Grassroots platforms are distributed systems with multiple instances that can (1) operate independently of each other and of any global resource other than the network, and (2) coalesce into ever larger instances, possibly resulting in a single global instance. Here, we present Grassroots Logic Programs (GLP), a multiagent concurrent logic programming language designed for the implementation of grassroots platforms. We introduce the language incrementally: We recall the standard operational semantics of logic programs; introduce the operational semantics of Concurrent (single-agent) GLP as a restriction of that of LP; recall the notion of multiagent transition systems and atomic transactions; introduce the operational semantics of multiagent GLP via a multiagent transition system specified via atomic transactions; and prove multiagent GLP to be grassroots. The accompanying programming example is the grassroots social graph -- the infrastructure grassroots platform on which all others are based. With the mathematical foundations presented here: a workstation-based implementation of Concurrent GLP was developed by AI, based on the operational semantics of Concurrent GLP; a distributed peer-to-peer smartphone-based implementation of multiagent GLP is being developed by AI, based on the operational semantics of multiagent GLP; a moded type system for GLP was implemented by AI, to facilitate the specification of GLP programs by human and AI designers, for their programming by AI; all reported in detail in companion papers.

翻译：基层平台是一种分布式系统，其包含多个可独立运行的实例，这些实例能够（1）在除网络外的任何全局资源缺失的情况下彼此独立运行，并且（2）合并成更大的实例，最终可能形成一个单一的全局实例。本文提出基层逻辑程序（GLP），这是一种专为实现基层平台而设计的多智能体并发逻辑编程语言。我们循序渐进地介绍该语言：首先回顾逻辑程序的标准操作语义；然后通过限制逻辑程序的操作语义，引入并发（单智能体）GLP的操作语义；接着回顾多智能体转移系统和原子事务的概念；再通过由原子事务定义的多智能体转移系统，引入多智能体GLP的操作语义；并证明多智能体GLP具有基层性。随附的编程示例是基层社交图——作为所有其他基层平台基础的基层基础设施平台。基于本文提出的数学基础：人工智能已根据并发GLP的操作语义，开发了基于工作站的并发GLP实现；人工智能正在根据多智能体GLP的操作语义，开发基于分布式点对点智能手机的多智能体GLP实现；人工智能还实现了GLP的模式类型系统，以方便人类和人工智能设计者规范GLP程序，并由人工智能进行编程；所有内容均在相关论文中详细报告。