Studia Logica

, Volume 103, Issue 4, pp 825–851 | Cite as

Classical Negation and Expansions of Belnap–Dunn Logic

  • Michael De
  • Hitoshi Omori


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.


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


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© Springer 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversität KonstanzKonstanzGermany
  2. 2.The Graduate Center, City University of New YorkNew YorkUSA

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