Reasoning about time and probability

Good decision making requires reasoning about chance and change in the world: how things change over time, the chances that things change in different possible ways, and how our actions affect these chances. Together with knowledge about the utility of outcomes, the preferences, it is possible to choose the best action in a given situation. As an example, consider the selection of a travel route. It requires thinking not only about geographic distance, but also about the time of day, the likelihood of delays and bottlenecks, and the scenery and amenities offered by each possible route. This dissertation is an account of thinking about chance and change for planning and making decisions in such domains. My approach is distinguished by: (1) I explicitly reason about chance with probability, and use survival analysis to reason about chance and time. Probability is a mature normative theory of reasoning about chance, (2) I use logic to write down basic knowledge about probability and time. Logic makes it easy to quantify knowledge, and to apply knowledge as needed, and (3) I use graph models of knowledge about probability for computation. Graph models are robust and efficient, and they make it easy to reason about chance from a normative basis. The program developed in my thesis, Goo, is a database for maintaining a picture of the likelihood of facts and events over time. Goo incrementally constructs and maintains graph models from logical knowledge in response to queries and assertions. Graph models are used to answer queries such as "What is the chance that I will arrive by noon?", and "Is there any plan where the probability of traffic jams is less than.5?"

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