Linguistic applications of first order intuitionistic linear logic

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Journal of Logic, Language and Information 10 (2):211-232 (2001)
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Abstract

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.

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2004

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10.1023/a:1008399708659

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Citations of this work

The Displacement Calculus.Glyn Morrill, Oriol Valentín & Mario Fadda - 2011 - Journal of Logic, Language and Information 20 (1):1-48.
Natural Language Semantics and Computability.Richard Moot & Christian Retoré - 2019 - Journal of Logic, Language and Information 28 (2):287-307.

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References found in this work

The proper treatment of quantification in ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
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The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Language in action.Johan Van Benthem - 1991 - Journal of Philosophical Logic 20 (3):225-263.
Categorial Type Logics.Michael Moortgat - 1997 - In J. F. A. K. Van Benthem, Johan van Benthem & Alice G. B. Ter Meulen (eds.), Handbook of Logic and Language. Elsevier.

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