We present an equivalence between the category of Nelson Paraconsistent lattices (NPc-lattices) and a category of pairs of Brouwerian algebras and regular filters. Specializing such category of pairs to Gödel hoops, we get the subvariety of Gödel NPc-lattices and, using the dual equivalence of finite Gödel hoops with finite trees, we obtain a duality for finite Gödel NPc-lattices. This duality is used to describe finitely generated free Gödel NPc-lattices.
On the category of Nelson paraconsistent lattices / S. Aguzzoli, M. Busaniche, B. Gerla, M.A. Marcos. - In: JOURNAL OF LOGIC AND COMPUTATION. - ISSN 0955-792X. - 27:7(2017), pp. 2227-2250. [10.1093/logcom/exx002]
On the category of Nelson paraconsistent lattices
S. Aguzzoli;
2017
Abstract
We present an equivalence between the category of Nelson Paraconsistent lattices (NPc-lattices) and a category of pairs of Brouwerian algebras and regular filters. Specializing such category of pairs to Gödel hoops, we get the subvariety of Gödel NPc-lattices and, using the dual equivalence of finite Gödel hoops with finite trees, we obtain a duality for finite Gödel NPc-lattices. This duality is used to describe finitely generated free Gödel NPc-lattices.
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