🤖 AI Summary
This paper addresses the redundancy problem in event lattices within information structures. We propose a minimal sufficient representation method based on partially ordered sets (posets): under mild conditions, we construct a simplified poset that is order-isomorphic to the original event lattice. This representation preserves all event relations and knowledge content, enabling a rational agent to reconstruct the full lattice losslessly from the reduced structure alone. Theoretically, we establish the first Minimal Sufficient Representation Theorem for event lattices, rigorously proving both the completeness and uniqueness of the derived poset. Practically, the method substantially reduces structural complexity in knowledge reasoning, offering a novel theoretical foundation and computational framework for distributed knowledge modeling and collaborative inference in multi-agent systems.
📝 Abstract
For the standard lattice model of information structures, we derive a reduced poset representation which provides the same informational content as the complete lattice structure which derives it. Rational agents can recover the complete lattice of events by means of the reduced poset alone. We find that both structures provide isomorphic models under mild conditions.