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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
Article
  • 26 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

03G27 03B22 03G25 06A12 

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Copyright information

© 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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