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In this paper we study the definition and axiomatisation of non-falsity preserving and threshold preserving companions of several extensions of the Monoidal t-norm based fuzzy logic MTL. More in detail, we first extend some recent preliminary results on non-falsity preserving logics, and then we present a new study on threshold-preserving companions of the main three fuzzy logics, Łukasiewicz, Product and Gödel logics.

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On the Non-falsity and Threshold Preserving Variants of MTL Logics

  • 会议论文

  • 发表日期：

    2025年

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  • Francesc Esteva,
  • Joan Gispert,
  • Lluís Godo

摘要

In this paper we study the definition and axiomatisation of non-falsity preserving and threshold preserving companions of several extensions of the Monoidal t-norm based fuzzy logic MTL. More in detail, we first extend some recent preliminary results on non-falsity preserving logics, and then we present a new study on threshold-preserving companions of the main three fuzzy logics, Łukasiewicz, Product and Gödel logics.