Paraconsistent algebras |
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Authors: | Walter Alexandre Carnielli Luiz Paulo de Alcantara |
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Institution: | (1) Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil;(2) Instituto de Matemática, Estatística e Ciência da Computação, Universidade Estadual de Campinas, Brazil |
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Abstract: | The prepositional calculiC
n
, 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum's algebra forC
n
. C. Mortensen settled the problem, proving that no equivalence relation forC
n
. determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC
n
, as well as the concept of paraconsistent closure system, are introduced in this paper.We show that every da Costa algebra is isomorphic with a paraconsistent algebra of sets, and that the closure system of all filters of a da Costa algebra is paraconsistent. |
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