The Jena2 reasoner subsystem is designed to allow a range of inference 
  engines to be plugged into Jena. Such reasoners are primarily used to derive 
  additional RDF assertions which are entailed from some base RDF together 
 with any optional ontology information and the axioms and rules associated 
 with the reasoner. In addition, they can be used to test global properties 
 of an RDF graph such as consistency.
This machinery, and the rest of this description, are appropriate for
developers working with Graphs and Nodes at the SPI level. Application developers
using Models should see the convenience methods built into ModelFactory.
Each available reasoner is represented by an factory object which is an
  instance of a ReasonerFactory.
     It is also given a URI through which it can be identified. This URI
is  used both as the base of a set of RDF assertions which describe the reasoner
 capabilitiesand as an identifier for registering the reasoner with a central
  registry. If you only need to access a specific built-in reasoner you can
  use the factory class directly or the convenience methods built into ModelFactory
  [TODO: ref]. However, if you need to dynamically check what reasoners are
  registered with the Jena2 installation and examine their capabilities use
 the  machinery in ReasonerRegistry.
Once you have an appropriate factory you can create a reasoner instance. The instance can then be bound to a set of RDF data for processing. The result of such binding is an InfGraph , this is a specialization of the standard Graph interface - all the RDF assertions entailed from the base data via the reasoner appear as "virtual" triples within this InfGraph. Some additional methods on InfGraph offer access to the reasoner, the raw data and some additional capabilities.
For example, using the SPI all of the steps involved in generated an RDFS closure of 
 a graph are:
  ReasonerFactory rf = RDFSReasonerFactory.theInstance();
  Reasoner reasoner  = rf.create(null);
  InfGraph graph     = reasoner.bindSchema(tbox) // optional
                               .bind(data);
  Model model        = new ModelMem(graph);
For application developers working with the API then this code is accessible through the convenience methods in ModelFactory.
If the resulting graph or model are queried using find/listStatements 
they contain the sum of all the assertions in the tbox graph, the data graph 
and the triples entailed from them via RDF+RDFS entailment.
The ability to separately bind rule or ontology information (tbox
  in the example) and raw assertional information (data in the example) 
is optional. Some reasoners may require a strict separation of terminology 
and instance data, others may allow both binds but be lax about the allowed 
contents of each, others may not support the bindSchema stage. 
The existing built-in reasoners allow a single tbox together with a single data bind but the tbox is optional and unrestricted. In the case of the RDFSReasoner in the example, some work is done at bindSchema time to cache information on property and class lattices that may be reused across multiple data sets but the extent of that reuse is lessened if the data graph also contains such schema assertions.