Soft Computing

, Volume 22, Issue 9, pp 2797–2807 | Cite as

The logic of distributive nearlattices

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Abstract

In this paper, we propose a sentential logic naturally associated, in the sense of Abstract Algebraic Logic, with the variety of distributive nearlattices. We show that the class of algebras canonically associated (in the sense of Abstract Algebraic Logic) with this logic is the variety of distributive nearlattices. We also present several properties of this sentential logic.

Keywords

Distributive nearlattices Sentential logic Gentzen system 

Notes

Acknowledgements

I greatly appreciate the comments and suggestions of the referees that helped to improve the paper. This paper was partially supported by Universidad Nacional de La Pampa (Fac. de Cs. Exactas y Naturales) under the Grant P.I. 64 M, Res. No. 432/14 CD and also by CONICET (Argentina) under the Grant PIP 112-20150-100412CO.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interests regarding the publishing of this paper.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Fac. de Cs. Exactas y NaturalesUniversidad Nacional de La PampaSanta RosaArgentina

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