A Normal Modal Logic for Trust in the Sincerity

Christopher Leturc, Grégory Bonnet

Abstract: In the field of multi-agent systems, as some agents may be not reliable or honest, a particular attention is paid to the notion of trust. There are two main approaches for trust: trust assessment and trust reasoning. Trust assessment is often realized with fuzzy logic and reputation systems which aggregate testimonies -- individual agents' assessments -- to evaluate the agents' global reliability. In the domain of trust reasoning, a large set of works focus also on trust in the reliability as for instance Liau's BIT modal logic where trusting a statement means the truster can believe it. However, very few works focus on trust in the sincerity of a statement -- meaning the truster can believe the trustee believes it. Consequently, we propose in this article a modal logic to reason about an agent's trust in the sincerity towards a statement formulated by another agent. We firstly introduce a new modality of trust in the sincerity and then we prove that our system is sound and complete. Finally, we extend our notion of individual trust about the sincerity to shared trust and we show that it behaves like a KD system.