Classical Negation and Expansions of Belnap–Dunn Logic

Abstract

We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev.

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Correspondence to Michael De.

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De, M., Omori, H. Classical Negation and Expansions of Belnap–Dunn Logic. Stud Logica 103, 825–851 (2015). https://doi.org/10.1007/s11225-014-9595-7

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Keywords

  • First-degree entailment
  • Belnap–Dunn logic
  • Classical negation
  • Many-valued logic
  • Paraconsistency
  • Paracompleteness
  • Maximality