A Logic of Knowledge and Belief for Recursive Modeling: A Preliminary Report

Piotr J. Gmytrasiewicz, Edmund H. Durfee

To make informed decisions in a multiagent environment, an agent needs to model itself, the world, and the other agents, including the models that those other agents might be employing. We present a framework for recursive modeling that uses possible worlds semantics, and is based on extending the Kripke structure so that an agent can model the information it thinks that another agent has in each of the possible worlds, which in turn can be modeled with Kripke structures. Using recursive nesting, we can define the propositional attitudes of agents to distinguish between the concepts of knowledge and belief. Through the Three Wise Men example, we show how our framework is useful for deductive reasoning, and we suggest that it might provide a meeting ground between decision theoretic and deductive methods for multiagent reasoning.

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