Chances are about even that Mary went to the hallway. Chances are slight that Daniel dropped the apple. It is impossible that Bernhard is a swan. We believe that if either 'Bernhard is a swan' or 'Mary went to the hallway' but not both then Greg is a frog. We believe that if 'Mary went to the hallway' or 'Bernhard is a swan' or both then Lily is a lion. It is unlikely that if 'Bernhard is a swan and Mary went to the hallway' then John put down the milk.
It is impossible that either 'John put down the milk' or 'Bernhard is a swan' but not both.
It is impossible that either 'John put down the milk' or 'Bernhard is a swan' but not both.
It is probable that either 'John put down the milk' or 'Bernhard 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
  0.5::factA.
  0.1::factB.
  0.0::factC.
  %hop1
  0.75::factX:-xor(factC,factA).
  0.75::factY:-or(factA,factC).
  0.2::factZ:-and(factC,factA).

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

  query(conclusion).
  
Either 'John put down the milk' or 'Bernhard is a swan' but not both.