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GRÁFICOS EXISTENCIALES PARACONSISTENTES ALFAK
ALFAK PARACONSISTENT EXISTENTIAL GRAPHS
DOI:
https://doi.org/10.15446/rev.fac.cienc.v11n2.99198Keywords:
Gráficos existenciales, lógica paraconsistente, semántica de mundos posibles, afirmación fuerte, negación débil (es)Existential graphs, paraconsistent logic, semantics of possible worlds, strong affirmation, weak neagation (en)
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En este trabajo, se presentan los gráficos existenciales para el cálculo proposicional paraconsistente, KT4P. Este sistema deductivo, es un fragmento de la lógica proposicional modal S4, y se construye a partir del cálculo proposicional clásico positivo, junto con un operador de negación débil. El sistema KT4P, se encuentra caracterizado por una semántica de mundos posibles, además, KT4P es paraconsistente, es decir, no colapsa en la presencia de contradicciones. Los gráficos existenciales para este sistema paraconsistente, se presentan en el estilo de los gráficos alfa de Charles Sanders Peirce, junto con reglas para bucles y rizos similares a las presentadas recientemente por Arnold Oostra, para los gráficos existenciales intuicionistas. Todas las pruebas, son presentadas de manera completa, rigurosa y detallada.
KT4P, are presented. This deductive system is a fragment of the modal propositional
logic S4, and is constructed from the positive classical propositional calculus,
together with a weak negation operator. The $KT4P$ system is characterized by a
semantics of possible worlds, in addition, KT4P is paraconsistent, that is, it does
not collapse in the presence of contradictions. The existential graphs for this
paraconsistent system are presented in the style of the alpha graphics of Charles
Sanders Peirce (late nineteenth century), along with rules for loops and scroll
similar to those recently introduced (early twenty-first century) by Arnold Oostra,
for intuitionistic existential graphics. All evidence is presented in a complete,
rigorous and detailed manner.
References
Bochenski, I. (1976). Historia de la lógica formal. Ed. Gredos. Madrid.
da Costa, N. (1993). Sistemas formais inconsistentes. Ed. UFPR. Universidade Federal Do Paraná. Curi-tiba. Brasil.
Brady, G., y Trimble, T. (2000). A categorical interpretation of C.S. Peirce's propositional logic Alpha. Journal of Pure and Applied Algebra. 149. 213-239. DOI: https://doi.org/10.1016/S0022-4049(98)00179-0
Doop, J. (1969). Nociones de lógica formal. Ed. Tecnos S.A. Madrid.
Hamilton, A. (1978). Logic for mathematicians. Cambridge University Press. Cambridge.
Henkin, L. (1949). The completeness of the first order functional calculus. The Journal of Symbolic Logic, 14(3), 159–166. DOI: https://doi.org/10.2307/2267044
Heyting, A. (1956). Intuitionism: An introduction (Studies in logic and the foundations of mathematics). North-holland publishing company.
Oostra, A. (2010). Los gráficos Alfa de Peirce aplicados a la lógica intuicionista. Cuadernos de Sistemáti-ca Peirceana 2, 25-60.
Oostra, A. (2011). Gráficos existenciales beta intuicionistas. Cuadernos de Sistemática Peirceana 3. 53-78.
Oostra, A. (2012). Los gráficos existenciales gama aplicados a algunas lógicas modales intuicionistas. Cuadernos de Sistemática Peirceana 4, 27-50.
Oostra A. (2021). Equivalence Proof for Intuitionistic Existential Alpha Graphs. Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science, vol 12909. Springer, Cham. DOI: https://doi.org/10.1007/978-3-030-86062-2_16
Peirce, C. (1965). Charles S. Peirce, Collected Papers of Charles Sanders Peirce. Charles Hartshorne, Paul Weiss and Arthur W. Burks (Eds.). Cambridge (Massachusetts): Harvard University Press (1931–1958).
Roberts, D. (1992). The existential graphs in Computters Math. Applie, 23, 6-9, 639-663. DOI: https://doi.org/10.1016/0898-1221(92)90127-4
Sierra, M. (2010). Argumentación deductiva con diagramas y árboles de forzamiento. Fondo Editorial Universidad EAFIT. Medellín.
Sierra, M. (2021). Lógica doble LD y gráficos existenciales gamma LD. Revista Facultad de Ciencias Básicas, 17, 1.
Smullyan, R. (1997). Como se llama este libro. Ed. Cátedra. Madrid.
van Dalen, D. (2013). Logic and structure. Springer-Verlag. London. DOI: https://doi.org/10.1007/978-1-4471-4558-5
Zalamea, F. (2010). Los gráficos existenciales Peirceanos. Universidad Nacional de Colombia. Bogotá.
Zeman, J. (1963). The Graphical Logic of C.S. Peirce, Ph.D. Thesis, University of Chicago.
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