The conjoinability relation in Lambek calculus and linear logic

In 1958 J. Lambek introduced a calculusL of syntactic types and defined an equivalence relation on types: x y means that there exists a sequence x=x1,...,xn=y (n 1), such thatx i x i+1 or xi+ x i (1 i n). He pointed out thatx y if and only if there is joinz such thatx z andy z. This paper gives an effective characterization of this equivalence for the Lambeck calculiL andLP, and for the multiplicative fragments of Girard's and Yetter's linear logics. Moreover, for the non-directed Lambek calculusLP and the multiplicative fragment of Girard's linear logic, we present linear time algorithms deciding whether two types are equal, and finding a join for them if they are.
Keywords Lambek calculus  linear logic  cyclic linear logic  free group interpretation  Church-Rosser property
Categories (categorize this paper)
DOI 10.1007/BF01110612
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 22,675
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
Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.

Add more references

Citations of this work BETA
Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681 - 710.
Michael Moortgat (2009). Symmetric Categorial Grammar. Journal of Philosophical Logic 38 (6):681-710.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

13 ( #298,354 of 2,149,850 )

Recent downloads (6 months)

2 ( #294,737 of 2,149,850 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.