The Systems of Relevance Logic
The system R, or more precisely the pure implicational fragment R→, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance...
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| Format: | Article |
| Language: | deu |
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Pedagogical University of Krakow
2011-06-01
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| Series: | Argument |
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| Online Access: | http://argumentwp.vipserv.org/wp-content/uploads/2011/pdf/08_argument-1-Ryszard_MIREK.pdf |
| _version_ | 1811252773229953024 |
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| author | Ryszard MIREK |
| author_facet | Ryszard MIREK |
| author_sort | Ryszard MIREK |
| collection | DOAJ |
| description | The system R, or more precisely the pure implicational fragment R→, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R→ yields the pure implicational fragment RM→ of the system? As concerns the weak systems there are at least two approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility. |
| first_indexed | 2024-04-12T16:39:41Z |
| format | Article |
| id | doaj.art-a2c070885c134d9fb18d6cb00407ae9a |
| institution | Directory Open Access Journal |
| issn | 2083-6635 2084-1043 |
| language | deu |
| last_indexed | 2024-04-12T16:39:41Z |
| publishDate | 2011-06-01 |
| publisher | Pedagogical University of Krakow |
| record_format | Article |
| series | Argument |
| spelling | doaj.art-a2c070885c134d9fb18d6cb00407ae9a2022-12-22T03:24:51ZdeuPedagogical University of KrakowArgument2083-66352084-10432011-06-011187102The Systems of Relevance LogicRyszard MIREKThe system R, or more precisely the pure implicational fragment R→, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R→ yields the pure implicational fragment RM→ of the system? As concerns the weak systems there are at least two approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility.http://argumentwp.vipserv.org/wp-content/uploads/2011/pdf/08_argument-1-Ryszard_MIREK.pdfrelevant logiclogicrelevant implicationaxiomsystemvaliditytheoremdeducibilitydeduction |
| spellingShingle | Ryszard MIREK The Systems of Relevance Logic Argument relevant logic logic relevant implication axiom system validity theorem deducibility deduction |
| title | The Systems of Relevance Logic |
| title_full | The Systems of Relevance Logic |
| title_fullStr | The Systems of Relevance Logic |
| title_full_unstemmed | The Systems of Relevance Logic |
| title_short | The Systems of Relevance Logic |
| title_sort | systems of relevance logic |
| topic | relevant logic logic relevant implication axiom system validity theorem deducibility deduction |
| url | http://argumentwp.vipserv.org/wp-content/uploads/2011/pdf/08_argument-1-Ryszard_MIREK.pdf |
| work_keys_str_mv | AT ryszardmirek thesystemsofrelevancelogic AT ryszardmirek systemsofrelevancelogic |