#illogicality__illogicalness__illogicalnes  invalid or incorrect reasoning
  exclusion:  logicality
  supertype:  quality  an essential and distinguishing attribute of something or someone; "the quality of mercy is not strained"--Shakespeare
  subtype:  invalidity__invalidness  illogicality as a consequence of having a conclusion that does not follow from the premisses
     subtype:  fallaciousness  result of a fallacy or error in reasoning

No statement uses or specializes illogicality; click here to add one.