Research Paper#Artificial Intelligence, Logic, Belief Representation🔬 ResearchAnalyzed: Jan 3, 2026 19:14
Hypergraph Semantics for Belief Logics
Published:Dec 28, 2025 21:49
•1 min read
•ArXiv
Analysis
This paper introduces a novel semantics for doxastic logics (logics of belief) using directed hypergraphs. It addresses a limitation of existing simplicial models, which primarily focus on knowledge. The use of hypergraphs allows for modeling belief, including consistent and introspective belief, and provides a bridge between Kripke models and the new hypergraph models. This is significant because it offers a new mathematical framework for representing and reasoning about belief in distributed systems, potentially improving the modeling of agent behavior.
Key Takeaways
- •Proposes a new semantics for doxastic logic using directed hypergraphs.
- •Addresses the limitations of simplicial models in representing belief.
- •Provides systems for consistent and introspective belief.
- •Establishes completeness through canonical hypergraph models.
- •Offers direct conversions between Kripke and hypergraph models.
Reference
“Directed hypergraph models preserve the characteristic features of simplicial models for epistemic logic, while also being able to account for the beliefs of agents.”