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Note on inter-expressibility of logical connectives in finitely-valued Gödel-Dummett logics

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Abstract

Let G m be the m-valued Gödel-Dummett fuzzy logic. If m≥3 then neither conjunction nor implication is in G m expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values.

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Authors and Affiliations

  1. Faculty of Arts, Dept. of Logic, Charles University, Palachovo nám. 2, 116 38, Praha 1, Czeh Republic

    V. Švejdar

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  1. V. Švejdar
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Correspondence to V. Švejdar.

Additional information

This work is a part of the research plan MSM 0021620839 that is financed by the Ministry of Education of the Czech Republic.

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Švejdar, V. Note on inter-expressibility of logical connectives in finitely-valued Gödel-Dummett logics. Soft Comput 10, 629–630 (2006). https://doi.org/10.1007/s00500-005-0514-8

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  • DOI: https://doi.org/10.1007/s00500-005-0514-8

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