Computable formal contexts.
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| Title: | Computable formal contexts. |
|---|---|
| Authors: | Wu, Huishan1 (AUTHOR) huishanwu@blcu.edu.cn |
| Source: | Theoretical Computer Science. Nov2025, Vol. 1054, pN.PAG-N.PAG. 1p. |
| Subjects: | Computable analysis, Computational complexity, Mathematical models, Applied sciences, Recursion theory, Equivalence relations (Set theory) |
| Abstract: | This paper studies effective aspects of mathematical structures in formal concept analysis from the standpoint of computability theory. Firstly, we consider the notion of formal concepts of formal contexts and prove that the first and second derivation of a subset of objects of a computable context are Π 1 0 - and Π 2 0 -complete, respectively. Secondly, we examine the complexity of two representative processes in finding reductions of a context. To study the complexity of the process of merging objects with the same object intents of a context, we define a natural equivalence relation on objects of the context and show that the object equivalence relation of a computable context is Π 1 0 -complete. We directly formalize the other process of removing reducible objects of a context via reducible objects themselves and prove that the set of reducible objects of a computable context is Π 3 0 -complete. The down-left arrow relation is a useful tool to find reducible objects of a context. Lastly, we show that the arrow relation of a computable context is Π 2 0 -complete. By dealing with dual contexts, we obtain the same complexity results on corresponding structures based on attributes of contexts. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 188494129 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Computable formal contexts. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wu%2C+Huishan%22">Wu, Huishan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> huishanwu@blcu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Nov2025, Vol. 1054, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computable+analysis%22">Computable analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+sciences%22">Applied sciences</searchLink><br /><searchLink fieldCode="DE" term="%22Recursion+theory%22">Recursion theory</searchLink><br /><searchLink fieldCode="DE" term="%22Equivalence+relations+%28Set+theory%29%22">Equivalence relations (Set theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper studies effective aspects of mathematical structures in formal concept analysis from the standpoint of computability theory. Firstly, we consider the notion of formal concepts of formal contexts and prove that the first and second derivation of a subset of objects of a computable context are Π 1 0 - and Π 2 0 -complete, respectively. Secondly, we examine the complexity of two representative processes in finding reductions of a context. To study the complexity of the process of merging objects with the same object intents of a context, we define a natural equivalence relation on objects of the context and show that the object equivalence relation of a computable context is Π 1 0 -complete. We directly formalize the other process of removing reducible objects of a context via reducible objects themselves and prove that the set of reducible objects of a computable context is Π 3 0 -complete. The down-left arrow relation is a useful tool to find reducible objects of a context. Lastly, we show that the arrow relation of a computable context is Π 2 0 -complete. By dealing with dual contexts, we obtain the same complexity results on corresponding structures based on attributes of contexts. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.tcs.2025.115457 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Computable analysis Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Applied sciences Type: general – SubjectFull: Recursion theory Type: general – SubjectFull: Equivalence relations (Set theory) Type: general Titles: – TitleFull: Computable formal contexts. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wu, Huishan IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 03043975 Numbering: – Type: volume Value: 1054 Titles: – TitleFull: Theoretical Computer Science Type: main |
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