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<p>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 <i>generalized logics of formal inconsistency</i> following a newly proposed notion of <i>generalized gentle explosion</i>.</p>

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Some New Three-valued Paraconsistent Logics

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • Bidhan Saha,
  • Soma Dutta,
  • Mohua Banerjee

摘要

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.