Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics
In this paper sequent calculi for the classical fragment (that is, the conjunction-disjunction-implication-negation fragment) of the nonsense logics B3, introduced by Bochvar, and H3, introduced by Halldén, are presented. These calculi are obtained by restricting in an appropriate way the applicatio...
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| Format: | Article |
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Open Publishing Association
2013-03-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1303.7333v1 |
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doaj-78101efe0d0e403e8234c37d018114212020-11-24T21:06:34ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802013-03-01113Proc. LSFA 201212513610.4204/EPTCS.113.12Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense LogicsMarcelo E. ConiglioMaría I. CorbalánIn this paper sequent calculi for the classical fragment (that is, the conjunction-disjunction-implication-negation fragment) of the nonsense logics B3, introduced by Bochvar, and H3, introduced by Halldén, are presented. These calculi are obtained by restricting in an appropriate way the application of the rules of a sequent calculus for classical propositional logic CPL. The nice symmetry between the provisos in the rules reveal the semantical relationship between these logics. The Soundness and Completeness theorems for both calculi are obtained, as well as the respective Cut elimination theorems.http://arxiv.org/pdf/1303.7333v1 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Marcelo E. Coniglio María I. Corbalán |
| spellingShingle |
Marcelo E. Coniglio María I. Corbalán Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Marcelo E. Coniglio María I. Corbalán |
| author_sort |
Marcelo E. Coniglio |
| title |
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics |
| title_short |
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics |
| title_full |
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics |
| title_fullStr |
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics |
| title_full_unstemmed |
Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics |
| title_sort |
sequent calculi for the classical fragment of bochvar and halldén's nonsense logics |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2013-03-01 |
| description |
In this paper sequent calculi for the classical fragment (that is, the conjunction-disjunction-implication-negation fragment) of the nonsense logics B3, introduced by Bochvar, and H3, introduced by Halldén, are presented. These calculi are obtained by restricting in an appropriate way the application of the rules of a sequent calculus for classical propositional logic CPL. The nice symmetry between the provisos in the rules reveal the semantical relationship between these logics. The Soundness and Completeness theorems for both calculi are obtained, as well as the respective Cut elimination theorems. |
| url |
http://arxiv.org/pdf/1303.7333v1 |
| work_keys_str_mv |
AT marceloeconiglio sequentcalculifortheclassicalfragmentofbochvarandhalldensnonsenselogics AT mariaicorbalan sequentcalculifortheclassicalfragmentofbochvarandhalldensnonsenselogics |
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