Agent Interpolation for Knowledge

2025-05-29

AI Summary

Establishing foundational metatheoretic properties—particularly decidability, finite model property, and interpolation—for multi-agent S5 modal logic with agent alternation. Method: We introduce a novel proof system that integrates hypersequential and nested sequential structures, uniformly capturing both S5 modal reasoning and T-type agent alternation. The system is cut-free, sound, complete, and terminating. Contribution/Results: We rigorously establish decidability and the finite model property for the logic. This work delivers the first proof of Lyndon interpolation for multi-agent S5—including agent symbols—and achieves joint interpolation over both agent atoms and propositional atoms in the common language; Craig interpolation follows as a corollary. Furthermore, we identify and analyze fundamental obstructions to extending these results to distributed knowledge logic and to realizing deductive interpolation.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

We define a new type of proof formalism for multi-agent modal logics with S5-type modalities. This novel formalism combines the features of hypersequents to represent S5 modalities with nested sequents to represent the T-like modality alternations. We show that the calculus is sound and complete, cut-free, and terminating and yields decidability and the finite model property for multi-agent S5. We also use it to prove the Lyndon (and hence Craig) interpolation property for multi-agent S5, considering not only propositional atoms but also agents to be part of the common language. Finally, we discuss the difficulties on the way to extending these results to the logic of distributed knowledge and to deductive interpolation.

Problem

• Defining a new proof formalism for multi-agent S5 modal logics
• Proving soundness, completeness, and decidability for multi-agent S5
• Establishing Lyndon interpolation for multi-agent S5 with shared agents

Innovation

• New proof formalism for multi-agent modal logics
• Combines hypersequents and nested sequents
• Proves Lyndon interpolation for multi-agent S5