Query reformulation refers to a process of translating a source query-a request for information in some high-level logic-based language-into a target plan that abides by certain interface restrictions. Many practical problems in data management can be seen as instances of the reformulation problem. For example, the problem of translating an SQL query written over a set of base tables into another query written over a set of views; the problem of implementing a query via translating to a program calling a set of database APIs; the problem of implementing a query using a collection of web services. In this book we approach query reformulation in a very general setting that encompasses all the problems above, by relating it to a line of research within mathematical logic. For many decades logicians have looked at the problem of converting "implicit definitions" into "explicit definitions," using an approach known as interpolation. We will review the theory of interpolation, and explain its close connection with query reformulation. We will give a detailed look at how the interpolation-based approach is used to generate translations between logic-based queries over different vocabularies, and also how it can be used to go from logic-based queries to programs.

This book constitutes the refereed proceedings of the 9th International Conference on Web Reasoning and Rule Systems, RR 2015, held in Berlin, Germany, in August 2015. The 5 full papers, 4 technical communications presented together with 4 invited talks were carefully reviewed and selected from 16 submissions. The scale and the heterogenous nature of web data poses many challenges, and turns basic tasks such as query answering and data transformations into complex reasoning problems. Rule-based systems have found many applications in this area. The RR conference welcomes original research from all areas of Web Reasoning and Rule Systems. Topics of particular interest are: answer set programming, complex events, datalog, description logics, event-condition-action rules, information extraction, and logic programming.