The Collaborative International Dictionary of English v.0.48:

Logicalness \Log"ic*al*ness\, n.
   The quality of being logical.
   [1913 Webster]

WordNet (r) 3.0 (2006):

logicalness
    n 1: correct and valid reasoning [syn: logicality,
         logicalness] [ant: illogic, illogicality,
         illogicalness, inconsequence]