It is probable that Bernhard is a swan. It is probably not the case that John discarded the apple. There is a very good chance that Mary went to the kitchen. There is little chance that if 'Mary went to the kitchen' or 'Bernhard is a swan' or both then Julius is a frog. There is a very good chance that if 'Bernhard is a swan and John discarded the apple' then Greg is yellow. It is highly unlikely that if either 'Mary went to the kitchen' or 'Bernhard is a swan' but not both then Lily is a rhino.
Chances are slight that either 'Bernhard is a swan' or 'John discarded the apple' but not both.
There is a better than even chance that either 'Bernhard is a swan' or 'John discarded the apple' but not both.
Chances are slight that either 'Bernhard is a swan' or 'John discarded the apple' 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.
  0.25::factB.
  0.8::factC.
  %hop1
  0.1::factX:-or(factC,factA).
  0.8::factY:-and(factA,factB).
  0.05::factZ:-xor(factC,factA).

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

  query(conclusion).
  
Either 'Bernhard is a swan' or 'John discarded the apple' but not both.