Solutions to Cintula's open problems

This paper answers Cintula's following open problems: (i) Whether the BCI logic is equivalent to the logic obtained by adding the prefixing axiom and the assertion axiom to weakly implicative logics? (ii) Whether the BCI logic is equivalent to the logic obtained by adding the suffixing rule and the exchange axiom to weakly implicative logics? (iii) Whether there is a finite axiomatic system for the fuzzy BCK logic? (iv) Whether the logic obtained by adding the axioms Fm,n to the BCI logic is the minimal fuzzy logic over BCI? In addition, these results also give Hájek's quasihoop logic a finite presentation.