It is probably the case that Julius is gray. It is unlikely that Bernhard is yellow. It is probably the case that Brian is a rhino. It is highly unlikely that if 'Bernhard is yellow and Brian is a rhino' then Sandra took the milk. Chances are slight that if 'Brian is a rhino and Bernhard is yellow' then Mary went to the kitchen. It is certain that if 'Bernhard is yellow and Brian is a rhino' then Lily is a lion.
It is highly unlikely that either 'Lily is a lion' or 'Bernhard is yellow' but not both.
It is highly unlikely that either 'Lily is a lion' or 'Bernhard is yellow' but not both.
Chances are about even that either 'Lily is a lion' or 'Bernhard is yellow' but not both.

  and(A,B) :- A,B.
  or(A,B) :- A;B.
  nand(A,B) :- not(and(A,B)).
  nor(A,B) :- not(or(A,B)).
  xor(A,B) :- or(A,B), nand(A,B).

  %hop0
  0.7::factA.
  0.2::factB.
  0.7::factC.
  %hop1
  0.05::factX:-and(factB,factC).
  0.1::factY:-and(factC,factB).
  1.0::factZ:-and(factB,factC).

  %hop2
  conclusion:-xor(factZ,factB).

  query(conclusion).
  
Either 'Lily is a lion' or 'Bernhard is yellow' but not both.