If I am to describe an ontology to run an inference engine on a mobile device, which of these data-interchange formats (JSON and XML) would be more appropriate in terms of computational cost and memory usage?
You need to be a bit more precise. What do you intend to do? As I understood, you plan to have a reasoner running on a mobile device. Where is the ontology located, on the mobile device or somewhere else? What data would you like to exchange? Ontologies? Queries?
I think the restrictive part on a mobile device is not the format you use for knowledge reperesentation, but the expressiveness of the underlying description language and the choice of the reasoner itself. Both will affect the efficiency of reasoning. As the description language I'd prefer OWL 2, a W3C Recommendation based on RDF and XML and understood by most of the reasoners. Depending on your application, you'd probably restrict to some OWL 2 Profile (see, e.g. http://www.w3.org/TR/owl-profiles/ for an overview). There are several OWL 2 syntaxes (formats) from which you can choose depending on your requirements (http://www.w3.org/TR/owl2-primer/#OWL_Syntaxes). Work on reasoners that work on mobile devices just has started. See e.g. this paper http://ceur-ws.org/Vol-1387/paper_2.pdf.
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