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

Abstract

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.