Continuous Domains in Formal Concept Analysis

• Autorzy: Wang Longchun , Guo Lankun , Li Qingguo

Identyfikatory

DOI

10.3233/FI-2021-2025

• Języki publikacji: EN

Abstrakty

EN

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

Słowa kluczowe

EN

attribute continuous formal context; categorical equivalence; continuous formal concept; domain theory; formal concept analysis

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2021
• Tom: Vol. 179, nr 3
• Strony: 295--319
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Wang Longchun

• School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, China

autor

Guo Lankun

• College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410012, China

autor

Li Qingguo

• School of Mathematics, Hunan University, Changsha, Hunan, 410082, China

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).