About: 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).   Goto Sponge  NotDistinct  Permalink

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  • 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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  • Concepts in logic
  • Logic
  • Object-oriented programming
  • Programming paradigms
  • Norwegian inventions
  • Boolean algebra
  • 1847 introductions
  • Algebraic logic
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