Abstract | ||
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This paper proposes a rough set theoretic approach to Domain theory, thereby establishing a direct connection between Rough Set Theory and Domain Theory. With a rough set theoretic mind-set, we tailor-made new approximation operators specially suited for Domain Theory. Our proposed approach not only offers a fresh perspective to existing concepts and results in Domain Theory through the rough set theoretic lens, but also reveals ways to establishing novel domain-theoretic results. For instance, (1) the well-known interpolation property of the way-below relation on a continuous poset is equivalent to the idempotence of a certain set-operator; (2) the continuity of a poset can be characterized by the coincidence of the Scott closure operator and the upper approximation operator induced by the way below relation; and as a result, (3) a new characterization of Scott closure is obtained. Additionally, we show how, to each approximating relation, an associated order-compatible topology can be defined in such a way that for the case of a continuous poset the topology associated to the way-below relation is exactly the Scott topology. A preliminary investigation is carried out on this new topology. |
Year | Venue | Field |
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2016 | arXiv: Logic in Computer Science | Discrete mathematics,Closure operator,Scott domain,Domain theory,Algorithm,Rough set,Operator (computer programming),Idempotence,Dominance-based rough set approach,Partially ordered set,Mathematics |
DocType | Volume | Citations |
Journal | abs/1607.01164 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Zhiwei Zou | 1 | 0 | 0.34 |
qingguo li | 2 | 20 | 10.66 |
Weng Kin Ho | 3 | 23 | 5.41 |