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Beyond the Spell: A Dynamic Logic Analysis of Misdirection

Benjamin Icard, Raul Fervari

TL;DR

This work develops $\\boldsymbol{\\mathsf{DLM}}$, a dynamic epistemic logic that jointly models verbal misdirection (affecting beliefs) and visual misdirection (affecting observations). It formalizes a concrete language with observation atoms, belief modalities, and action-model updates, and proves soundness and completeness for the static and dynamic fragments. The French Drop trick serves as a running case study to illustrate how simulation and dissimulation can be captured, including the emergence of stronger beliefs, epistemic observations, and surprise. The framework offers a principled tool for analyzing deception and has potential applications in epistemic planning and multi-agent reasoning about misdirection in real-world contexts.

Abstract

Misdirection can be defined as the intentional action of causing some misrepresentation in an agent, or in a group of agents. Such misrepresentations may result from verbal actions, as in linguistic deception, or from visual actions, as in visual misdirection. Examples of visual misdirection abound (e.g. in nature, in the military), with magic tricks providing a vivid illustration. So far, various types of verbal misdirection have been investigated from a formal perspective (e.g. lying, bluffing) but little attention has been paid to the particular case of visual misdirection. In this paper, we introduce a dynamic epistemic logic to represent not only verbal misdirection on agents' beliefs but also visual misdirection on agents' observations. We illustrate the dynamics of the logic by modelling a classic magic trick known as the French Drop. We also provide a sound and complete axiom system for the logic, and discuss the expressivity and scope of the setting.

Beyond the Spell: A Dynamic Logic Analysis of Misdirection

TL;DR

This work develops , a dynamic epistemic logic that jointly models verbal misdirection (affecting beliefs) and visual misdirection (affecting observations). It formalizes a concrete language with observation atoms, belief modalities, and action-model updates, and proves soundness and completeness for the static and dynamic fragments. The French Drop trick serves as a running case study to illustrate how simulation and dissimulation can be captured, including the emergence of stronger beliefs, epistemic observations, and surprise. The framework offers a principled tool for analyzing deception and has potential applications in epistemic planning and multi-agent reasoning about misdirection in real-world contexts.

Abstract

Misdirection can be defined as the intentional action of causing some misrepresentation in an agent, or in a group of agents. Such misrepresentations may result from verbal actions, as in linguistic deception, or from visual actions, as in visual misdirection. Examples of visual misdirection abound (e.g. in nature, in the military), with magic tricks providing a vivid illustration. So far, various types of verbal misdirection have been investigated from a formal perspective (e.g. lying, bluffing) but little attention has been paid to the particular case of visual misdirection. In this paper, we introduce a dynamic epistemic logic to represent not only verbal misdirection on agents' beliefs but also visual misdirection on agents' observations. We illustrate the dynamics of the logic by modelling a classic magic trick known as the French Drop. We also provide a sound and complete axiom system for the logic, and discuss the expressivity and scope of the setting.
Paper Structure (25 sections, 9 theorems, 13 equations, 3 figures, 1 table)

This paper contains 25 sections, 9 theorems, 13 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Outline of the paper.
  3. Setting the Stage for Misdirection
  4. Believing and observing
  5. Two main strategies of misdirection
  6. Misdirection as Dissimulation of the Truth
  7. Misdirection as Simulation of the False
  8. Modelling verbal and visual misdirection
  9. Misdirection in the French Drop Trick
  10. Casting the magic spell logically
  11. A Dynamic Logic of Misdirection
  12. Syntax and Semantics
  13. Axiomatic System
  14. Misdirection via Action Types
  15. Defining Action Types
  16. ...and 10 more sections

Key Result

Lemma 10

Let $\Gamma$ be a consistent set. Then, there exists an MCS $\Gamma'$ such that $\Gamma\subseteq\Gamma'$.

Figures (3)

  • Figure 1: Possible interactions between agent's perspectives, or attitudes, regarding verbal versus visual informational modalities.
  • Figure 2: Types of Action Models Based on Distinct Modal Preconditions.
  • Figure 3: Types of Action Models Based on Distinct Observation-Based Preconditions.

Theorems & Definitions (34)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Remark 7
  • Definition 8
  • Definition 9: Canonical Model
  • Lemma 10: Lindenbaum Lemma
  • ...and 24 more