categorial Type Logics.Michael Moortgat - 1997 - In J. van Benthem & A. ter Meulen (eds.), Handbook of Logic and Language. Elsevier.
Agnostic Hyperintensional Semantics.Carl Pollard - 2015 - Synthese 192 (3):535-562.

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