Archive for Mathematical Logic

, Volume 58, Issue 1–2, pp 219–243 | Cite as

Selfextensional logics with a distributive nearlattice term

  • Luciano J. GonzálezEmail author


We define when a ternary term m of an algebraic language \(\mathcal {L}\) is called a distributive nearlattice term (\(\mathrm {DN}\)-term) of a sentential logic \(\mathcal {S}\). Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a \(\mathrm {DN}\)-term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras (under the point of view of Abstract Algebraic Logic) associated with a selfextensional logic with a \(\mathrm {DN}\)-term is a variety, and we obtain that the logic is in fact fully selfextensional.


Selfextensional logic Distributive nearlattice Logics based on partial orders Abstract algebraic logic 

Mathematics Subject Classification

03G27 03B22 03G25 06A12 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de La PampaSanta RosaArgentina

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