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A Concrete Categorical Model for the Lambek Syntactic Calculus

✍ Scribed by Marcelo Da Silva Corrêa; Edward Hermann Haeusler

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
530 KB
Volume
43
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We present a categorical/denotational semantics for the Lambek Syntactic Calculus (LSC), indeed for a λlD‐typed version Curry‐Howard isomorphic to it. The main novelty of our approach is an abstract noncommutative construction with right and left adjoints, called sequential product. It is defined through a hierarchical structure of categories reflecting the implicit permission to sequence expressions and the inductive construction of compound expressions. We claim that Lambek's noncommutative product corresponds to a noncommutative bi‐endofunctor into a category, which encloses all categories of such hierarchical structure. A soundness theorem for LSC is shown with respect to this semantical framework.

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