Rules and meta-rules in the framework of possibility theory and possibilistic logic

Abstract

The contribution of Lotfi Zadeh to the development of fuzzy logic goes far beyond the introduction of the seminal concept of a fuzzy set, and has multiple facets. This article, as a small tribute to the corpus of ideas, notions and results brought together over almost five decades by Zadeh, singles out and illustrates two of his most stimulating, thought-provoking and fruitful creations: fuzzy rules, on the one hand, and possibility theory, on the other. Indeed, the modeling of conditional statements of the form, “if x is A, then y is B”, plays a crucial role in any attempt at formalizing human reasoning. Starting from the expression of different forms of fuzzy rules that have been identified in the setting of possibility theory, we study their counterparts in the extensions of possibilistic logic. A distinction between rules and meta-rules is especially emphasized in the representational setting of possibility theory. It amounts to viewing rules as pieces of knowledge that contribute to the partial specification of a unique epistemic state, while meta-rules characterize constraints between specified epistemic states, as in possibilistic answer set programming.