A complete fuzzy logical system to deal with trust management systems

  • Authors:
  • Tommaso Flaminio;G. Michele Pinna;Elisa B. P. Tiezzi

  • Affiliations:
  • Dipartimento di Matematica e Scienze Informatiche, Università di Siena, Italy;Dipartimento di Matematica e Informatica, Università di Cagliari, Italy;Dipartimento di Matematica e Scienze Informatiche, Università di Siena, Italy

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2008

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Abstract

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 FT"n(L@P12) built up over the many-valued logic L@P12. In particular, we enlarge the L@P12 language by means of a binary modality says acting on pairs (p"i,@f) 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,@f) as the degree of confidence the principalp"iputs in the assertion@f. For FT"n(L@P12) 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 FT"n(L@P12) to allow principals to be hierarchically organized.