Extended symbolic approximate reasoning based on linguistic modifiers

Approximate reasoning allows inferring with imperfect knowledge. It is based on a generalization of modus ponens (MP) known as generalized modus ponens (GMP). We are interested in approximate reasoning within symbolic multi-valued logic framework. In a previous work, we have proposed a new GMP based on linguistic modifiers in the multi-valued logic framework. The use of linguistic modifiers allows having a gradual reasoning; moreover, it allows checking axiomatics of approximate reasoning. In this paper, we extend our approximate reasoning to hold with complex rules, i.e., rules whose premises are conjunction or disjunction of propositions. For this purpose, we introduce a new operator that aggregates linguistic modifiers and verifies the required properties of logical connectives within the multi-valued logic framework.