Ronald Fagin, Joseph Halpern, Moshe Vardi
It has been argued that knowledge is a useful tool for designing and analyzing complex systems in AI. The notion of knowledge that seems most relevant in this context is an external, information-based notion that can be shown to satisfy all the axioms of the modal logic S5. We carefully examine the properties of this notion of knowledge, and show that they depend crucially, and in subtle ways, on assumptions we make about the system. We present a formal model in which we can capture the types of assumptions frequently made about systems (such as whether they are deterministic or nondeterministic, whether knowledge is cumulative, and whether or not the environment affects the transitions of the system). We then show that under some assumptions certain states of knowledge are not attainable, and the axioms of S5 do not completely characterize the properties of knowledge; extra axioms are needed. We provide complete axiomatizations for knowledge in a number of cases of interest.