A General Form of Cautious Approximate Reasoning for Symbolic and Complex Data

Abstract

Decision-makers are increasingly confronted with the problem of data imprecision. Thereby,the representation and manipulation of such knowledge play a crucial role in the performance of intelligent systems. Among the well-known logics for imprecise data, we can find symbolic multi-valued logic. This logic extends classical logic to consider a scale of degrees including intermediate symbolic degrees, between \emph{True} and \emph{False}. It is based on multi-set theory, where every predicate is modeled by a multi-set. Approximate reasoning in that context consists of inferring with an observation whose degree is different from that of the rule premise. We are interested in an approximate reasoning based on the implication operator. In this paper, we prove that this approximate reasoning checks the axiomatics of approximate reasoning. Furthermore, we improve this approximate reasoning to deal with multi-sets having different scales bases. And thus, propositions of the rule premise and rule conclusion can be associated with different scale bases. We then give solutions for deduction schema in more complex cases. More precisely, we pointed out the presence of complex rules and the combination of conclusions.