An Algebraic Approach to Canonical Formulas: Modal Case

Studia Logica 99 (1-3):93-125 (2011)
We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we give an algebraic description of canonical, subframe, and cofinal subframe formulas, and provide a new algebraic proof of Zakharyaschev’s theorem that each logic over K4 is axiomatizable by canonical formulas
Keywords Modal logic  duality theory  relativization
Categories (categorize this paper)
DOI 10.1007/s11225-011-9348-9
 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: 24,479
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

View all 7 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Yde Venema (1995). Cylindric Modal Logic. Journal of Symbolic Logic 60 (2):591-623.
Holger Sturm (2000). Modal Horn Classes. Studia Logica 64 (3):301-313.

Monthly downloads

Added to index


Total downloads

10 ( #409,420 of 1,925,795 )

Recent downloads (6 months)

1 ( #418,414 of 1,925,795 )

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.