Abstract
That there are only three different kinds of α-tautologies in revised Kleene systems is proved first; then in finite case the diversity theorem of α-tautologies with α's larger than the mid-value is established. Lastly, also in finite case, a representation theorem of α-tautologies by means of tautologies is given.
Similar content being viewed by others
References
Dubois, D., Lang, J., Prade, H., Fuzzy set in approximate reasoning,Fuzzy Sets and Systems, 1991, 40: 143.
Pavelka, J., On fuzzy logic I, II, III,Zeitschr. f. Math. Logik und Grundlagen d. Math., 1979, 25: 45–52; 119–134; 447–464.
Ying, M. S., The fundamental theorem of ultraproduct in Pavelka's logic,Zeitschr. f. Math. Logik und Grundlagen d. Math., 1992, 38: 197.
Ying, M. S., Compactness, the Löwenheim-Skolem property and the direct product of lattices of truth values,Zeitschr. f. Math. Logik und Grundlagen d. Math., 1992, 38: 521.
Wang, G. J., Quasi-formal deductive system for fuzzy propositional calculus,Chinese Science Bulletin, 1997, 42(14): 1154.
Wang, G. J., On the logic foundations of fuzzy modus ponens and fuzzy modus tollens,J. Fuzzy Math., 1997, 5(1): 229.
Wang, G. J., On the logic foundation of fuzzy reasoning,Lecture Notes in Fuzzy Mathematics and Computer Science, Omaha, Nebraska: Creighton University, 1997, 4: 1.
Chen, Y. Y.,Fuzzy Control Technique and Its Applications (in Chinese), Beijing: Beijing Normal University Press, 1993.
Wang, G. J., Logic foundations of fuzzy reasoning,Proc. 4th Chinese Computer Conference (in Chinese), Beijing: Beijing Electronic Industry Press, 1997, 1108–1113.
Wang, G. J., Logic on certain algebras (I),J. Shaanxi Normal University (in Chinese), 1997, 25(1): 1.
Zhang, W. X., Liang, Y.,The Uncertainty Reasoning Principles (in Chinese), Xi'an: Xi'an Jiaotong University Press, 1996.
Rescher, N.,Many-valued Logic, New York: McGraw-Hill Book Company, 1969.
Bloc L., Borowik, P.,Many-valued Logic, Warsawa: Springer-Verlag, 1993.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China (Grant No. 19331030).
Rights and permissions
About this article
Cite this article
Wang, G. Theory of Ω-(α-tautologies) in revised Kleene systems. Sci. China Ser. E-Technol. Sci. 41, 188–195 (1998). https://doi.org/10.1007/BF02919682
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02919682