Paraconsistency and Consistency Understood as the Absence of the Negation of any Implicative Theorem
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RIS BIB ENDNOTEParaconsistency and Consistency Understood as the Absence of the Negation of any Implicative Theorem
Publication date: 28.08.2012
Reports on Mathematical Logic, 2012, Number 47, pp. 147-171
https://doi.org/10.4467/20842589RM.12.007.0688Authors
Paraconsistency and Consistency Understood as the Absence of the Negation of any Implicative Theorem
As is stated in its title, in this paper consistency is understood as the absence of the negation of any implicative theorem. Then, a series of logics adequate to this concept of consistency is defined within the context of the ternary relational semantics with a set of designated points, negation being modelled with the Routley operator. Soundness and completeness theorems are provided for each one of these logics. In some cases, strong (i.e., in respect of deducibility) soundness and completeness theorems are also proven. All logics in this paper are included in Lewis’ S4. They are all paraconsistent, but none of them is relevant.
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Information: Reports on Mathematical Logic, 2012, Number 47, pp. 147-171
Article type: Original article
Dpto. de Psicologa, Sociologa y Filosofa, Universidad de Leon Campus de Vegazana, s/n, 24071, Leon, Spain
Published at: 28.08.2012
Article status: Open
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