Four-valued modal logic: Kripke semantics and duality

Umberto Rivieccio, Achim Jung, Ramon Jansana

Research output: Contribution to journalArticleScientificpeer-review

16 Citations (Scopus)


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
Pages (from-to)155-199
Number of pages45
JournalJournal of Logic and Computation
Issue number1
Publication statusPublished - 2017


  • Belnap logic
  • Bilattices
  • Many-valued modal logic
  • Paraconsistent Nelson logic

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