Knowledge, probability, and adversaries

J. Y. Halpern, M. R. Tuttle
1989 Proceedings of the eighth annual ACM Symposium on Principles of distributed computing - PODC '89  
What should it mean for an agent t o k n o w or believe an assertion is true with probability :99? Di erent papers FH88, FZ88, HMT88] give di erent answers, choosing to use quite di erent probability spaces when computing the probability a n a g e n t assigns to an event. We s h o w that each c hoice can be understood in terms of a betting game, and that each c hoice corresponds to betting against a di erent opponent. We consider three types of adversaries. The rst selects the outcome of all
more » ... e outcome of all nondeterministic choices in the system the second represents the knowledge of the agent's opponent (this is the key place the papers mentioned above di er) the third is needed in asynchronous systems to choose the time the bet is placed. We illustrate the need for considering all three types of adversaries with a number of examples. Given a class of adversaries, we show h o w to assign probability spaces to agent s i n a w ay m o s t appropriate for that class, where \most appropriate" is made precise in terms this betting game. We c o nclude by showing how di erent assignments of probability spaces (corresponding to di erent opponents) yield di erent levels of guarantees in coordinated attack.
doi:10.1145/72981.72988 dblp:conf/podc/HalpernT89 fatcat:tv336ivegjbaxlnlzf7w5mkt6i