Abstract
A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.
Similar content being viewed by others
References
Gottwald, S., 1988, Mehrwertige Logik, Akademie-Verlag, Berlin.
HÁjek, P., 'Fuzzy logic and arithmetical hierarchy', Fuzzy Sets and Systems, (to appear).
HÁjek, P., 'Fuzzy logic as logic', In: Mathematical Models of Handling Partial Knowledge in Artificial Intelligence, Erice, Italy, (to appear), G. Coletti et al., Eds., Pergamon Press.
NovÁk, V., 1987, 'First-order fuzzy logic', Studia Logica 46, 87-109.
NovÁk, V., 1990, 'On the syntactico-semantical completeness of first-order fuzzy logic I, II', Kybernetika 2, 47-26, 134–152.
NovÁk, V., 1990, 'Fuzzy logic revisited', In: EUFIT'94, Aachen.
NovÁk, V., 1995, 'A new proof of completeness of fuzzy logic and some conclusions for approximate reasoning', In: Proc. of IFES'95, Yokohama.
Pavelka, J., 1979, 'On fuzzy logic I, II, III', Zeitschr. f. math. Logik und Grundl. der Math. 25, 45-52, 119–134, 447–464.
Rogers, H.,Jr., 1967, Theory of recursive functions and effective computability. McGraw-Hill.
Rose, A., and J. B. Rosser, 1958, 'Fragments of many-valued statement calculi', Trans. A.M.S. 87, 1-53.
Scarpellini, B., 1962, 'Die Nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz', Journ. Symb. Log. 27, 159-170.
Takeuti, A., and S. Titani, 1992, 'Fuzzy logic and fuzzy set theory', Arch. Math. Logic 32.
Ragaz, M., 1981, 'Arithmetische Klassifikation von Formelnmengen der unendlich-wertigen Logik', Thesis, ETH Zürich.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hájek, P. Fuzzy Logic and Arithmetical Hierarchy, II. Studia Logica 58, 129–141 (1997). https://doi.org/10.1023/A:1004948116720
Issue Date:
DOI: https://doi.org/10.1023/A:1004948116720