Loglan is one of the most popular logical conlangs of the 20th century. Created by Dr. James Cooke Brown in 1955, Loglan succeeded in attracting a number of followers until copyright disputes caused a schism. This eventually led to the creation of Lojban.
Loglan was created (according to Wikipedia) with the "goal of making a language so different from natural languages that people learning it would think in a different way if the hypothesis were true", so as to prove or disprove the Sapir-Whorf Hypothesis.
The Academy of Loglan was recreated in year 2013. It is lead by Randall Holmes. Among it's members are famous Lojbanists John Waldemar Cowan and la selpa'i.
For more on Loglan, please read the Wikipedia page.