TitleSecure and Optimal Base Contraction in Graded {Ł}ukasiewicz Logics
Publication TypeConference Paper
Year of Publication2009
AuthorsPardo P, Dellunde P, Godo L
EditorM. Sandri S-MS, Cortés U.
Conference NameArtificial Intelligence Research and Development. Proceedings of the 12th International Conference of the Catalan Association fo Artificial Intelligence
PublisherIOS Press
Conference LocationCardona, Catalonia, Spain
Date Published21/10/2009
ISBN Number978-1-60750-061-2
KeywordsBase Contraction, Partial meet, T-norm fuzzy logic

The operation of base contraction was characterized using remainder sets for several logics. The case of {Ł}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.