AI logicians crack distributed knowledge cut problem for multi-agent logic
New proof enables efficient reasoning about what groups collectively know in multi-agent systems…
Ryo Murai, Sizhuo Liu (Hokkaido University), and Katsuhiko Sano (Hokkaido University) investigate sequent calculi for epistemic logics of distributed knowledge (K45, KD45, S5). While cut elimination fails in these systems, the authors establish the analytic cut property by adapting Takano's (2018) strategy, which restricts cut formulas to subformulas of the conclusion. As a corollary, the Craig interpolation theorem holds for all considered logics. The proof-theoretic results remain valid when the empty group is allowed for the distributed‑knowledge operator, interpreted as the global modality.
- Proves analytic cut property for distributed knowledge logics K45, KD45, and S5 where full cut elimination fails
- Adapts Takano's (2018) strategy to restrict cut formulas to subformulas of the conclusion in sequent calculi
- Extends results to empty group (global modality) and establishes Craig interpolation as a corollary
Why It Matters
Enables efficient automated reasoning about group knowledge in multi-agent AI systems, from robotics to distributed consensus.