On the Attitude of Trust: A Formal Characterization of Trust, Distrust, and Associated Notions

Abstract

Using modal logics to represent an agent’s beliefs, knowledge and wants, an analysis is given of trust in terms of an agent’s certainty that a particular, desired state-of-affairs will be realized. Similarly, a corresponding analysis of distrust is given. Placing these formal representations of trust and distrust at each of the ends of a spectrum, four intermediary structures may be identified, representing hope, two species of anxiety, and fear. In this way the relationships between the attitudes of trust/distrust and some basic types of emotional state may be precisely articulated. Some suggestions are also made regarding the analysis of some more complex types, including regretting that one trusted, and being ashamed that one trusted. The paper employs modalities of type KD and KT for, respectively, the logics of belief and knowledge. It is shown that use of stronger doxastic and epistemic logics – of the kind often favoured in Artificial Intelligence – containing the positive and negative introspection axioms, would make three of the spectrum’s four intermediary positions logically inconsistent. It is suggested that this result provides good reason for rejecting the stronger logics, and that their adoption in AI has often been motivated primarily by considerations of computational convenience, rather than by considerations of conceptual accuracy.