Operators of Knowledge and Ignorance in Heyting Algebras
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Multiple-Valued Logic and Soft Computing |
| MU Faculty or unit | |
| Citation | |
| web | https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-45-number-1-3-2025/mvlsc-45-1-3-p-5-30/ |
| Keywords | Heyting algebra; modal operator; operator of knowledge; operator of ignorance |
| Description | 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, Graziani, 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. |
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