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Operators of Knowledge and Ignorance in Heyting Algebras
Ivan Chajda and Jan Paseka
The operator of knowledge was introduced and explored in various logical systems by numerous researchers. Nevertheless, its formalization on Heyting algebras, which serve as the algebraic representation of intuitionistic logic, remained unexplored.
Motivated by this gap, this study delves into the formalization of knowledge on Heyting algebras. In addition, it adapts the formula for the severe ignorance operator, presented by Bonzio, Fano, Graziano, and Pra Baldi, to the context of Heyting algebras.
We comprehensively explore the properties of both the knowledge and severe ignorance operators and examine their interplay. The paper provides illuminating examples to showcase the behavior and characteristics of these operators.
AMS Subject Classification: 06D20, 03B42, 03B45, 03B56.
Keywords: Heyting algebra, modal operator, operator of knowledge, operator of ignorance