The concept of strong left-continuous t-norm and SMTL propositional logic system is introduced.It is proved that the left continuous t-norm is the strong left-continuous t-norm if and only if its adjoining implication operator is strong regular implication operator.Based on the fuzzy propositional logic of strong regular implication operator the integral truth degree of formula is defined and inference rules w.r.t the integral truth degree of formula is proved.Moreover

a pseudo-metric is defined therefrom on the set of formulas in SMTL system

and three models for approximate reasoning are given

hence a possible framework suitable for developing approximate reasoning theory in SMTL propositional logic is established.