People acquire new beliefs in various ways. One of the most important of these is that new beliefs are acquired as a response to experiencing events that one did not expect. This involves a form of inference distinct from both deductive and inductive inference: abductive inference. The concept of abduction is due to the American pragmatist philosopher C. S. Peirce. Davies and Coltheart elucidated what Peirce meant by abduction, and identified two problems in his otherwise promising account requiring solution if (...) that account were to become fully workable. Here we propose solutions to these problems and offer an explicit cognitive model of how people derive new beliefs from observations of unexpected events, based on Peirce's work and Sokolov's ideas about prediction error triggering new beliefs. We consider that this model casts light not only upon normal processes of belief formation but also upon the formation of delusional beliefs. (shrink)