It is probable that Julius is white. It is almost certain that Sandra dropped the milk. It is impossible that Greg is gray. There is a better than even chance that if either 'Julius is white' or 'Greg is gray' but not both then Emily is a cat. We believe that if 'Greg is gray and Sandra dropped the milk' then Mary went to the garden. It is highly likely that if 'Greg is gray' or 'Julius is white' or both then John picked up the apple.
It is highly unlikely that either 'John picked up the apple' or 'Greg is gray' but not both.
There is a better than even chance that either 'John picked up the apple' or 'Greg is gray' but not both.
It is highly unlikely that either 'John picked up the apple' or 'Greg is gray' 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.
  0.95::factB.
  0.0::factC.
  %hop1
  0.6::factX:-xor(factA,factC).
  0.75::factY:-and(factC,factB).
  0.9::factZ:-or(factC,factA).

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

  query(conclusion).
  
Either 'John picked up the apple' or 'Greg is gray' but not both.