@inproceedings { 3565, title = {Secure and Optimal Base Contraction in Graded {\L}ukasiewicz Logics}, booktitle = {Artificial Intelligence Research and Development. Proceedings of the 12th International Conference of the Catalan Association fo Artificial Intelligence}, editor = {S. Sandri, M. S\'anchez-Marr\`e and U. Cort\'es}, volume = {202}, year = {2009}, month = {21/10/2009}, pages = {265-274}, publisher = {IOS Press}, organization = {IOS Press}, address = {Cardona, Catalonia, Spain}, abstract = {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. }, keywords = {Base Contraction, T-norm fuzzy logic, Partial meet}, ISBN = {978-1-60750-061-2}, author = {Pere Pardo and Pilar Dellunde and Llu\'{\i}s Godo} }