NPc-algebras and Gödel hoops

MARCOS, MIGUEL ANDRÉS; BUSANICHE, MANUELA; GERLA, BRUNELLA; AGUZZOLI, STEFANO

Bahía Blanca

Congreso; XIV Congreso Dr. Antonio Monteiro; 2017

Departamento de Matemática, UNS ; INMABB, CONICET-UNS

The algebraic models of paraconsistent Nelson logic were introduced byOdinstov under the name of N4-lattices.NPc-lattices are a variety of residuated lattices turn out to be termwiseequivalent to eN4-lattices, the expansions of N4-lattices by a constant e, thusparaconsistent Nelson logic can be studied within the framework of substructurallogics (see [3]).The rst aim of this work is to prove a categorical equivalence between thecategory of NPc-lattices and its morphisms and a category whose objects arepairs of Brouwerian algebras and certain lters that we call regular. For this wefollow the ideas of Odintsov in [4].We then dene Gödel NPc-lattices as those NPc-lattices with a prelinearnegative cone, which turn to be equivalent to pairs of Gödel hoops and regularlters. For the case of nite Gödel NPc-lattices, by the duality of nite Gödelhoops and nite trees (see [1]) we also obtain a dual category, which consists inpairs of nite trees and certain subtrees.Therefore we have a duality between a category of algebras and a categoryof combinatorics, which we use to characterize the free algebras in the varietyof Gödel NPc-lattices.