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On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics

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Abstract

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable.

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References

  • Kneale, W. and Kneale, M. (1962) The Development of Logic, Clarendon Press.

  • Lakoff, G. (1973) Hedges: A study in meaning criteria and the logic of fuzzy concepts, Journal of Philosophical Logic 2, 458–508.

    Article  Google Scholar 

  • Lukasiewicz, J. and Tarski, A. (1930) Investigations into the sentential calculus, in L. Borkowski (ed.), Jan Lukasiewicz: Selected Works, North-Holland Publishing Company.

  • Morgan, C. and Pelletier, F. (1977) Some notes concerning fuzzy logics, Linguistics and Philosophy 1, 79–97.

    Article  Google Scholar 

  • Rescher, N. (1969) Many-Valued Logic, McGraw-Hill.

  • Scarpellini, B. (1962) Die Nicht-Axiomatisierbarkeit des Unednlichwertigen Pradikatenkalkuls von-Lukasiewicz, Journal of Symbolic Logic 27, 159–170.

    Google Scholar 

  • Slupecki, J. (1946) The complete three-valued propositional calculus, Annales Universitatis Mariae Curie-Sklodawska 1, 193–209.

    Google Scholar 

  • Zadeh, L. (1975) Fuzzy logic and approximate reasoning, Synthese 30, 407–428.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Philosophy, Fairfield University, Fairfield, CT, 06430

    Richard DeWitt

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  1. Richard DeWitt
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Correspondence to Richard DeWitt.

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DeWitt, R. On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. J Philos Logic 34, 545–560 (2005). https://doi.org/10.1007/s10992-005-1520-0

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  • DOI: https://doi.org/10.1007/s10992-005-1520-0

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