A complete fuzzy logical system to deal with trust management systems
In this paper we approach trust management systems in a fuzzy logical setting. The idea is to provide a generalization of the classical framework, where trust is understood via the dichotomy "true-false". In order to overcome the classical approach proposed by Weeks, following the ideas used by Hajek, Esteva, Godo and others to deal with probability, possibility, and necessity in a many-valued logical setting, we introduce the modal logic FTn(L Pi 1/2) built up over the many-valued logic L Pi 1/2. In particular, we enlarge the L Pi 1/2 language by means of a binary modality says acting on pairs (p(i), phi) of principals and assertions, where a principal is a propositional variable and an assertion is a propositional formula of a suited many-valued logic. The idea is to regard the evaluation of the modal formula says(p(i), phi) as the degree of confidence theprincipal p(i) puts in the assertion phi. For FTn(L Pi 1/2) we introduce a syntax, a semantic and we show completeness. Then we discuss the validity of generalized modus ponens rule in our setting. Finally we deal with a Pavelka-style extension of our logic, and we also extend FTn(L Pi 1/2) to allow principals to be hierarchically organized. (c) 2007 Elsevier B.V. All rights reserved.
many-valued logic generalized modus ponens trust systems