creators_name: Pagliani, Piero
editors_name: Polkowski,  Skowron
type: confpaper
datestamp: 2001-12-18
lastmod: 2011-03-11 08:54:51
metadata_visibility: show
title: Intrinsic co-Heyting boundaries and information incompleteness in Rough Set Analysis
ispublished: pub
subjects: comp-sci-art-intel
subjects: phil-logic
full_text_status: public
keywords: rough sets, co-Heyting algebras, boudary regions,Leibniz rule
abstract: Rough Set Systems, can be made into several logic-algebraic structures (for instance, semi-simple Nelson algebras, Heyting algebras, double Stone algebras, three-valued £ukasiewicz algebras and Chain Based Lattices). In the present paper, Rough Set Systems are analysed from the point of view of co-Heyting algebras. This new chapter in the algebraic analysis of Rough Sets does not follow from aesthetic or completeness issues, but it is a pretty immediate consequence of interpreting the basic features of co-Heyting algebras (originally introduced by C. Rauszer and investigated by W. Lawvere in the context of Continuum Physics), through the lenses of incomplete information analysis. Indeed Lawvere pointed out the role that the co-intuitionistic negation ''non'' (dual to the intuitionistic negation ''not'') plays in grasping the geometrical notion of ''boundary'' as well as the physical concepts of ''sub-body'' and ''essential core of a body'' and we aim at providing an outline of how and to what extent they are mirrored by the basic features of incomplete information analysis. 
date: 1998
date_type: published
volume: 1424
publisher: Springer
pagerange: 123-130
refereed: TRUE
referencetext: M. Banerjee & M. Chakraborthy, “Rough Sets Through Algebraic Logic”. Fundamenta Informaticae, 28, 1996, pp. 211-221.

P. T. Johnstone, “Conditions related to De Morgan's law”. In M. P. Fourman, C. J. Mulvey & D. S. Scott (eds.), Applications of Sheaves (Durham 1977), LNM 753, Springer-Verlag, 1979, pp. 479-491. 

F. W. Lawvere, “Introduction” to F. W. Lawvere & S. Schanuel (eds.), Categories in Continuum Physics, (Buffalo 1982), LNM 1174, Springer-Verlag, 1986. 

F. W. Lawvere, “Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes”. In A. Carboni, M. C. Pedicchio & G. Rosolini (eds.), Category Theory. (Como 1990), LNM 1488, Springer-Verlag 1991, pp. 279-297. 

E: Or³owska, “Logic for reasoning about knowledge”. In W. P. Ziarko (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, 1994, pp. 227-236. 

Z. Pawlak, Rough Sets: A Theoretical Approach to Reasoning about Data. Kluwer, 1991. 

P. Pagliani, “Rough Set System and Logic-algebraic Structures”. In E. Or³owska (ed.): \Incomplete Information: Rough Set Analysis} Physica-Verlag, 1997, pp. 109-190. 

C. Rauszer, “Semi-Boolean algebras and their application to intuitionistic logic with dual operations”. Fundamenta Mathematicae. LXXIII, 1974, pp. 219-249. 

G. E. Reyes & N. Zolfaghari, “Bi-Heyting Algebras, Toposes and Modalities”. Journ.of Philosophical Logic, 25, 1996, pp. 25-43. 

citation:   Pagliani, Piero  (1998) Intrinsic co-Heyting boundaries and information incompleteness in Rough Set Analysis.  [Conference Paper]     
document_url: http://cogprints.org/1990/2/co-Heyt.ps