The logic of distributive nearlattices
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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.
KeywordsDistributive nearlattices Sentential logic Gentzen system
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.
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The author declares that there is no conflict of interests regarding the publishing of this paper.
- Blok WJ, Pigozzi D (1989) Algebraizable logics. 396. Memoirs of the American Mathematical SocietyGoogle Scholar
- Calomino I (2015) Supremo álgebra distributivas: una generalización de las álgebras de tarski. Ph.D. thesis, Universidad Nacional del SurGoogle Scholar
- Font JM, Jansana R (2009) A general algebraic semantics for sentential logics, Lecture Notes in Logic, vol. 7, 2 edn. The Association for Symbolic LogicGoogle Scholar
- Rebagliato J, Verdú V (1995) Algebraizable gentzen systems and the deduction theorem for gentzen systems. Mathematics Preprint Series 175Google Scholar