It is improbable that Mary went to the kitchen. We believe that John picked up the apple. We doubt that Fred dropped the milk. There is a better than even chance that if either 'Fred dropped the milk' or 'Mary went to the kitchen' but not both then Yann is tired. It is unlikely that if either 'Fred dropped the milk' or 'Mary went to the kitchen' but not both then Emily is a mouse. It is impossible that if 'John picked up the apple' or 'Mary went to the kitchen' or both then Lily is white.
It is probable that either 'John picked up the apple' or 'Mary went to the kitchen' but not both.
It is probable that either 'John picked up the apple' or 'Mary went to the kitchen' but not both.
It is improbable that either 'John picked up the apple' 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
  0.1::factA.
  0.75::factB.
  0.2::factC.
  %hop1
  0.6::factX:-xor(factC,factA).
  0.2::factY:-xor(factC,factA).
  0.0::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'John picked up the apple' or 'Mary went to the kitchen' but not both.