Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking (e.g., ‘you believe that I believe that you believe’). To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove that theory of mind reasoning, so formalized, indeed is intractable (specifically, PSPACE-complete). Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind.

中文翻译：

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动态认知逻辑中心理推理理论的参数化复杂性

心理理论是指人类根据对其行为和正在发生的事件的观察来推理他人心理状态的能力。这种类型的推理在认知科学文献中因其假定的计算难以处理而臭名昭著。一个可能的原因可能是它可能涉及更高层次的思考（例如，“你相信我相信你相信”）。为了研究这一点，我们将心理推理理论形式化为使用动态认知逻辑更新关于信念的信念，因为这种形式主义允许参数化“思维顺序”。我们证明了如此形式化的思维推理理论确实是棘手的（特别是 PSPACE-complete）。然而，我们使用参数化复杂性证明，“顺序参数”不是难以处理的来源。我们进一步考虑了一组替代参数，并调查其中哪些是难以处理的来源。我们讨论了这些结果对理解心理理论的影响。