Logic Journal of the IGPL 28 (5):973-999 (2020)

Abstract
A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability results for the corresponding logics.
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DOI 10.1093/jigpal/jzy070
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References found in this work BETA

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Reasoning with Logical Bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
The Logic of Distributive Bilattices.Félix Bou & Umberto Rivieccio - 2011 - Logic Journal of the IGPL 19 (1):183-216.

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