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Theory of truth degrees of formulas in Łukasiewiczn-valued propositional logic and a limit theorem

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Abstract

The concept of truth degrees of formulas in Łukasiewiczn-valued propositional logicL n is proposed. A limit theorem is obtained, which says that the truth functionτ n induced by truth degrees converges to the integrated truth functionτ whenn converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Łukasiewicz logic and the continuous valued Łukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.

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Authors and Affiliations

  1. Institute of Mathematics, Shaanxi Normal University, 710062, Xi’an, China

    Bijing Li & Wang Guojun

  2. Research Center for Science, Xi’an Jiaotong University, 710049, Xi’an, China

    Wang Guojun

Authors
  1. Bijing Li
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  2. Wang Guojun
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Correspondence to Wang Guojun.

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Li, B., Wang, G. Theory of truth degrees of formulas in Łukasiewiczn-valued propositional logic and a limit theorem. Sci China Ser F 48, 727–736 (2005). https://doi.org/10.1360/122005-47

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  • DOI: https://doi.org/10.1360/122005-47

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