Distributed Knowing How
Bin Liu, Yanjing Wang
TL;DR
This paper introduces a logic of distributed knowledge-how (DKH) that blends planning-based multi-step know-how with coalition-based one-step know-how, capturing how groups can achieve goals via irreducible, inherited, and joint group actions. It defines a robust semantic framework with action closures $A_G^*$ and a multi-step strategy-based semantics for $\mathsf{Kh}_G\varphi$, alongside distributed knowledge-that $\mathsf{K}_G$. A central contribution is a sound and strongly complete axiomatization $\mathbb{SDKH}$, proved via a canonical model with unraveling that handles complex multi-step transitions. The framework lays groundwork for future exploration of decidability, model subclasses, and connections to related logics like ATL and distributed knowledge-that.
Abstract
Distributed knowledge is a key concept in the standard epistemic logic of knowledge-that. In this paper, we propose a corresponding notion of distributed knowledge-how and study its logic. Our framework generalizes two existing traditions in the logic of know-how: the individual-based multi-step framework and the coalition-based single-step framework. In particular, we assume a group can accomplish more than what its individuals can jointly do. The distributed knowledge-how is based on the distributed knowledge-that of a group whose multi-step strategies derive from distributed actions that subgroups can collectively perform. As the main result, we obtain a sound and strongly complete proof system for our logic of distributed knowledge-how, which closely resembles the logic of distributed knowledge-that in both the axioms and the proof method of completeness.