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Some New Three-valued Paraconsistent Logics
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DOI：10.1007/s11225-025-10222-9.png)
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Abstract
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This paper presents some new three-valued paraconsistent systems for which a one-to-one correspondence between the notions of consequence and inconsistency can be established following Dutta and Chakraborty (in: New Directions in Paraconsistent Logic Springer Proc Math Stat, vol 152, pp 269 283, Springer, India, 2015). A natural deduction style proof system and soundness-completeness result for each of these logics is established. Moreover, some of the logics are identified as generalized logics of formal inconsistency following a newly proposed notion of generalized gentle explosion.
Keywords:
Paraconsistent logic
3-valued logic
Natural deduction
Gentle explosion
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