Graph databases are now playing an important role, not only because they allow us to overcome some limitations of relational databases, but also because they provide a good model for searching the web. In particular, graph databases differ from relational databases in that the topology of data is as important as the data itself. Thus, typical graph database queries are navigational, asking whether some nodes are connected by paths satisfying some specific properties. While relational databases were designed upon logical and algebraic foundations, the development of graph databases has been quite ad-hoc. In this sense, the aim of this paper is to provide them with some logical foundations. More precisely, in previous work we introduced a navigational logic, called +AFw-GNL+AFw (Graph Navigational Logic) that allows us to describe graph navigational properties. Moreover, this logic is equipped with a deductive tableau method that we proved to be sound and complete.In the current paper, we show how graph queries +AHsAXA-it +AOA la+AH0 Cypher can be expressed using a fragment of +AFw-GNL, defining for them a logical and an operational semantics. Moreover, we show that this operational semantics is sound and complete.