A Concrete Categorical Model for the Lambek Syntactic Calculus
作者:
Marcelo Da Silva Corrêa,
Edward Hermann Haeusler,
期刊:
Mathematical Logic Quarterly
(WILEY Available online 1997)
卷期:
Volume 43,
issue 1
页码: 49-59
ISSN:0942-5616
年代: 1997
DOI:10.1002/malq.19970430107
出版商: WILEY‐VCH Verlag Berlin GmbH
关键词: Lambek syntactic calculus;Categorical model;Typed λlD‐calculus
数据来源: WILEY
摘要:
AbstractWe 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 fra
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