A Logic of Limited Belief with Introspection Based on Possible Worlds

The starting point of this paper is earlier work, where we proposed an epistemic logic which characterizes the beliefs of a knowledge-based agent in terms of increasing levels of complexity. At the lowest level, the agent is only able to draw simple conclusions from its knowledge base. Higher levels lead to more and more inferences and computing the beliefs at any particular level turns out to be tractable. What makes this logic arguably appealing is the fact that the underlying semantics is based on possible worlds. However, the work is still limited in that only beliefs about what is true in the world are considered, that is, an agent's beliefs about its own beliefs are ignored. In this paper we will close this gap and generalize the earlier work by proposing a model of limited belief where an agent is able to fully introspect on its own beliefs without sacrificing tractability.