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Where Common Knowledge Cannot Be Formed, Common Belief Can -- Planning with Multi-Agent Belief Using Group Justified Perspectives

Guang Hu, Tim Miller, Nir Lipovetzky

TL;DR

This work extends the epistemic planning framework by introducing Group Justified Perspective (GJP), enabling uniform, distributed, and common beliefs among multi-agent groups. Building on Planning with Perspectives (PWP) and the Justified Perspective (JP) model, it defines group belief operators EB_G, DB_G, and CB_G with corresponding ternary semantics and proofs of KD45/KD4 properties. The approach is instantiated in a Group GJP planner and validated on Number and Grapevine benchmarks, demonstrating efficiency for group beliefs and practical convergence for common beliefs. The results highlight the method's expressiveness and potential for scalable multi-agent epistemic planning, with future work targeting more advanced search, non-Markovian dynamics, and human-belief modeling.

Abstract

Epistemic planning is the sub-field of AI planning that focuses on changing knowledge and belief. It is important in both multi-agent domains where agents need to have knowledge/belief regarding the environment, but also the beliefs of other agents, including nested beliefs. When modeling knowledge in multi-agent settings, many models face an exponential growth challenge in terms of nested depth. A contemporary method, known as Planning with Perspectives (PWP), addresses these challenges through the use of perspectives and set operations for knowledge. The JP model defines that an agent's belief is justified if and only if the agent has seen evidence that this belief was true in the past and has not seen evidence to suggest that this has changed. The current paper extends the JP model to handle \emph{group belief}, including distributed belief and common belief. We call this the Group Justified Perspective (GJP) model. Using experimental problems crafted by adapting well-known benchmarks to a group setting, we show the efficiency and expressiveness of our GJP model at handling planning problems that cannot be handled by other epistemic planning tools.

Where Common Knowledge Cannot Be Formed, Common Belief Can -- Planning with Multi-Agent Belief Using Group Justified Perspectives

TL;DR

This work extends the epistemic planning framework by introducing Group Justified Perspective (GJP), enabling uniform, distributed, and common beliefs among multi-agent groups. Building on Planning with Perspectives (PWP) and the Justified Perspective (JP) model, it defines group belief operators EB_G, DB_G, and CB_G with corresponding ternary semantics and proofs of KD45/KD4 properties. The approach is instantiated in a Group GJP planner and validated on Number and Grapevine benchmarks, demonstrating efficiency for group beliefs and practical convergence for common beliefs. The results highlight the method's expressiveness and potential for scalable multi-agent epistemic planning, with future work targeting more advanced search, non-Markovian dynamics, and human-belief modeling.

Abstract

Epistemic planning is the sub-field of AI planning that focuses on changing knowledge and belief. It is important in both multi-agent domains where agents need to have knowledge/belief regarding the environment, but also the beliefs of other agents, including nested beliefs. When modeling knowledge in multi-agent settings, many models face an exponential growth challenge in terms of nested depth. A contemporary method, known as Planning with Perspectives (PWP), addresses these challenges through the use of perspectives and set operations for knowledge. The JP model defines that an agent's belief is justified if and only if the agent has seen evidence that this belief was true in the past and has not seen evidence to suggest that this has changed. The current paper extends the JP model to handle \emph{group belief}, including distributed belief and common belief. We call this the Group Justified Perspective (GJP) model. Using experimental problems crafted by adapting well-known benchmarks to a group setting, we show the efficiency and expressiveness of our GJP model at handling planning problems that cannot be handled by other epistemic planning tools.

Paper Structure

This paper contains 22 sections, 6 theorems, 17 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction and Motivation
  2. Background
  3. Epistemic planning
  4. Planning with Perspectives
  5. Justified Perspective Model
  6. Group Justified Perspective Model
  7. Uniform Belief
  8. Distributed Belief
  9. Common Belief
  10. Experiments
  11. Results
  12. Conclusion and Future work
  13. Examples
  14. Distributed Perspective Function
  15. Common Perspective Function
  16. ...and 7 more sections

Key Result

Theorem 1

Given a state sequence $\Vec{s}$, the iterations needed for $\mathit{cf}\!_G(\{\vec{s}\})$ to converge are bounded above $2^{|V|\times |\Vec{s}|}$.

Figures (2)

  • Figure 1: Plan \ref{['plan:1']}.
  • Figure 2: State sequence $\vec{s}$ and $df_G(\vec{s})$ in Example \ref{['example:distributed']}

Theorems & Definitions (30)

  • Example 1
  • Definition 1: PWP Signature
  • Definition 2: State Override Function
  • Definition 3: Observation Function
  • Definition 4: JP Model
  • Definition 5: Retrieval Function
  • Definition 6: Justified Perspective Function
  • Definition 7: Ternary semantics
  • Definition 8: Language
  • Definition 9
  • ...and 20 more