A Dynamic Epistemic Logic with Lying and Theory of Mind Limitations.

Theory of mind (ToM) is the ability to attribute and reason about unobservable mental states of others, such as knowledge, beliefs, and intentions. ToM is needed in social interactions, negotiations, cooperation, and deception, but there is a limit to the recursive depth of ToM attributions humans can make. Researchers in epistemic logic classically assume that agents have common knowledge of honesty and perfect rationality, whereas humans lie and have ToM limitations. In our present work, we bridge this gap by developing a sound and strongly complete dynamic epistemic logic that models both lying and human ToM limitations. The design of our logic is inspired by findings from prior behavioural research. Our logic makes use of action models to model belief change caused by lying and other types of announcements. Using theoretical examples, we show how a listener deals with lies that she cannot understand due to her ToM limits.