What Can Machines Know?: On the Properties of Knowledge in Distributed Systems

It has been argued that knowledge is a useful tool for designing and analyzing complex systems. The notion of knowledge that seems most relevant in this context is an external, zrzforrnatzorr-based notion that can be shown to satisfy all the axioms of the modal logic S5. The properties of this notion of knowledge are examined, and it is shown that they depend crucially. and in subtle ways, on assumptions made about the system and about the language used for describing knowledge. A formal model is presented in which one can capture various assumptions frequently made about systems, such as whether they are deterministic or nondeterministic, whether knowledge is cumulative (which means that processes never �forget�), and whether or not the �environment� affects the state transitions of the processes. It 1s then shown that under some assumptions about the system and the language, certain states of knowledge are not attainable and the axioms of S5 do not completely characterize the properties of knowledge; extra axioms are needed. Complete axiomatlzations for knowledge in a number of cases of interest are provided. © 1992, ACM. All rights reserved.