 During the first two decades of the twentieth century, the algebra of logic was further developed in the works of Platon Sergeevich Poretzsky (1846–1907), Louis Couturat (1868–1914), Leopold Löwenheim (1878–1957), and Heinrich Behmann (1891–1970) (see Styazhkin 1969). In particular, elimination theorems in the algebra of logic influenced decision procedures for fragments of first-order and second-order logic (see Mancosu, Zach, Badesa 2009).