Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

Studia Logica 101 (5):1073-1092 (2013)
Abstract
In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the quasiorder R forms an effective lattice, that is, an algebraic model of the logic E 0, which is characterised by a modal operator grasping the notion of “to be classically valid”. We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder
Keywords Rough sets  Nelson algebras  Quasiorders (preorders)  Knowledge representation  Boolean congruence  Glivenko congruence  Logics with strong negation
Categories (categorize this paper)
Options
 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: 11,371
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
Jon Barwise & John Perry (1981). Situations and Attitudes. Journal of Philosophy 78 (11):668-691.
David Nelson (1949). Constructible Falsity. Journal of Symbolic Logic 14 (1):16-26.

View all 7 references

Citations of this work BETA

No citations found.

Similar books and articles
Maarten De Rijke (1995). The Logic of Peirce Algebras. Journal of Logic, Language and Information 4 (3):227-250.
Claes Strannegård (1999). Interpretability Over Peano Arithmetic. Journal of Symbolic Logic 64 (4):1407-1425.
Analytics

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index

2012-10-11

Total downloads

1 ( #445,994 of 1,102,884 )

Recent downloads (6 months)

1 ( #297,281 of 1,102,884 )

How can I increase my downloads?

My notes
Sign in to use this feature


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