Both explanation-based and inductive learning techniques have proven successful in a variety of distributed domains. However, learning in multi-agent systems does not necessarily involve the participation of other agents directly in the inductive process itself. Instead, many systems frequently employ multiple instances of induction separately, or single-agent learning. In this paper we present a new framework, named the Multi-Agent Inductive Learning System (MAILS), that tightly integrates processes of induction between agents. The MAILS framework combines inverse entailment with an epistemic approach to reasoning about knowledge in a multi-agent setting, facilitating a systematic approach to the sharing of knowledge and invention of predicates when required. The benefits of the new approach are demonstrated for inducing declarative program fragments in a multi-agent distributed programming system.