NMŁ, a schematic extension of F.Esteva and L.Godo's logic MTL

A schematic extension NMŁ of F.Esteva and L.Godo's Logic MTL is introduced in this paper. Based on a new left-continuous but discontinuous t-norm, which was proposed by S.Jenei and can be regarded as a kind of distorted nilpotent minimum, the semantics of NMŁ is interpreted and the standard completeness theorem of NMŁ is proved. The fact that the maximum and the minimum are definable from the negation and implication in NMŁ and NM is discovered, which also leads to a modification of the NM axiom system.