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

摘要

A schematic extension NML 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 NML is interpreted and the standard completeness theorem of NML is proved. The fact that the maximum and the minimum are definable from the negation and implication in NML and NM is discovered, which also leads to a modification of the NM axiom system.