It is probably the case that Jessica is a cat. It is unlikely that Lily is a frog. There is a better than even chance that John went to the office. We doubt that if 'Jessica is a cat' or 'John went to the office' or both then Bernhard is white. It is likely that if 'Lily is a frog' or 'Jessica is a cat' or both then Mary dropped the milk. There is almost no chance that if 'John went to the office' or 'Jessica is a cat' or both then Greg is a swan.
It is impossible that either 'Mary dropped the milk' or 'Greg is a swan' but not both.
Chances are about even that either 'Mary dropped the milk' or 'Greg is a swan' but not both.
It is impossible that either 'Mary dropped the milk' or 'Greg is a swan' 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.
  0.2::factB.
  0.6::factC.
  %hop1
  0.2::factX:-or(factA,factC).
  0.7::factY:-or(factB,factA).
  0.02::factZ:-or(factC,factA).

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

  query(conclusion).
  
Either 'Mary dropped the milk' or 'Greg is a swan' but not both.