A complete fuzzy logical system to deal with trust management systems

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• 作者：Tommaso Flaminio ; G. Michele Pinna ; Elisa B.P. Tiezzi
• 关键词：Trust systems ; Many-valued logic ; Generalized modus ponens
• 刊名：Fuzzy Sets and Systems
• 出版年：2008
• 期刊代码：55_01650114
• 类别：cp
• 出版时间：16 May 2008
• 卷：159
• 期：10
• 页码：1191-1207
• 文件大小：296 K

摘要

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 itle="View the MathML source" align="absbottom" border="0" height=23 width="79"/> built up over the many-valued logic itle="View the MathML source" align="absbottom" border="0" height=23 width="32"/>. In particular, we enlarge the itle="View the MathML source" align="absbottom" border="0" height=23 width="32"/> language by means of a binary modality says acting on pairs itle="Click to view the MathML source" alt="Click to view the MathML source">(p_i,ities/3d5.gif" alt="phi" title="phi" border="0">) 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 itle="Click to view the MathML source" alt="Click to view the MathML source">says(p_i,ities/3d5.gif" alt="phi" title="phi" border="0">) as the degree of confidence the principal itle="Click to view the MathML source" alt="Click to view the MathML source">p_i puts in the assertion itle="Click to view the MathML source" alt="Click to view the MathML source">ities/3d5.gif" alt="phi" title="phi" border="0">. For itle="View the MathML source" align="absbottom" border="0" height=23 width="79"/> 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 itle="View the MathML source" align="absbottom" border="0" height=23 width="79"/> to allow principals to be hierarchically organized.