Hybrid-Logical Reasoning in False-Belief Tasks

TL;DR

This paper formalizes false-belief tasks in cognitive psychology using hybrid modal logic, revealing their shared logical structure and analyzing belief preservation principles across different task versions.

Contribution

It introduces a formal proof system for hybrid modal logic to model and analyze false-belief tasks, highlighting their underlying logical similarities.

Findings

Both Smarties task versions share the same logical structure

The Sally-Anne task involves a more complex logical framework

Belief preservation over time is formalized through the principle of inertia

Abstract

The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called falsebelief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same underlying logical structure. We also consider the Sally-Anne task, having a somewhat more complicated logical structure, presupposing a "principle of inertia" saying that a belief is preserved over time, unless there is belief to the contrary.