The Collaborative International Dictionary of English v.0.48:

Logicality \Log`i*cal"i*ty\, n.
   Logicalness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

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