It is certain that Jessica is a mouse. It is highly likely that John left the apple. It is improbable that Fred dropped the milk. It is improbable that if either 'Fred dropped the milk' or 'Jessica is a mouse' but not both then Antoine is thirsty. It is improbable that if either 'Jessica is a mouse' or 'Fred dropped the milk' but not both then Bernhard is a frog. It is certain that if either 'John left the apple' or 'Jessica is a mouse' but not both then Mary went to the kitchen.
It is unlikely that either 'Bernhard is a frog' or 'Mary went to the kitchen' but not both.
It is unlikely that either 'Bernhard is a frog' or 'Mary went to the kitchen' but not both.
It is highly likely that either 'Bernhard is a frog' or 'Mary went to the kitchen' 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
  1.0::factA.
  0.9::factB.
  0.1::factC.
  %hop1
  0.1::factX:-xor(factC,factA).
  0.1::factY:-xor(factA,factC).
  1.0::factZ:-xor(factB,factA).

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

  query(conclusion).
  
Either 'Bernhard is a frog' or 'Mary went to the kitchen' but not both.