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On the Beth Property in Extension of Lukasiewicz Logics

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Abstract

It is proved that a necessary condition for conservative axiomatic extensions of the infinite-valued (or n-valued) Lukasiewicz logic to possess the Beth definability property consists in the presence in the language of these extensions of a countable set (resp. a set of power n) of constant terms nonequivalent with respect to the given extensions.

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References

  1. Wojcicki R., “On matrix representation of consequence operations of Lukasiewicz's sentential calculi,” in: Selected Papers on Lukasiewicz Sentential Calculi. Ed. by R. Wojcicki, Wydawnictwo Polskiej Akademii Nauk, Warshawa, 1977, pp. 101–112.

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  2. Maksimova L. L., “Modal logics and varieties of modal logics: Beth's conditions, interpolation, and amalgamability,” Algebra i Logika, 31, No. 2, 145–166 (1992).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Russia

    D. E. Tishkovsky

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  1. D. E. Tishkovsky
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Tishkovsky, D.E. On the Beth Property in Extension of Lukasiewicz Logics. Siberian Mathematical Journal 43, 147–150 (2001). https://doi.org/10.1023/A:1013841008704

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  • DOI: https://doi.org/10.1023/A:1013841008704

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