Four-valued modal logic: Kripke semantics and duality

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  • TU Delft
  • Universitat de Barcelona


We introduce a family of modal expansions of Belnap–Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice and some of its axiomatic extensions. We study the algebraic models of these systems, relating them to the algebraic semantics of classical multi-modal logic. This link allows us to prove that both local and global consequence of the least four-valued modal logic enjoy the finite model property and are therefore decidable.


Original languageEnglish
Number of pages43
JournalJournal of Logic and Computation
Early online date15 Jun 2015
Publication statusPublished - 15 Jun 2015


  • Many-valued modal logic, Belnap logic, bilattices, paraconsistent Nelson logic

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