It is highly likely that Mary took the football. We doubt that Julius is a frog. There is a very good chance that Bernhard is yellow. There is a better than even chance that if 'Mary took the football' or 'Julius is a frog' or both then Brian is a swan. There is almost no chance that if 'Julius is a frog and Mary took the football' then Sandra got the milk. It is probably not the case that if either 'Mary took the football' or 'Bernhard is yellow' but not both then John moved to the office.
We believe that either 'Julius is a frog' or 'Mary took the football' but not both.
We believe that either 'Julius is a frog' or 'Mary took the football' but not both.
It is improbable that either 'Julius is a frog' 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
  0.9::factA.
  0.2::factB.
  0.8::factC.
  %hop1
  0.6::factX:-or(factA,factB).
  0.02::factY:-and(factB,factA).
  0.25::factZ:-xor(factA,factC).

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

  query(conclusion).
  
Either 'Julius is a frog' or 'Mary took the football' but not both.