Reasoning over Impossible Worlds

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We study the desired/required abilities of an intelligent agent capable of reasoning about worlds that it knows to be nonexistent. Special attention is given to the Probabilistic Reasoning Model and some extensions to this model are proposed and discussed. The notion of independence in this model and the concept of extended probability functions (EPF) are introduced. Independence for assertions that are known to be true or false in all worlds can thus be represented within the EPF framework. The concept of degree of independence is defined as well, and its relationship to the PR model is exemplified.

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