Double Negation Semantics for Generalisations of Heyting Algebras
| Autor: | Rob Arthan, Paulo Oliva |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Logic Semantics (computer science) 010102 general mathematics Classical logic 0102 computer and information sciences Intuitionistic logic 01 natural sciences Algebra History and Philosophy of Science 010201 computation theory & mathematics Bounded function Double negation Gödel 0101 mathematics Algebraic number computer Mathematics computer.programming_language |
| Zdroj: | Studia Logica. 109:341-365 |
| ISSN: | 1572-8730 0039-3215 |
| Popis: | This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these asvariant semanticsand present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned translation schemes behaves on two generalisations of Heyting algebras: bounded pocrims and bounded hoops. When a translation fails for a particular class of algebras, we demonstrate that failure via specific finite examples. Using these, we prove that the syntactic version of these translations will fail to satisfy Troelstra’s criteria in the corresponding substructural logical setting. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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