Second-order false-belief tasks: Analysis and formalization

We first give a coarse-grained modal-logical analysis of the four best known second-order false-belief tasks. This preliminary analysis shows that the four tasks share a common logical structure in which a crucial role is played by a “principle of inertia” which says that an agent’s belief is preserved over time unless the agent gets information to the contrary. It also reveals informational symmetries (all four possibilities inherent in the two dimensions of deception versus no-deception and change-in-world versus change-in-belief-only are realized) and reveals a rather puzzling feature common to all four tasks. We then take a closer look at how the principle of inertia is used, which leads to a fine-grained analysis in terms of perspective shifting. We formalize this analysis using a natural deduction system for hybrid logic, and show that the proof modelling the solution to the first-order Sally-Anne task is nested inside the proof modelling the second-order solution.