There is a mistake... No ?
It is :
SELECT z, z$RDFVTYP, z$RDFLTYP
FROM visibility t1,
TABLE (SDO_RDF_MATCH('(?z ?y <http://www.example.org/family/Matt>)',
SDO_RDF_Models('familly'),
null,
null,
null
)) t2
WHERE t1.Description LIKE 'public' and t2.id_visibility = t1.ID

But there is not the column id_visibility in the table visibility.
Ok so can I navigate in the graphe with a parameter like as the visibility (public, private,...) ?

Example :
-- John is the father of Suzie.
INSERT INTO family_rdf_data VALUES (1,
SDO_RDF_TRIPLE_S('family', 'http://www.example.org/family/John',
'http://www.example.org/family/fatherOf','http://www.example.org/family/Suzie'),Private);
-- John is the father of Matt.
INSERT INTO family_rdf_data VALUES (2,
SDO_RDF_TRIPLE_S('family', 'http://www.example.org/family/John',
'http://www.example.org/family/fatherOf', 'http://www.example.org/family/Matt'),Public);
-- Suzie is the mother of Jack.
INSERT INTO family_rdf_data VALUES (8,
SDO_RDF_TRIPLE_S('family', 'http://www.example.org/family/Suzie',
'http://www.example.org/family/motherOf', 'http://www.example.org/family/Jack'),Public);
-- Matt is the father of Tom.
INSERT INTO family_rdf_data VALUES (9,
SDO_RDF_TRIPLE_S('family', 'http://www.example.org/family/Matt',
'http://www.example.org/family/fatherOf', 'http://www.example.org/family/Tom'),Public);

With the request (?x :grandParentOf ?y), the admin can see the result :
<http://www.example.org/family/John> <http://www.example.org/family/grandParentOf> <http://www.example.org/family/Jack>
<http://www.example.org/family/John> <http://www.example.org/family/grandParentOf> <http://www.example.org/family/Tom>

With the request (?x :grandParentOf ?y), another people can see (without the rights) :
<http://www.example.org/family/John> <http://www.example.org/family/grandParentOf> <http://www.example.org/family/Tom>

I don't know if it's clear ? (sorry for my english)