It is certain that John picked up the apple. It is improbable that Mary took the milk. It is improbable that Gertrude is a cat. It is probably not the case that if 'John picked up the apple and Mary took the milk' then Julius is yellow. It is highly unlikely that if 'Mary took the milk and John picked up the apple' then Greg is a swan. We believe that if either 'Mary took the milk' or 'John picked up the apple' but not both then Emily is a mouse.
There is little chance that either 'Julius is yellow' or 'Gertrude is a cat' but not both.
There is little chance that either 'Julius is yellow' or 'Gertrude is a cat' but not both.
There is a better than even chance that either 'Julius is yellow' or 'Gertrude is a cat' 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
  1.0::factA.
  0.1::factB.
  0.1::factC.
  %hop1
  0.25::factX:-and(factA,factB).
  0.05::factY:-and(factB,factA).
  0.75::factZ:-xor(factB,factA).

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

  query(conclusion).
  
Either 'Julius is yellow' or 'Gertrude is a cat' but not both.