Parameterized Complexity Results for a Model of Theory of Mind Based on Dynamic Epistemic Logic
This formalizes intractability claims for computational models of theory of mind in cognitive science, which is incremental as it applies existing methods to a specific domain.
The authors tackled the computational complexity of a theory of mind model based on dynamic epistemic logic, showing that model checking is PSPACE-hard even under restricted conditions, solving an open problem.
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.