3 Pere Pardo Pilar Dellunde LluĂ­s Godo 2009 S. Sandri, M. Sánchez-Marrč and U. Cortés Artificial Intelligence Research and Development. Proceedings of the 12th International Conference of the Catalan Association fo Artificial Intelligence Cardona, Catalonia, Spain IOS Press 202 265-274 Frontiers in Aritficial Intelligence and Applications 21/10/2009 978-1-60750-061-2 Base Contraction, T-norm fuzzy logic, Partial meet The operation of base contraction was characterized using remainder sets for several logics. The case of {\L}ukasiewicz logics with truth-constants requires to switch from remainders to maximal consistent subsets. We characterize first contraction operators that establish a security-threshold, and use these to define optimal operators, which are provably sound w.r.t. axioms. Finally, these are shown to collapse to the former case for any finite base.