Studia Logica 104 (3):567-592 (2016)

Abstract
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 a natural duality for any bilattice-based variety which has a suitable product representation over a dualisable base variety. This procedure allows us systematically to present economical natural dualities for many bilattice-based varieties, for most of which no dual representation has previously been given. Among our results we highlight that for bilattices with a generalised conflation operation. Here both the associated product representation and the duality are new. Finally we outline analogous procedures for pre-bilattice-based algebras.
Keywords Product representation  Natural duality  Bilattice  Conflation  Double Ockham algebra
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DOI 10.1007/s11225-016-9651-6
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Reasoning with Logical Bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
Bilattices Are Nice Things.Melvin Fitting - 2006 - In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. CSLI Publications.

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