On theories and models in fuzzy predicate logics
Petr Cintula and Petr Hájek
Source: J. Symbolic Logic Volume 71, Issue 3
(2006), 863-880.
Abstract
In the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories and on witnessed models.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1154698581
Digital Object Identifier: doi:10.2178/jsl/1154698581
Mathematical Reviews number (MathSciNet): MR2251545
Zentralblatt MATH identifier: 1111.03030
References
Matthias Baaz, Infinite-valued Gödel logic with 0-1-projections and relativisations, Gödel'96: Logical foundations of mathematics, computer science, and physics (Petr Hájek, editor), Lecture Notes in Logic, vol. 6, Springer-Verlag, 1996, pp. 23--33.
Mathematical Reviews (MathSciNet): MR1441100
Petr Cintula, Weakly implicative $($fuzzy$)$ logics I: Basic properties, Archive for Mathematical Logic, 2006, to appear.
Mathematical Reviews (MathSciNet): MR2252249
Digital Object Identifier: doi:10.1007/s00153-006-0011-5
Zentralblatt MATH: 1101.03015
--------, Advances in the \L$\Pi$ and \L$\Pi\frac12$ logics, Archive for Mathematical Logic, vol. 42 (2003), no. 5, pp. 449--468.
Mathematical Reviews (MathSciNet): MR1990735
Michael Dummett, A propositional calculus with denumerable matrix, Journal of Symbolic Logic, vol. 27 (1959), pp. 97--106.
Mathematical Reviews (MathSciNet): MR123476
Digital Object Identifier: doi:10.2307/2964753
Project Euclid: euclid.jsl/1183733575
Zentralblatt MATH: 0089.24307
Francesc Esteva, Joan Gispert, Lluís Godo, and Carles Noguera, Adding truth-constants to continuous t-norm based logics: Axiomatization and completeness results, submitted, 2005.
Francesc Esteva and Lluís Godo, Monoidal t-norm based logic: Towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, vol. 123 (2001), no. 3, pp. 271--288.
Mathematical Reviews (MathSciNet): MR1860848
Digital Object Identifier: doi:10.1016/S0165-0114(01)00098-7
Zentralblatt MATH: 0994.03017
Francesc Esteva, Lluís Godo, Petr Hájek, and Mirko Navara, Residuated fuzzy logics with an involutive negation, Archive for Mathematical Logic, vol. 39 (2000), no. 2, pp. 103--124.
Mathematical Reviews (MathSciNet): MR1742377
Digital Object Identifier: doi:10.1007/s001530050006
Zentralblatt MATH: 0965.03035
Francesc Esteva, Lluís Godo, and Franco Montagna, The \L$\Pi$ and \L$\Pi\frac12$ logics: Two complete fuzzy systems joining Łukasiewicz and product logics, Archive for Mathematical Logic, vol. 40 (2001), no. 1, pp. 39--67.
Zentralblatt MATH: 0966.03022
Francesc Esteva, Lluís Godo, and Carles Noguera, On rational Weak Nilpotent Minimum logics, Journal of Multiple-Valued Logic and Soft Computing, vol. 12 (2006), pp. 9--32.
Mathematical Reviews (MathSciNet): MR2211525
Josep Maria Font, Ramon Jansana, and Don Pigozzi, A survey of Abstract Algebraic Logic, Studia Logica, vol. 74 (2003), no. 1--2, pp. 13--97.
Mathematical Reviews (MathSciNet): MR1996592
Digital Object Identifier: doi:10.1023/A:1024621922509
Siegfried Gottwald and Petr Hájek, Triangular norm based mathematical fuzzy logic, Logical, algebraic, analytic and probabilistic aspects of triangular norms (Erich Petr Klement and Radko Mesiar, editors), Elsevier, Amsterdam, 2005, pp. 275--300.
Mathematical Reviews (MathSciNet): MR2165239
Zentralblatt MATH: 1078.03020
Digital Object Identifier: doi:10.1016/B978-044451814-9/50010-0
Petr Hájek Metamathematics of fuzzy logic, Trends in Logic, vol. 4, Kluwer, Dordercht, 1998.,
Mathematical Reviews (MathSciNet): MR1900263
--------, Fuzzy logic and arithmetical hierarchy III, Studia Logica, vol. 68 (2001), no. 1, pp. 129--142.
Mathematical Reviews (MathSciNet): MR1950037
Digital Object Identifier: doi:10.1023/A:1011906423560
Zentralblatt MATH: 0988.03042
--------, Fuzzy logic and arithmetical hierarchy IV, First-order logic revised (V. Hendricks, F. Neuhaus, S. A. Pedersen, U. Scheffler, and H. Wansing, editors), Logos Verlag, Berlin, 2004, pp. 107--115.
--------, Arithmetical complexity of fuzzy predicate logics---a survey, Soft Computing, vol. 9 (2005), no. 12, pp. 935--941.
Zentralblatt MATH: 05009488
--------, Making fuzzy description logic more general, Fuzzy Sets and Systems, vol. 154 (2005), no. 1, pp. 1--15.
Mathematical Reviews (MathSciNet): MR2150521
Digital Object Identifier: doi:10.1016/j.fss.2005.03.005
Zentralblatt MATH: 1094.03014
Petr Hájek and Petr Cintula, Triangular norm based predicate fuzzy logics, Proceedings of Linz Seminar 2005, to appear.
Petr Hájek, Jeff Paris, and John C. Shepherdson, The liar paradox and fuzzy logic, Journal of Symbolic Logic, vol. 65 (2000), no. 1, pp. 339--346.
Mathematical Reviews (MathSciNet): MR1782124
Digital Object Identifier: doi:10.2307/2586541
Project Euclid: euclid.jsl/1183746025
Zentralblatt MATH: 0945.03031
--------, Rational Pavelka logic is a conservative extension of Łukasiewicz logic, Journal of Symbolic Logic, vol. 65 (2000), no. 2, pp. 669--682.
Project Euclid: euclid.jsl/1183746068
Mathematical Reviews (MathSciNet): MR1771076
Digital Object Identifier: doi:10.2307/2586560
Petr Hájek and John C. Shepherdson, A note on the notion of truth in fuzzy logic, Annals of Pure and Applied Logic, vol. 109 (2001), pp. 65--69.
Mathematical Reviews (MathSciNet): MR1835238
Digital Object Identifier: doi:10.1016/S0168-0072(01)00041-0
Zentralblatt MATH: 1004.03020
Rostislav Horčík and Petr Cintula, Product Łukasiewicz logic, Archive for Mathematical Logic, vol. 43 (2004), no. 4, pp. 477--503.
Franco Montagna, Three complexity problems in quantified fuzzy logic, Studia Logica, vol. 68 (2001), no. 1, pp. 143--152.
Mathematical Reviews (MathSciNet): MR1950038
Digital Object Identifier: doi:10.1023/A:1011958407631
Zentralblatt MATH: 0985.03014
Helena Rasiowa An algebraic approach to non-classical logics, North-Holland, Amsterdam, 1974.,
Mathematical Reviews (MathSciNet): MR446968
Zentralblatt MATH: 0299.02069
Gaisi Takeuti and Satoko Titani, Intuitionistic fuzzy logic and intuitionistic fuzzy set theory, Journal of Symbolic Logic, vol. 49 (1984), no. 3, pp. 851--866.
Mathematical Reviews (MathSciNet): MR758937
Digital Object Identifier: doi:10.2307/2274139
Project Euclid: euclid.jsl/1183741626
Zentralblatt MATH: 0575.03015
