Studia Logica 101 (4):651-675 (2013)

In a previous work we studied, from the perspective ofAlgebraic Logic, the implicationless fragment of a logic introduced by O. Arieli and A. Avron using a class of bilattice-based logical matrices called logical bilattices. Here we complete this study by considering the Arieli-Avron logic in the full language, obtained by adding two implication connectives to the standard bilattice language. We prove that this logic is algebraizable and investigate its algebraic models, which turn out to be distributive bilattices with additional implication operations. We axiomatize and state several results on these new classes of algebras, in particular representation theorems analogue to the well-known one for interlaced bilattices
Keywords Bilattice  Representation of bilattices  Brouwerian lattice  Disjunctive lattice  Generalized Boolean algebra  Category of bilattices  Algebraic logic
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DOI 10.1007/s11225-013-9494-3
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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.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
The Value of the Four Values.Ofer Arieli & Arnon Avron - 1998 - Artificial Intelligence 102 (1):97-141.
On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.

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Citations of this work BETA

Bilattice Public Announcement Logic.Umberto Rivieccio - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 459-477.

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