First Order Paths in Ordered Trees

We give two sufficient conditions on XPath like languages for having first order expressivity, meaning that every first order definable set of paths in an ordered node-labeled tree is definable in that XPath language. They are phrased in terms of expansions of navigational (sometimes called “Core”) XPath. Adding either complementation, or the more elegant conditional paths is sufficient. A conditional path is an axis relation of the form (one step axis::n[F]), denoting the transitive closure of the relation expressed by one step axis::n[F]. As neither is expressible in navigational XPath we also give characterizations in terms of first order logic of the answer sets and the sets of paths navigational XPath can define. The first in terms of a suitable two variable fragment, the second in terms of unions of conjunctive queries.