In this work we discuss the Bandler-Kohout Subproduct (BKS) relational inference system with the fuzzy implication interpreted as the Yager's classes of implications which do not form a residuated lattice structure on [0,1]. We show that many of the desirable properties, viz., interpolativity, continuity, robustness and computational efficiency, that are known for BKS with residuated implications are also available under this framework, thus expanding the choice of operations available to practitioners. © 2012 Springer-Verlag Berlin Heidelberg.