Secure and Optimal Base Contraction in Graded Lukasiewicz Logics

Abstract. The operation of base contraction was successfully characterized for a very general class of logics using the notion of remainder sets. Although, in the general case, this notion is inadequate for revision, where it is replaced by maximal consistent subsets. A natural question is wether this latter notion allows for a definition of contractionlike 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 logic RPL: we characterize contraction operators with a fixed security-threshold > 0; we prove soundness of (an optimal) -contraction operation, and a collapse theorem from - to some -contraction for finite theories. Keywords. Base contraction, monotonic logics, fuzzy logics, involutive negation

• Type: Conference
• Year: 2009
• Where: CCIA
• Authors: Pere Pardo, Pilar Dellunde, Lluis Godo
• Keywords: Artificial Intelligence, Base Contraction, CCIA 2009, Maximal Consistent Subsets, Standard Contraction