  We consider Hoare-style verification for the graph programming language GP 2.
In previous work, graph properties were specified by so-called E-conditions
which extend nested graph conditions. However, this type of assertions is not
easy to comprehend by programmers that are used to formal specifications in
standard first-order logic. In this paper, we present an approach to verify GP
2 programs with a standard first-order logic. We show how to construct a
strongest liberal postcondition with respect to a rule schema and a
precondition. We then extend this construction to obtain strongest liberal
postconditions for arbitrary loop-free programs. Compared with previous work,
this allows to reason about a vastly generalised class of graph programs. In
particular, many programs with nested loops can be verified with the new
calculus.
