Chances are about even that Mary took the football. We believe that Julius is white. It is probably not the case that Fred discarded the apple. We doubt that if either 'Julius is white' or 'Mary took the football' but not both then Daniel put down the milk. It is certain that if 'Fred discarded the apple and Mary took the football' then Brian is green. Chances are about even that if 'Julius is white and Fred discarded the apple' then Gertrude is a cat.
There is little chance that either 'Daniel put down the milk' or 'Mary took the football' but not both.
There is a better than even chance that either 'Daniel put down the milk' or 'Mary took the football' but not both.
There is little chance that either 'Daniel put down the milk' or 'Mary took the football' 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
  0.5::factA.
  0.75::factB.
  0.25::factC.
  %hop1
  0.2::factX:-xor(factB,factA).
  1.0::factY:-and(factC,factA).
  0.5::factZ:-and(factB,factC).

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

  query(conclusion).
  
Either 'Daniel put down the milk' or 'Mary took the football' but not both.