It is impossible that Julius is yellow. It is certain that Gertrude is a sheep. It is highly unlikely that Bernhard is gray. We doubt that if 'Julius is yellow and Bernhard is gray' then Fred left the football. It is likely that if either 'Gertrude is a sheep' or 'Bernhard is gray' but not both then John went to the bedroom. It is unlikely that if 'Bernhard is gray' or 'Gertrude is a sheep' or both then Brian is a frog.
It is almost certain that either 'Brian is a frog' or 'Julius is yellow' but not both.
It is unlikely that either 'Brian is a frog' or 'Julius is yellow' but not both.
It is almost certain that either 'Brian is a frog' or 'Julius 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
  0.0::factA.
  1.0::factB.
  0.05::factC.
  %hop1
  0.2::factX:-and(factA,factC).
  0.7::factY:-xor(factB,factC).
  0.2::factZ:-or(factC,factB).

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

  query(conclusion).
  
Either 'Brian is a frog' or 'Julius is yellow' but not both.