Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras

The notion of a protoconcept in the framework of Yao’s object oriented concepts is proposed. Approximations by object oriented concepts are defined and these ‘object oriented protoconcepts’ are characterized using them. It is shown that the object oriented protoconcepts form a double Boolean algebra...

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Autores principales: Howlader, Prosenjit, Banerjee, Mohua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7338182/
http://dx.doi.org/10.1007/978-3-030-52705-1_23
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author Howlader, Prosenjit
Banerjee, Mohua
author_facet Howlader, Prosenjit
Banerjee, Mohua
author_sort Howlader, Prosenjit
collection PubMed
description The notion of a protoconcept in the framework of Yao’s object oriented concepts is proposed. Approximations by object oriented concepts are defined and these ‘object oriented protoconcepts’ are characterized using them. It is shown that the object oriented protoconcepts form a double Boolean algebra, and any double Boolean algebra is quasi-embedded in an algebra of protoconcepts. A logic DBL for the class of double Boolean algebras is proposed along with an extension PDBL for the class of pure double Boolean algebras. Utilizing the representation result for (pure) double Boolean algebras, it is established that DBL (PDBL) is sound and complete with respect to a semantics based on object oriented protoconcepts (semiconcepts).
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spelling pubmed-73381822020-07-07 Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras Howlader, Prosenjit Banerjee, Mohua Rough Sets Article The notion of a protoconcept in the framework of Yao’s object oriented concepts is proposed. Approximations by object oriented concepts are defined and these ‘object oriented protoconcepts’ are characterized using them. It is shown that the object oriented protoconcepts form a double Boolean algebra, and any double Boolean algebra is quasi-embedded in an algebra of protoconcepts. A logic DBL for the class of double Boolean algebras is proposed along with an extension PDBL for the class of pure double Boolean algebras. Utilizing the representation result for (pure) double Boolean algebras, it is established that DBL (PDBL) is sound and complete with respect to a semantics based on object oriented protoconcepts (semiconcepts). 2020-06-10 /pmc/articles/PMC7338182/ http://dx.doi.org/10.1007/978-3-030-52705-1_23 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Howlader, Prosenjit
Banerjee, Mohua
Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title_full Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title_fullStr Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title_full_unstemmed Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title_short Object Oriented Protoconcepts and Logics for Double and Pure Double Boolean Algebras
title_sort object oriented protoconcepts and logics for double and pure double boolean algebras
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7338182/
http://dx.doi.org/10.1007/978-3-030-52705-1_23
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