SecondOrder FalseBelief Tasks Analysis and Form

Authors: Torben Braüner Patrick Blackburn Irina Polyanskaya

Publish Date: 2016/8/16

Volume: , Issue: , Pages: 125-144

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Abstract

We first give a coarsegrained modallogical analysis of the four best known secondorder falsebelief 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 nodeception and changeinworld versus changeinbeliefonly 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 finegrained 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 firstorder SallyAnne task is nested inside the proof modelling the secondorder solution

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