Inconsequence :: Inconsequence (n.) The quality or state of being inconsequent; want of just or logical inference or argument; inconclusiveness.
Inconsequent :: Inconsequent (a.) Not following from the premises; not regularly inferred; invalid; not characterized by logical method; illogical; arbitrary; inconsistent; of no consequence.
Inconsequential :: Inconsequential (a.) Not regularly following from the premises; hence, irrelevant; unimportant; of no consequence..