Abstract
In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.
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References
Cignoli, R., D'Ottaviano, IML., Mundici, D.: Algebraic Foundation of Many-Valued Reasoning. Kluwer Academic Publ., Dordrecht 2000
Drăgulici, DD.: The Conservative Extension of MV-algebras to Pavelka Algebras. Annals of University of Bucharest, Computer Science, 1, 117–126 (2003)
Drăgulici, D., Georgescu, G.: Algebraic Logic for Rational Pavelka Predicate Calculus. Mathematical Logic Quarterly 47, 315–326 (2001)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publ., Dordrecht 1998
Hájek, P., Paris, J., Shepherdson, J.: Rational Pavelka predicate logic is a conservative extension of Łukasiewicz predicate logic. Journal of Symbolic Logic 2000
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publ., Dordrecht 1999
Schwartz, D.: Theorie der polyadischen MV-algebren endlicher Ordnung. Math. Nachr. 78, 131–138 (1977)
Schwartz, D.: Polyadic MV-algebras. Zeitschr. f. math. Logik und Grundlagen d. Math. 26, 561–564 (1980)
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Drăgulici, D. Conservative extension of polyadic MV-algebras to polyadic pavelka algebras. Arch. Math. Logic 45, 601–613 (2006). https://doi.org/10.1007/s00153-005-0277-z
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DOI: https://doi.org/10.1007/s00153-005-0277-z