Basic logic for true and false LBVF
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Keywords
truth, falsity, alternating affirmation, alternating negation, paracomplete, good foundation, liar’s paradox.
Abstract
System LBVF is an extension of the classical positive logic, the system includes operators of alternating affirmation, alternating negation and determinability, and the operators of classical negation and good foundation are defined as from them. The system is characterized by a semantic of traditional valuations. Respect to the negation and affirmation operators the system is paracomplete.In the system the definitions of truth and falsity presented by Aristotle are really characterized, representing the Aristotelian falsity with the operator of alternating negation and the Aristotelian truth with the operator of alternating affirmation. This interpretation gives solution to a variant of the liar’s paradox.
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References
[1] Aristóteles. Metafísica, Libro 4, capítulo 7, 1011 b.
[2] Xavier Caicedo Ferrer. Elementos de lógica y calculabilidad, ISBN 970-625-190-5. Editorial Universidad de los Andes, Bogotá. 1990.
[3] A. G. Hamilton, Lógica para matemáticos. Editorial Paraninfo S.A. Madrid. 1981.
[4] Alfred Tarski. Logic, semantics and metamathematics, second edition, 978- 0915144761. Hackett Publishing Company, Indianapolis, 1983.
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[7] Nicola Grana. Sulla Teoría delle Valutazioni di N. C. A. da Costa, ISBN 9788820719425. N`apoli: Liguri Editore, 1990.
[8] Manuel Sierra A. Sistema paraconsistente y paracompleto LBPcPo. Revista Universidad EAFIT, ISSN 0120-341X, 44(147), 2007.
[9] I. M. Bochenski. Historia de la lógica formal , ISBN 84-249-2153-4. Editorial Gredos, Madrid, 1976.
[10] A. Arruda y E. Alves. A semantical study of some systems of vagueness logic, Bulletin of the Section of Logic, ISSN 0138-0680. Polish Academy of Sciences 8, 1979.
[2] Xavier Caicedo Ferrer. Elementos de lógica y calculabilidad, ISBN 970-625-190-5. Editorial Universidad de los Andes, Bogotá. 1990.
[3] A. G. Hamilton, Lógica para matemáticos. Editorial Paraninfo S.A. Madrid. 1981.
[4] Alfred Tarski. Logic, semantics and metamathematics, second edition, 978- 0915144761. Hackett Publishing Company, Indianapolis, 1983.
[5] Manuel Sierra A. Lógica básica con afirmación alterna. Ingeniería y Ciencia, ISSN 1794–9165, 1(1), 2005.
[6] Leon Henkin. The completeness of the first order functional calculus. The journal of symbolic logic, 14(3), 1949.
[7] Nicola Grana. Sulla Teoría delle Valutazioni di N. C. A. da Costa, ISBN 9788820719425. N`apoli: Liguri Editore, 1990.
[8] Manuel Sierra A. Sistema paraconsistente y paracompleto LBPcPo. Revista Universidad EAFIT, ISSN 0120-341X, 44(147), 2007.
[9] I. M. Bochenski. Historia de la lógica formal , ISBN 84-249-2153-4. Editorial Gredos, Madrid, 1976.
[10] A. Arruda y E. Alves. A semantical study of some systems of vagueness logic, Bulletin of the Section of Logic, ISSN 0138-0680. Polish Academy of Sciences 8, 1979.