So far, we have developed dynamic logics that deal with knowledge, inference, and questions, all based on information and truth. Now we want to look at another pervasive attitude that agents have toward information, namely, their beliefs. This chapter will show how belief change fits well with our dynamic framework, and develop some of its logical theory. This puts one more crucial aspect of rational agents in place: not their being right about everything, but their being wrong, and acts of self-correction.

From knowledge to belief as a trigger for actions

While knowledge is important to agency, our actions are often driven by fallible beliefs. I am riding my bicycle this evening because I believe it will get me home, even though my epistemic range includes worlds where the San Andreas Earthquake strikes. Decision theory is about choice and action on the basis of beliefs, as knowledge may not be available. Thus, our next step in the logical dynamics of rational agency is the study of beliefs, viewed as concretely as possible. Think of our scenarios in Chapter 3. The cards have been dealt. I know that there are 52 of them, and I know their colours. But I have more fleeting beliefs about who holds which card, or about how the other agents will play.