Wordnet 3.0
ADVERB (2)
1. 
 according to logical reasoning; 
- Example: "logically, you should now do the same to him"2. 
 in a logical manner; 
- Example: "he acted logically under the circumstances"
The Collaborative International Dictionary of English v.0.48:
Logically \Log"ic*al*ly\, adv.
   In a logical manner; as, to argue logically.
   [1913 Webster]
WordNet (r) 3.0 (2006):
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]