<FONT face=Verdana>The semantic properties of logic systems MTL induced by regular implication operators were disscussed

the integral truth degree theory of formulas on [0

1] can be founded in MTL. However

the logic pseudo-metric space defined by the integral similarity degree between formulas cannot always be constructed. Moreover

those logic systems which could construct such pseudo-metric spaces have the same properties

i.e. all the logic operators are continuous in terms of pseudo-metric

then a possible framework about approximate reasoning is formed in those logic systems.