Logical foundations of rule-based systems

The evolution of a theory of fuzzy IF–THEN rules and its contribution to the establishment of fuzzy logic is a focus of this paper. I am advocating in favour of Hájek's fuzzy logic regarding it as a right methodology for special logical theories. A theory of fuzzy IF–THEN rules (as a special theory in the above considered sense) is proposed. This theory is for all practitioners who want to create a system of fuzzy IF–THEN rules free of conflicts (logically consistent) and rich enough to be able to make non-trivial conclusions or answer inquires.