Secure and Optimal Base Contraction in Graded Łukasiewicz Logics

The operation of base contraction was successfully characterized for a very general class of logics using the notion of remainder sets. Nevertheless, in the general case, this notion is inadequate for revision, where it is replaced by maximal consistent subsets. A natural question is whether this latter notion allows for a definition of contraction-like operators and, in case it does, what differences there exist w.r.t. standard contraction. We make some steps towards this direction for the case of graded expansions of one of the most prominent fuzzy logics, Łukasiewicz logic. We characterize contraction operators with a fixed security-threshold ! > 0; we prove soundness of (an optimal) ω-contraction operation, and a collapse theorem from ωto some !-contraction for finite theories.