Approximate Reasoning about Combined Knowledge

Just as cooperation in multi-agent systems is a central issue for solving complex decision problems, so too is the ability for an intelligent agent to reason about combined knowledge, coming from its background knowledge and the communicated information. Specifically, such an agent is confronted with three main difficulties: the prospect of inconsistency which arises when different beliefs are grouped together, the presence of uncertainty which may occur due to not fully reliable beliefs, and the high computational complexity of reasoning with very large pools of collected information. The purpose of this paper is to define a formal framework which handles these three aspects and which is useful to specify resource bounded agents. Based on the concept of approximate reasoning, our framework includes several major features. First, a model checking approach is advocated, which enables an agent to perform decidable reasoning with a first-order representation language. Second, a stepwise procedure is included for improving approximate answers and allowing their convergence to the correct answer. Third and finally, both sound approximations and complete ones are covered. This method is flexible enough for modeling tractable reasoning in very large, inconsistent and uncertain sets of knowledge.