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Effectiveness and multivalued logics

Published online by Cambridge University Press:  12 March 2014

Giangiacomo Gerla
Giangiacomo Gerla*
Affiliation:
Department of Mathematics and Computer Science, University of Salerno, Via Ponte Don Melillo 84084, Fisciano (Sa), Italy. E-mail: gerla@unisa.it
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Abstract

Effective domain theory is applied to fuzzy logic. The aim is to give suitable notions of semi-decidable and decidable L-subset and to investigate about the effectiveness of the fuzzy deduction apparatus.

Keywords

Multi-valued logicfuzzy logiccomputabilitydomain theory

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 137 - 162
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[1]Biacino, L. and Gerla, G., Decidability, recursive enumerability and Kleene hierarchy for L-subsets, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 35 (1989), pp. 49–62.CrossRefGoogle Scholar
[2]Biacino, L. and Gerla, G., Fuzzy logic, continuity and effectiveness, Archive for Mathematical Logic, vol. 41 (2002), pp. 643–667.CrossRefGoogle Scholar
[3]Di Nola, A. and Gerla, G., Fuzzy models of first order languages, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 32 (1986), pp. 331–340.CrossRefGoogle Scholar
[4]Dubois, D. and Prade, H., Possibility theory: An approach to computerized processing of uncertainty. Plenum Press, New York, 1988.Google Scholar
[5]Gerla, G., Decidability, partial decidability and sharpness relation for L-subsets, Studia Logica, vol. 46 (1987), pp. 227–238.CrossRefGoogle Scholar
[6]Gerla, G., Inferences in probability logic, Artificial Intelligence, vol. 70 (1994), pp. 33–52.CrossRefGoogle Scholar
[7]Gerla, G., Probability-like functionals and fuzzy logic, Journal of Mathematical Analysis and Application, vol. 216 (1997), pp. 438–465.CrossRefGoogle Scholar
[8]Gerla, G., Fuzzy logic: Mathematical tools for approximate reasoning, Kluwer Academic Publishers, Dordrecht, 2001.CrossRefGoogle Scholar
[9]Goguen, J. A., The logic of inexact concepts, Synthese, vol. 19 (1968/1969), pp. 325–373.CrossRefGoogle Scholar
[10]Gottwald, S.. A treatise on many-valued logics. Research Studies Press, Baldock, 2000.Google Scholar
[11]Hájek, P., Metamathematics of fuzzy logic, Kluwer Academic Publishers, Dordrecht, 1998.CrossRefGoogle Scholar
[12]Montagna, F., Three complexity problems in quantified fuzzy logic, Studia Logica, vol. 68 (2001), pp. 143–152.CrossRefGoogle Scholar
[13]Mundici, D., Cignoli, R., and D'Ottaviano, I., Algebraic foundations of many-valued reasoning, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar
[14]Novák, V., Perfilieva, I., and Mockor, J., Mathematical principles of fuzzy logic, Kluwer Academic Publishers, Dordrecht, 1999.CrossRefGoogle Scholar
[15]Pavelka, J., On fuzzy logic I: Many-valued rules of inference, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 25 (1979), pp. 45–52.CrossRefGoogle Scholar
[16]Scarpellini, B., Die Nichaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz, this Journal, vol. 27 (1962), pp. 159–170.Google Scholar
[17]Shafer, G., A mathematical theory of evidence, Princeton University Press, Princeton, 1976.CrossRefGoogle Scholar
[18]Smyth, M., Effectively given domains, Theoretical Computer Science, vol. 5 (1977), pp. 257–274.CrossRefGoogle Scholar
[19]Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning I, II, III, Information Sciences, vol. 8, 9 (1975), pp. 199–275, 301–357, 43–80.CrossRefGoogle Scholar