AbstractsMathematics

This thesis investigates logical formalizations of Castelfranchi and Falcone's (C&F) theory of trust [9, 10, 11, 12]. The C&F theory of trust defines trust as an essentially mental notion, making the theory particularly well suited for formalizations in multi-modal logics of beliefs, goals, intentions, actions, and time. Three different multi-modal logical formalisms intended for multi-agent systems are compared and evaluated along two lines of inquiry. First, I propose formal definitions of key concepts of the C&F theory of trust and prove some important properties of these definitions. The proven properties are then compared to the informal characterisation of the C&F theory. Second, the logics are used to formalize a case study involving an Internet forum, and their performances in the case study constitute grounds for a comparison. The comparison indicates that an accurate modelling of time, and the interaction of time and goals in particular, is integral for formal reasoning about trust. Finally, I propose a Horn fragment of the logic of Herzig, Lorini, Hubner, and Vercouter [25]. The Horn fragment is shown to be too restrictive to accurately express the considered case study.