alogically

a·log·i·cal

 (ā-lŏj′ĭ-kəl)
adj.
Beyond or outside the bounds of logic.

a·log′i·cal·ly adv.
a·log′i·cal·ness n.

alogically

(əˈlɒdʒɪkəlɪ; eɪˈlɒdʒɪkəlɪ)
adv
in an alogical manner