Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose \, which is NL supplemented with a single structural inference rule.ion closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction inference, there has been some doubt that \ should count at a legitimate substructural logic. This paper argues that \ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames.
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DOI 10.1007/s10849-019-09288-1
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References found in this work BETA

Parasitic Scope.Chris Barker - 2007 - Linguistics and Philosophy 30 (4):407-444.
An Introduction to Substructural Logics (Review).Kosta Dosen - 2001 - Bulletin of Symbolic Logic 7 (4):527-530.
Term-Labeled Categorial Type Systems.Richard T. Oehrle - 1994 - Linguistics and Philosophy 17 (6):633 - 678.
The Displacement Calculus.Glyn Morrill, Oriol Valentín & Mario Fadda - 2011 - Journal of Logic, Language and Information 20 (1):1-48.

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