Parameterized complexity results for a model of theory of mind based on dynamic epistemic logic

Contains fulltext : 163041.pdf (publisher's version ) (Open Access)In this paper we introduce a computational-level model of theory of mind (ToM) based on dynamic epistemic logic (DEL), and we analyze its computational complexity. The model is a special case of DEL model checking. We provide a parameterized complexity analysis, considering several aspects of DEL (e.g., number of agents, size of preconditions, etc.) as parameters. We show that model checking for DEL is PSPACE-hard, also when restricted to single-pointed models and S5 relations, thereby solving an open problem in the literature. Our approach is aimed at formalizing current intractability claims in the cognitive science literature regarding computational models of ToM.18 p

Parameterized complexity of theory of mind reasoning in dynamic epistemic logic

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