Seeing is Believing: Formalising False-Belief Tasks in Dynamic Epistemic Logic

In this paper we show how to formalise false-belief tasks like the Sally-Anne task and the second-order chocolate task in Dynamic Epistemic Logic (DEL). False-belief tasks are used to test the strength of the Theory of Mind (ToM) of humans, that is, a human’s ability to attribute mental states to other agents. Having a ToM is known to be essential to human social intelligence, and hence likely to be essential to social intelligence of arti_cial agents as well. It is therefore important to _nd ways of implementing a ToM in arti_cial agents, and to show that such agents can then solve false-belief tasks. In this paper, the approach is to use DEL as a formal framework for representing ToM, and use reasoning in DEL to solve false-belief tasks. In addition to formalising several false-belief tasks in DEL, the paper introduces some extensions of DEL itself: edge-conditioned event models and observability propositions. These extensions are introduced to provide better formalisations of the false-belief tasks, but expected to have independent future interest.