A logic of negative trust

We present a logic to model the behaviour of an agent trusting or not trusting messages sent by another agent. The logic formalises trust as a consistency checking function with respect to currently available information. Negative trust is modelled in two forms: distrust, as the rejection of incoming inconsistent information; mistrust, as revision of previously held information becoming undesirable in view of new incoming inconsistent information, which the agent wishes to accept. We provide a natural deduction calculus, a relational semantics and prove soundness and completeness results. We overview a number of applications which have been investigated for the proof-theoretical formulation of the logic.