Conditionally firing rules; Compositional Rule of Inference; Bandler-Kohout subproduct; Implicative rules; Fuzzy interpolation

Conditionally firing rules have been proposed by B. Moser and M. Navara in order to preserve natural properties that are not preserved by the usual setting of fuzzy inference systems such as Mamdani- Assilian rules joined to the CRI inference mechanism. In this paper, we follow this direction and show, that if the axioms are naturally modified in order to capture the same semantic for the implicative rules, we can also define conditionally firing implicative rules that jointly with the Bandler-Kohout subproduct preserve exactly the same properties.