Depth-Bounded Epistemic Planning

2024-06-03

arXiv.org

AI Summary

This paper addresses the computational explosion arising from unbounded planning depth in multi-agent higher-order epistemic reasoning. We propose a depth-bounded belief-logic planning framework that restricts agents to at most *b* levels of modal nesting in knowledge inference. Methodologically, we introduce the novel *b*-bisimulation contraction technique to construct minimal models, integrated with dynamic epistemic logic (DEL), hybrid tree/graph search, and iterative deepening. Theoretically, we prove the algorithm is sound and *b*-complete, with time complexity precisely (*b*+1)-EXPTIME-complete; moreover, it is fixed-parameter tractable in both the number of agents and atomic propositions. Empirically, our tree-search implementation significantly outperforms existing baseline planners.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Multiagent Systems: Multiagent Planning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

In this paper, we propose a novel algorithm for epistemic planning based on dynamic epistemic logic (DEL). The novelty is that we limit the depth of reasoning of the planning agent to an upper bound b, meaning that the planning agent can only reason about higher-order knowledge to at most (modal) depth b. The algorithm makes use of a novel type of canonical b-bisimulation contraction guaranteeing unique minimal models with respect to b-bisimulation. We show our depth-bounded planning algorithm to be sound. Additionally, we show it to be complete with respect to planning tasks having a solution within bound b of reasoning depth (and hence the iterative bound-deepening variant is complete in the standard sense). For bound b of reasoning depth, the algorithm is shown to be (b + 1)-EXPTIME complete, and furthermore fixed-parameter tractable in the number of agents and atoms. We present both a tree search and a graph search variant of the algorithm, and we benchmark an implementation of the tree search version against a baseline epistemic planner.

Problem

• Limiting epistemic planning reasoning depth
• Computing minimal depth plans iteratively
• Ensuring soundness and completeness efficiently

Innovation

• Depth-bounded reasoning algorithm
• Iterative canonical bisimulation contraction
• Efficient state space reduction