Knowledge, Probability, and Adversaries

: What should it mean for an agent to know 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 an agent assigns to an event. We show that each choice can be understood in terms of a betting game, and that each choice corresponds to betting against a di erent opponent. We consider three types of adversaries. The rst selects the 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 how to assign probability spaces to agents in a way most appropriate for that class, where \most appropriate" is made precise in ter...

• Type: Conference
• Year: 1989
• Where: PODC
• Authors: Joseph Y. Halpern, Mark R. Tuttle
• Keywords: Di Erent Opponents, Di Erent Probability, Distributed And Parallel Computing, PODC 1989, Probability Spaces