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Paraconsistent algebras

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The prepositional calculiC n , 1 ⩽n ⩽ ω 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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Carnielli, W.A., de Alcantara, L.P. Paraconsistent algebras. Stud Logica 43, 79–88 (1984). https://doi.org/10.1007/BF00935742

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  • Equivalence Relation
  • Mathematical Logic
  • Closure System
  • Special Kind
  • Computational Linguistic