This paper presents a Logic Programming approach to parsing and production in Fluid Construction Grammar (FCG). It builds on previous work on the formalisation of FCG in terms of First Order Logic (FOL) concepts, more specifically on the definition of its core inference operations, unification and merge, in terms of FOL unification and search in the space of a particular set of FOL terms called structure arrangements. An implementation of such inference operations based on Logic Programming and Artificial Intelligence techniques such as unification and heuristic search is outlined.