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SELECT fact
  FROM Facts
...
   and AliasFacts.Type = 2
   and BaseFacts.Type = 1
-- and this all works only if you do not ever have an alias to an alia
+s!

SELECT fact
  FROM Facts
...
  FROM Facts
  JOIN Aliases ON Aliases.fact_id = Facts.fact_id
 WHERE Aliases.name = ?

SELECT fact
  FROM Facts
  JOIN Names ON Names.Fact_id = Facts.fact_id
 WHERE Names.Name = ?