A probabilistic modal logic for context-aware trust based on evidence

Trust is an extremely helpful construct when reasoning under uncertainty. Thus, being able to logically formalize the concept in a suitable language is important. However, doing so is problematic for three reasons. First, in order to keep track of the contextual nature of trust, situation trackers are required inside the language. Second, in order to produce trust estimations, agents rely on evidence personally gathered or reported by other agents; this requires elements in the language that can track which agents are used as referrals and how much weight is placed on their opinions. Finally, trust is subjective in nature, thus, personal thresholds are needed to track the trust-propensity of different evaluators. In this paper we propose an interpretation of a probabilistic modal language à la Hennessy-Milner in order to capture a context-aware quantitative notion of trust based on evidence. We also provide an axiomatization for the language and prove soundness, completeness, and decidability results.