Philosophical languages are made to follow philosophical principles. They are often oligosynthetic, an more extreme kind of polysynthesis. This means that they make all their words from only a few really simple words. aUI is a famous philosophical language.
Logical languages are made to be unambiguous. Lojban is a famous logical language.
Experimental languages are made for test hypotheses in linguistics. They are usually made to test the Sapir-Whorf hypothesis. Toki Pona, Lojban, and Láadan are famous experimental languages.