Lewis & Short

syllŏgistĭcus, a, um, adj., = συλλογιστικός, of or belonging to a syllogism, syllogistic: (Cicero) statum syllogisticum ratiocinativum appellat, Quint. 5, 10, 6.
Hence, adv.: syllŏgistĭcē, syllogistically, in syllogisms, Boëth. Arist. Anal. Post. 1, 9, p. 530.