What Delusions are an unsolved problem in the mathematical modelling of mental processes. They are defined as false beliefs that are held with absolute conviction and cannot be changed by countervailing evidence. Delusions are particularly difficult to describe formally (i.e., mathematically) because of the tension between their emergence and their maintenance. While the emergence of a false belief requires jumping to conclusions (being too quick to believe), the maintenance of the same belief requires stubbornly resisting to form new conclusions (being too slow to believe). I will attempt to address this by developing formal models of delusionality that can be used to simulate delusional thinking in artificially intelligent agents. Why Delusional thinking is widespread in the general population, reaching far beyond patients with psychiatric disorders. Delusional views of reality held by individuals or groups are detrimental to social cohesion, mutual understanding, and solidarity. Understanding how they emerge and are maintained is an important part of mitigating their consequences. It is therefore all the more unfortunate that we lack a formal understanding of their mechanisms. How We will aim to construct artificially intelligent agents capable of the same kind of aberrant thinking we see in delusional humans, based on a framework using Dirichlet process mixture models recently developed in my group. This allows us to tune our simulated agents to develop a central belief about the structure of their environment which becomes stronger over time while all observations that do not fit the central belief exactly are explained away with ad-hoc explanations. We will apply these models to data from human participants doing newly developed tasks in game-like environments. The structure of these environments needs to be learned by engaging with them in order to resolve ambiguities. Critically, these ambiguities can be resolved in realistic as well as delusional ways. SSR Ideally, the results of this project will equip us with an enhanced mechanistic understanding of delusional phenomena, which could form the basis of preventive and remedial interventions. This could allow us to identify ways to tweak environments such that they retain their key characteristics while becoming less likely to elicit delusions. Preventing or mitigating delusional thinking in this manner would contribute to social cohesion and mutual understanding.