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 Hájek, Esteva, Godo and others to deal with probability, possibility, and necessity in a many-valued logical setting, we introduce the modal logic built up over the many-valued logic . In particular, we enlarge the language by means of a binary modality says acting on pairs (pi,ϕ) 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(pi,ϕ) as the degree of confidence the principalpiputs in the assertionϕ. For 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 to allow principals to be hierarchically organized.