I suspect this article may be defining "logical language" too narrowly.  Ithkuil for instance seems to me like a logical language of some sort, though it's not based on predicate logic or another formal logic system.  Maybe we need a separate article on Philosophical language that would describe languages like Ithkuil, Ro, John Wilkins' "Real Character", etc. 

 Ithkuil was deleted once before and is probably going to be deleted again, but I think it deserves a paragraph or so in a more general article on logical or philosophical languages.  |