Towards a theory of small worlds

Practical probabilistic reasoning requires that a reasoning agent be able to construct and reason from small, problem-specific inference models. Such inference models are sometimes called small worlds, because they involve reasoning from a limited set of facts, hypotheses and outcomes. A truly general purpose probabilistic reasoning sytem must have the ability to construct and reason from small worlds. There are difficult philosophical and practical issues associated with the question of how to construct, reason from, and revise small worlds. Unfortunately, Bayesian decision theory provides little theoretical guidance for addressing these issues. This is because the axioms of Bayesian theory imply global coherence, which in turn implies that these issues do not exist. The authors overview some work addressing these issues