Crypto-preorders, topological relations, information and logic

Journal of Applied Non-Classical Logics 34 (2-3):330-367 (2024)
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Abstract

As is well known, any preorder R on a set U induces an Alexandrov topology on U. In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R is a crypto-preorder and how to transform a crypto-preorder into a proper preorder.

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10.1080/11663081.2024.2336374

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