We present a logic to model the behaviour of an agent trusting or not trusting messages sent by another agent. The logic formalizes trust as a consistency checking function with respect to currently available information. Negative trust is modeled 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.

G.Primiero, A Logic of Negative Trust, Journal of Applied Non-Classical Logic,
https://doi.org/10.1080/11663081.2020.1789404