A Kripke semantics for the logic of Gelfand quantales

Studia Logica 68 (2):173-228 (2001)
Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for complete lattices. A Rasiowa/Sikorski style semantic tableau system is also presented with the property that if all branches of a tableau are closed, then the formula in question is a theorem of Gelfand Logic. An open branch in a completed tableaux guarantees the existence of an Kripke model in which the formula is not valid; hence it is not a theorem of Gelfand Logic
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.1023/A:1012495106338
 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: 24,470
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

No references found.

Add more references

Citations of this work BETA
Norihiro Kamide (2005). On a Logic of Involutive Quantales. Mathematical Logic Quarterly 51 (6):579-585.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

23 ( #205,858 of 1,925,544 )

Recent downloads (6 months)

1 ( #418,152 of 1,925,544 )

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.