We believe that John took the football. It is highly unlikely that Mary picked up the milk. There is almost no chance that Julius is a frog. It is highly likely that if 'Mary picked up the milk' or 'John took the football' or both then Greg is white. It is unlikely that if 'Julius is a frog' or 'John took the football' or both then Fred went to the garden. It is probable that if 'John took the football' or 'Julius is a frog' or both then Gertrude is a mouse.
There is almost no chance that either 'John took the football' or 'Julius is a frog' but not both.
We believe that either 'John took the football' or 'Julius is a frog' but not both.
There is almost no chance that either 'John took the football' or 'Julius is a frog' 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
  0.75::factA.
  0.05::factB.
  0.02::factC.
  %hop1
  0.9::factX:-or(factB,factA).
  0.2::factY:-or(factC,factA).
  0.7::factZ:-or(factA,factC).

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

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