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Intrinsic co-Heyting boundaries and information incompleteness in Rough Set Analysis

By Piero Pagliani

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

Topics: Artificial Intelligence, Logic
Publisher: Springer
Year: 1998
DOI identifier: 10.1007/3-540-69115-4_18
OAI identifier: oai:cogprints.org:1990
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