Trust: Formal Semantics and Transitivity

Social networks based trust is a promising approach to supporting people and software agents to interact with “strangers” on the Web. A necessary condition for trust propagation in social networks is that trust is transitive. However, is trust transitive? What types of trust are transitive and why? There are few theories and models found to answer these fundamental questions in a formal manner. To fill this gap, this paper proposes a logic system of trust in situation calculus, in which the semantics of trust is formalized; based on the formal semantics, two types of trust – trust in belief and trust in performance are identified; the transitivity of trust in belief is revealed and proved, and the conditions for trust propagation in social networks are derived. This study provides a theoretical analysis on the transitivity of trust and supports trust propagation in social networks.