It is probable that Julius is yellow. It is highly unlikely that Bernhard is gray. It is highly likely that John discarded the apple. We believe that if either 'Bernhard is gray' or 'John discarded the apple' but not both then Brian is white. Chances are about even that if either 'John discarded the apple' or 'Bernhard is gray' but not both then Lily is green. It is probably the case that if 'Bernhard is gray and John discarded the apple' then Mary took the milk.
It is probably not the case that 'Julius is yellow' or 'Brian is white' or both.
It is highly likely that 'Julius is yellow' or 'Brian is white' or both.
It is probably not the case that 'Julius is yellow' or 'Brian is white' or 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.
  0.05::factB.
  0.9::factC.
  %hop1
  0.75::factX:-xor(factB,factC).
  0.5::factY:-xor(factC,factB).
  0.7::factZ:-and(factB,factC).

  %hop2
  conclusion:-or(factA,factX).

  query(conclusion).
  
'Julius is yellow' or 'Brian is white' or both.