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Tractable Meta-Reasoning in Propositional Logics of Belief

Finding adequate semantic models of deductive reasoning is a difficult problem, if deductions are to be performed efficiently and in a semantically appropriate way. The model of reasoning provided by possible-worlds semantics has been found deficient both for computational and intuitive reasons. Existing semantic approaches that were proposed as alternatives to possible-worlds semantics either suffer from computational intractability or do not allow agents to have meta-beliefs. This work, based on relevance logic, proposes a model of belief where an agent can hold met a-beliefs and reason about them and other world knowledge efficiently. It is also shown how the model can be extended to include positive introspection without losing efficiency.