Mathematical Logic Quarterly 43 (1):49-59 (1997)

Authors
Edward Haeusler
Pontifícia Universidade Católica do Rio de Janeiro
Marcelo Corrêa
Universidade Federal de Minas Gerais
Abstract
We present a categorical/denotational semantics for the Lambek Syntactic Calculus , 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
Keywords Categorical model  Lambek syntactic calculus  Typed λlD‐calculus
Categories (categorize this paper)
DOI 10.1002/malq.19970430107
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,160
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
Proofs and Types.Jean-Yves Girard - 1989 - Cambridge University Press.

View all 7 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Analytics

Added to PP index
2013-11-03

Total views
14 ( #729,045 of 2,499,274 )

Recent downloads (6 months)
1 ( #418,195 of 2,499,274 )

How can I increase my downloads?

Downloads

My notes