Pedigreed belief change
Yoav Shoham, Pedrito Maynard-Reid · 2001
Revising beliefs given new information has long been a problem in artificial intelligence (AI). Much of this work has assumed little about the source of the information. However, such pedigree information is often readily accessible and useful in determining how to incorporate the new input. We should treat very differently the information “It is raining” when we receive it from the weather reporter, from a notorious liar, or from our own eyes. The goal of this work is to enable the use of such pedigree information in semantically-justified ways. One source of information that Al has been interested in is perception, e.g., sensors. We introduce a logical framework for reasoning about how the modalities of perception and belief interrelate. We describe a number of agent types in this framework along different axes such as accuracy, awareness, and confidence. We give both model-theoretical and axiomatic characterizations, and provide soundness and completeness results for each. We also provide qualitative definitions for relative precision and accuracy of percepts and sensors. Another source of information that AI has been interested in is a group of experts of varying credibility, e.g., doctors. We address the core problem of aggregating these experts' beliefs. We consider the framework where experts' beliefs are specified as conditional beliefs in a logical language. We describe a novel representation for collective beliefs that generalizes traditional representations for individuals' beliefs by allowing us to represent and manipulate conflicting opinions. We propose an aggregation operator that takes advantage of this representation so that an agent can combine the belief states of a set of experts totally preordered by credibility. We show that the operator has many desirable properties including circumventing old dilemmas in aggregation such as Arrow's Impossibility Theorem. We then show how to combine or fuse the belief states of agents that use the proposed aggregation mechanism so that the resulting belief state is equivalent to aggregating the combined sets of informant experts. We prove that fusion is a formal generalization of belief revision. Finally, we describe a complementary diffusion operator for those agents that only trust universally accepted experts.