  Trust is a central component of the interaction between people and AI, in
that 'incorrect' levels of trust may cause misuse, abuse or disuse of the
technology. But what, precisely, is the nature of trust in AI? What are the
prerequisites and goals of the cognitive mechanism of trust, and how can we
promote them, or assess whether they are being satisfied in a given
interaction? This work aims to answer these questions. We discuss a model of
trust inspired by, but not identical to, sociology's interpersonal trust (i.e.,
trust between people). This model rests on two key properties of the
vulnerability of the user and the ability to anticipate the impact of the AI
model's decisions. We incorporate a formalization of 'contractual trust', such
that trust between a user and an AI is trust that some implicit or explicit
contract will hold, and a formalization of 'trustworthiness' (which detaches
from the notion of trustworthiness in sociology), and with it concepts of
'warranted' and 'unwarranted' trust. We then present the possible causes of
warranted trust as intrinsic reasoning and extrinsic behavior, and discuss how
to design trustworthy AI, how to evaluate whether trust has manifested, and
whether it is warranted. Finally, we elucidate the connection between trust and
XAI using our formalization.
