Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic

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.

Theory Before the Test: How to Build High-Verisimilitude Explanatory Theories in Psychological Science

“…Tractability/intractability analyses apply widely, not just to simple examples such as the ones above. The approach has been used to assess constraints that render tractable/intractable computational accounts for various capacities relevant for psychological science that span across domains and levels ( Table 1 ), such as coherence-based belief updating ( van Rooij et al, 2019 ), action understanding and theory of mind ( Blokpoel et al, 2013 ; van de Pol et al, 2018 ; Zeppi & Blokpoel, 2017 ), analogical processing ( van Rooij et al, 2008 ; Veale & Keane, 1997 ), problem-solving ( Wareham, 2017 ; Wareham et al, 2011 ), decision-making ( Bossaerts & Murawski, 2017 ; Bossaerts et al, 2019 ), neural-network learning ( Judd, 1990 ), compositionality of language ( Pagin, 2003 ; Pagin & Westerståhl, 2010 ), evolution, learning or development of heuristics for decision-making ( Otworowska et al, 2018 ; Rich et al, 2019 ), and evolution of cognitive architectures generally ( Rich et al, 2020 ). This existing research (for an overview, see Compendium C in van Rooij et al, 2019 ) shows that tractability is a widespread concern for theories of capacities relevant for psychological science and moreover that the techniques of tractability analysis can be fruitfully applied across psychological domains.…”

Theory before the test: How to build high-verisimilitude explanatory theories in psychological science

“…≤ max ( c ( s , s' )) + ; see Blokpoel et al 2013;Bourgin et al, 2017, (Blokpoel et al, 2013;Zeppi and Blokpoel, 2017;van de Pol et al 2018), analogical processing (Veale & Keane, 1997;van Rooij et al, 2008), problem solving (Wareham, 2017;Wareham, Evans, & van Rooij, 2011), decision-making (Bossaerts & Murawski, 2017;Bossaerts, Yadav, & Murawski, 2019), neural network learning (Judd, 1990), compositionality of language (Pagin, 2003;Pagin & Westerståhl, 2010), evolution, learning or development of heuristics for decision-making (Otworowska et al, 2018, Rich et al, 2019) and evolution of cognitive architectures generally (Rich et al, 2020). This existing research shows that tractability is a widespread concern for theories of capacities relevant for psychological science, and moreover that the techniques of tractability analysis can be fruitfully applied across psychological domains.…”

On the Computational Complexity of Model Checking for Dynamic Epistemic Logic with S5 Models

“…For several cases, we prove PSPACE-hardness. Since the problem was recently shown to be in PSPACE for the most general variant of dynamic epistemic logic that we consider in this paper [2,23,24], these hardness results suffice to show PSPACE-completeness.…”

“…However, these hardness proofs crucially depend on the use of multi-pointed models, and therefore do not apply for the case where the problem is restricted to single-pointed S5 models. This open question was answered with a PSPACE-hardness proof for the restricted case where all models are single-pointed S5 models, but where the number of agents is unbounded [23,24]. It remained open whether these PSPACE-hardness results extend to more restrictive settings (e.g., only two agents and single-pointed S5 models).…”