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.
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This work was partially supported by Universidad Nacional de La Pampa (Facultad de Ciencias Exactas y Naturales) under the Grant P.I. 64 M, Res. 432/14 CD; and also by Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) under the Grant PIP 112-20150-100412CO.
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González, L.J. Selfextensional logics with a distributive nearlattice term. Arch. Math. Logic 58, 219–243 (2019). https://doi.org/10.1007/s00153-018-0628-1
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DOI: https://doi.org/10.1007/s00153-018-0628-1