Agent Interpolation for Knowledge

TL;DR

This paper introduces a new proof formalism for multi-agent S5 modal logics that combines hypersequents and nested sequents, proving key properties like soundness, completeness, and decidability.

Contribution

It presents a novel proof calculus for multi-agent S5 logics that supports interpolation and decidability, advancing formal proof methods in multi-agent modal logic.

Findings

The calculus is sound, complete, cut-free, and terminating.

Decidability and finite model property are established for multi-agent S5.

Interpolation properties are proven for the logic.

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.