Main Article Content
incompatibility, weak negation, paraconsistent deductive system.
The language of the LBPc¬I system extends the language of the classical positive logic when including an operator of weak negation and an operator of incompatibility, and permit to deﬁne an operator of strong negation; this last one has all the characteristics of the classical negation. The system is characterized by a traditional semantics with which test that, with respect to the operator of weak negation, the system is paraconsistent. When the formulas involved in an argument behave classically, that is to say, are incompatible with his weak negation, then the weak negation behaves like the classical negation, but this requirement not always is necessary, the weak negation can precise be as powerful as the classical negation although the involved formulas do not behave classically.
MSC: 03Bxx, 03B53
 W. Carnielli and J. Marcos. A Taxonomy of C-Systems. En Paraconsistency: The LogicalWay to the Inconsistent. Lecture Notes in Pure and Applied Mathematics, New York: Ed. Marcel Dekker, 228, 2002.
 X. Caicedo. Elementos de lógica y calculabilidad. Bogotá: Universidad de los Andes, 1990.
 A. Hamilton. Lógica para matemáticos. Madrid: Paraninfo S.A., 1981.
 A. Tarski. Logic, semantics and metamathematics. Second edition, Indianapolis: Hackett Publ., 1983.
 M. Sierra. Lógica básica con afirmación alterna. Ingeniería y Ciencia, 1(1), 2005.
 L. Henkin. The completeness of the first order functional calculus. The journal of symbolic logic, 14(3), 1949.