Peer to peer information integration takes place when, within internetworking systems, a dependency between provided and consumed information is maintained. At large, the Semantic Web could be seen as a semantically integrated peer to peer system. These systems have been thoroughly studied by means of multi-agent epistemic logic frameworks. Most of the proposed approaches, however, in seek of generality, fail to provide means to implement the vast array of integration strategies that peers could adopt. We propose here a formal framework to overcome these limitations. Our approach resorts on a logic that prevents peer to peer mappings from causing direct knowledge transfers, and introduces a class of specific knowledge construction axioms to model concrete integration in a flexible way.