Efficient Approximate Reasoning with Positive and Negative Information

Starting from the generic pattern of the Generalized Modus Ponens, we develop an efficient yet expressive quantitative model of approximate reasoning that tries to combine “the best of different worlds”; following a recent trend, we make a distinction between positive or observed (“guaranteed”) fuzzy rules on one hand, and negative or restricting ones on the other hand, which allows to mend some persistent misunderstandings about classical inference methods. To reduce algorithm complexity, we propose inclusion–based reasoning, which at the same time offers an efficient way to approximate “exact” reasoning methods, as well as an attractive implementation to the concept of reasoning by analogy.