On Some Semi-Intuitionistic Logics
Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original on...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/77848 |
| Acceso en línea: | http://hdl.handle.net/11336/77848 |
| Access Level: | acceso abierto |
| Palabra clave: | Heyting Algebras Intuitionistic Logic Semi-Heyting Algebras Semi-Intuitionistic Logic https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics. |
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