The non-equational notion of abstract approximation space for roughness theory is introduced, and its relationship with the equational definition of lattice with Tarski interior and closure operations is studied. Their categorical isomorphism is proved, and the role of the Tarski interior and closure with an algebraic semantic of a S4-like model of modal logic is widely investigated. A hierarchy of three particular models of this approach to roughness based on a concrete universe is described, listed from the stronger model to the weaker one: (1) the partition spaces, (2) the topological spaces by open basis, and (3) the covering spaces. © 2009 Springer.

Cattaneo, G., Ciucci, D. (2009). Lattices with Interior and Closure Operators and Abstract Approximation Spaces. TRANSACTIONS ON ROUGH SETS, 5656, 67-116 [10.1007/978-3-642-03281-3_3].

Lattices with Interior and Closure Operators and Abstract Approximation Spaces

CATTANEO, GIANPIERO;CIUCCI, DAVIDE ELIO
2009

Abstract

The non-equational notion of abstract approximation space for roughness theory is introduced, and its relationship with the equational definition of lattice with Tarski interior and closure operations is studied. Their categorical isomorphism is proved, and the role of the Tarski interior and closure with an algebraic semantic of a S4-like model of modal logic is widely investigated. A hierarchy of three particular models of this approach to roughness based on a concrete universe is described, listed from the stronger model to the weaker one: (1) the partition spaces, (2) the topological spaces by open basis, and (3) the covering spaces. © 2009 Springer.
Articolo in rivista - Articolo scientifico
lattices, interior, closure, operators, abstract, approximation, spaces
English
2009
5656
67
116
none
Cattaneo, G., Ciucci, D. (2009). Lattices with Interior and Closure Operators and Abstract Approximation Spaces. TRANSACTIONS ON ROUGH SETS, 5656, 67-116 [10.1007/978-3-642-03281-3_3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/23412
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