Zou, Zhiwei and Li, Qingguo and Ho, Weng Kin - Domains via approximation operators

lmcs:1525 - Logical Methods in Computer Science, April 27, 2018, Volume 14, Issue 2 - https://doi.org/10.23638/LMCS-14(2:6)2018
Domains via approximation operators

Authors: Zou, Zhiwei and Li, Qingguo and Ho, Weng Kin

In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal 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; (3) meet-continuity can be established from a certain property of the topological closure operator. 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.

Volume: Volume 14, Issue 2
Published on: April 27, 2018
Submitted on: July 6, 2016
Keywords: Computer Science - Logic in Computer Science,06B35


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