A New Approximate Reasoning for Multi-bases Symbolic Data

Approximate reasoning aims to manage knowledge imprecision in the inference process. It is a generalization of the Modus Ponens of classical logic. Originally, it is defined in fuzzy logic context, where knowledge are modeled by a quantitative way. We are interested in this paper to approximate reasoning in the symbolic multi-valued logic context. This logic allows presenting imprecise knowledge in a qualitative way, where every predicate is modeled by a multi-set. In order to express imprecision, each multi-set is associated to a scale base of ordered symbolic degrees. In a previous work where a symbolic approximate reasoning has been defined, it has been assumed that all multi-sets of the inference schema have the same scale base. This has the disadvantage to prevent free definition of knowledge. For that, we propose in this paper a new approximate reasoning which can infer with multi-sets having different scale bases. Our solution consists of interfacing all the multi-sets in order to avoid information loss.