Abstract
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.
Highlights
We analyze the computational complexity of the Dynamic Belief Update model that we presented in the previous section
Our aim is to investigate whether the ‘order’ of higher-order theory of mind reasoning is a source of intractability
We analyzed the computational complexity of theory of mind, formalized as the updating of beliefs about beliefs in dynamic epistemic logic (DEL)
Summary
You look at your phone, no message yet Does this mean she is not interested, or is she waiting for you to send a message first? This kind of reasoning is an example of the cognitive capacity called ‘theory of mind,’ which is the capacity for attributing mental states to oneself and others and to reason about these to explain behavior This capacity is widely studied in various fields such as psychology, philosophy, biology, and cognitive (neuro)science (see, e.g., Frith 2001; Nichols and Stich 2003; Premack and Woodruff 1978; Verbrugge 2009; Wellman et al 2001).
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