Source : Webster's Revised Unabridged Dictionary (1913)

Logically \Log"ic*al*ly\, adv.
   In a logical manner; as, to argue logically.

Source : WordNet®

logically
     adv 1: according to logical reasoning; "logically, you should now
            do the same to him"
     2: in a logical manner; "he acted logically under the
        circumstances" [ant: {illogically}]