SPARQL - Inverse Path of dynamic discovered relationship - sparql

Question

I have a Graph Database that implements only one side of relationships in the model structures. For instance, All Broader relationships are mapped as skos:broader. All Narrower relationships are mapped as ^skos:broader (for whatever reasons they chose to do this, I have no control over this.)
I am trying to write a SPARQL Query that delivers something like
Query for all relationships of a given IRI, and their associated values.
The goal is to make a JSON or XML Representation of all the content.
Here is what I have working.
PREFIX skosxl: <http://www.w3.org/2008/05/skos-xl#>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX skos: <http://www.w3.org/2004/02/skos/core#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
select ?relation ?value
where
{
<CONCEPT_URI> ?r ?c
OPTIONAL {
?r rdfs:label|skosxl:prefLabel ?l
}
OPTIONAL {
?c skosxl:prefLabel/skosxl:literalForm|skosxl:literalForm ?d .
}
BIND ( if (bound(?d), ?d, ?c) as ?value )
BIND ( if (bound(?l), ?l, strafter(?r, '#')) as ?relation )
}
This works to give me all the concept relationships (IE: Broader), but it does not give me the narrower items (IE: ^broader).
Is there anyway that I can extend this generic query to produce the inverses of any relationships it finds, as well? I Tried simply adding the ^ to the ?r in the where clause but it does not like that syntactically.
Thanks,