A Criticism of Kripke’s Semantic for Intuitionistic Logic
This note aims to examine critically Kripke’s semantics for propositional intuitionistic logic. Kripke’s semantic is extensionally correct with respect to propositional intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. The fragment of propositional intu...
| Main Author: | |
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| Format: | Article |
| Language: | Portuguese |
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Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)
2016-12-01
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| Series: | O Que Nos Faz Pensar |
| Online Access: | http://www.oquenosfazpensar.fil.puc-rio.br/index.php/oqnfp/article/view/519 |
| _version_ | 1811273717023506432 |
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| author | Wagner de Campos Sanz |
| author_facet | Wagner de Campos Sanz |
| author_sort | Wagner de Campos Sanz |
| collection | DOAJ |
| description | This note aims to examine critically Kripke’s semantics for propositional intuitionistic logic. Kripke’s semantic is extensionally correct with respect to propositional intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. The fragment of propositional intuitionist logic containing disjunction and implication is also sound and complete with respect to the respective semantical clauses. However, we´ll argue, Kripke semantics is intensionallymisleading, since Kripke’ssemantical implication clause is intensionallymisleading. And the problem can be exemplified when we consider the fragment with disjunction and implication. |
| first_indexed | 2024-04-12T23:05:33Z |
| format | Article |
| id | doaj.art-1e58cf2d10594ad599a45c0a9b49d64a |
| institution | Directory Open Access Journal |
| issn | 0104-6675 |
| language | Portuguese |
| last_indexed | 2024-04-12T23:05:33Z |
| publishDate | 2016-12-01 |
| publisher | Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio) |
| record_format | Article |
| series | O Que Nos Faz Pensar |
| spelling | doaj.art-1e58cf2d10594ad599a45c0a9b49d64a2022-12-22T03:12:56ZporPontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)O Que Nos Faz Pensar0104-66752016-12-01253999104519A Criticism of Kripke’s Semantic for Intuitionistic LogicWagner de Campos SanzThis note aims to examine critically Kripke’s semantics for propositional intuitionistic logic. Kripke’s semantic is extensionally correct with respect to propositional intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. The fragment of propositional intuitionist logic containing disjunction and implication is also sound and complete with respect to the respective semantical clauses. However, we´ll argue, Kripke semantics is intensionallymisleading, since Kripke’ssemantical implication clause is intensionallymisleading. And the problem can be exemplified when we consider the fragment with disjunction and implication.http://www.oquenosfazpensar.fil.puc-rio.br/index.php/oqnfp/article/view/519 |
| spellingShingle | Wagner de Campos Sanz A Criticism of Kripke’s Semantic for Intuitionistic Logic O Que Nos Faz Pensar |
| title | A Criticism of Kripke’s Semantic for Intuitionistic Logic |
| title_full | A Criticism of Kripke’s Semantic for Intuitionistic Logic |
| title_fullStr | A Criticism of Kripke’s Semantic for Intuitionistic Logic |
| title_full_unstemmed | A Criticism of Kripke’s Semantic for Intuitionistic Logic |
| title_short | A Criticism of Kripke’s Semantic for Intuitionistic Logic |
| title_sort | criticism of kripke s semantic for intuitionistic logic |
| url | http://www.oquenosfazpensar.fil.puc-rio.br/index.php/oqnfp/article/view/519 |
| work_keys_str_mv | AT wagnerdecampossanz acriticismofkripkessemanticforintuitionisticlogic AT wagnerdecampossanz criticismofkripkessemanticforintuitionisticlogic |