This paper formalizes the semantics of trust and studies the transitivity of trust. On the Web, people and software agents have to interact with "strangers". This makes trust a crucial factor on the Web. Basically trust is established in interaction between two entities and any one entity only has a finite number of direct trust relationships. However, activities on the Web require entities to interact with other unfamiliar or unknown entities. As a promising remedy to this problem, social networks-based trust, in which A trusts B, B trusts C, so A indirectly trusts C, is receiving considerable attention. A necessary condition for trust propagation in social networks is that trust needs to be transitive. However, is trust transitive? What types of trust are transitive and why? There are no theories and models found so far to answer these questions in a formal manner. Most models either directly assume trust transitive or do not give a formal discussion of why trust is transi...