Rivieccio, UmbertoJung, AchimJansana, Ramon2024-12-022024-12-022017-02Umberto Rivieccio, Achim Jung and Ramon Jansana, Four-valued modal logic: Kripke semantics and duality. Journal of Logic and Computation, 27, 2017, pp. 155-199; https://doi.org/10.1093/logcom/exv0380955-792X; e-ISSN:1465-363Xhttps://doi.org/10.1093/logcom/exv038https://hdl.handle.net/20.500.14468/24642Este es el manuscrito aceptado del artículo. La versión registrada fue publicada por primera vez en Journal of Logic and Computation, 27, 2017, pp. 155-199, está disponible en línea en el sitio web del editor: https://doi.org/10.1093/logcom/exv038 This is the accepted manuscript of the article. The registered version was first published in Journal of Logic and Computation, 27, 2017, pp. 155-199, is available online at the publisher's website: https://doi.org/10.1093/logcom/exv038We 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.eninfo:eu-repo/semantics/openAccess11 Lógicaartículo