A logic for reasoning about (negative) trust under uncertainty

The notion of trust is a major player, in many epistemic and computational contexts. Such notion appears especially relevant in all those situations where verification or evaluation of knowledge is missing, not reachable or non-existent, and agents must rely on information received by others. This includes cases where expert knowers may not yet be able to ground their claims, and the public has to build an opinion by considering the dynamic of the information exchange. Formal logic approaches to this aim have been increasingly important and diverse in the last decades. A natural and important extension of such multi-agent contexts is where epistemic acts are performed under uncertainty, at several levels: the claims of the agents may be graded; information may reach agents with a certain degree of probability; and the degree of acceptance or rejection of the information received may not be binary. We present a multi-agent logic of negative trust applied to uncertain judgements. We offer a proof theory and a relational semantics for which standard soundness and completeness results hold.