Solution:

The code...

declare
proc {Abians_Bebians Sol}
  E AY OY O I U A
in
   Sol=sol(nese_knesi:E nay_knasi:AY
           noy_knosi:OY nose_knosi:O
           nise_knisi:I nuse_knusi:U
           nase_knasi:A)
   Sol ::: 0#1   % 0 are the liars - that is, the Bebians
   
   {FD.impl {FD.nega E} {FD.exor AY OY} A}
   {FD.impl O {FD.impl {FD.nega I} OY} E}
   {FD.equi U AY I}
   {FD.impl {FD.nega OY} A O}
   {FD.nega O U}
   {FD.impl {FD.nega U} O AY} 
   {FD.exor A AY OY}
   
   {FD.distribute ff !Sol}
end

{ExploreAll Abians_Bebians}

sol(nase_knasi: 1 nay_knasi: 1 nese_knesi: 0 nise_knisi: 0
    nose_knosi: 1 noy_knosi: 0 nuse_knusi: 0)