A logical approach to graph databases

Graph databases are now playing an important role because they allow us to overcome some limitations of relational databases. In particular, in graph databases we are interested not only on the data contained but also on its topology. As a consequence, most graph database queries are navigational, asking whether some nodes are connected by edges or paths. Up to now, most foundational work has concentrated on the study of computational models and query languages, analyzing their expressivity, computability, and complexity. However, in our work we address a different kind of foundational work. We are not concerned with expressibility, efficiency or feasibility issues, but with correctness. More precisely, given an algorithm or an implementation for solving queries, how can we be sure that the answers obtained are correct (soundness) and that all possible correct answers are obtained by our implementation (completeness). In this sense, in this paper we first present a core query language, similar to Cypher or G-Core. Then, we define a simple logic whose formulas are precisely the database queries, and whose satisfaction relation defines what is a correct answer. Finally, we define an operational semantics, which could be seen as an abstract implementation of our language, showing that the semantics is correct, i.e. sound and complete with respect to our logic.