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Priestley Duality for Bilattices

Studia Logica 100 (1-2):223-252 (2012)

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  1. Natural Dualities Through Product Representations: Bilattices and Beyond.L. M. Cabrer & H. A. Priestley - 2016 - Studia Logica 104 (3):567-592.
    This paper focuses on natural dualities for varieties of bilattice-based algebras. Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying bilattices-based algebras is product representation. The authors recently set up a widely applicable algebraic framework which enabled product representations over a base variety to be derived in a uniform and categorical manner. By combining this methodology with that of natural duality theory, we demonstrate how to build (...)
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  • On Definability of Connectives and Modal Logics Over FDE.Sergei P. Odintsov, Daniel Skurt & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
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  • A General Framework for Product Representations: Bilattices and Beyond.L. M. Cabrer & H. A. Priestley - 2015 - Logic Journal of the IGPL 23 (5):816-841.
  • Disentangling FDE -Based Paraconsistent Modal Logics.Sergei P. Odintsov & Heinrich Wansing - 2017 - Studia Logica 105 (6):1221-1254.
    The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...)
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