On axiomatization of fuzzy logic

During the last two decades, Group for intelligent systems at Mathematical faculty in Belgrade developed several theorem provers for different kind of formal systems. Lately, we turn our attention to fuzzy logic and development of the corresponding theorem proven . The first step is to find suitable axiomatization, i.e., the formalization of fuzzy logic that is sound, complete and decidable. Mere we will discuss first order approach to the axiomatization of Lukasiewicz logic and Product logic.