Some Computational Constraints in Epistemic Logic
This paper concerns limits that some epistemic logics impose on the complexity of an epistemic agent’s reasoning, rather than limits on the complexity of the epistemic logic itself.
As an epistemic agent, one theorizes about a world which contains the theorizing of epistemic agents, including oneself. Epistemic logicians theorize about the abstract structure of epistemic agents’ theorizing. This paper concerns the comparatively simple special case of epistemic logic in which only one agent is considered. Such an epistemic agent theorizes about a world which contains that agent’s theorizing. One has knowledge about one’s own knowledge, or beliefs about one’s own beliefs. The considerations of this paper can be generalized to multi-agent epistemic logic, but that will not be done here. Formally, single-agent epistemic logic is just standard monomodal logic; we call it ‘epistemic’ in view of the envisaged applications.
KeywordsModal Logic Turing Machine Normal Logic Epistemic Logic Epistemic Agent
Material based on this paper was presented to colloquia of the British Society for the Philosophy of Science and the Computer Science Laboratory at Oxford. I thank participants in both for useful comments.
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