We doubt that Greg is white. It is highly likely that Bernhard is a frog. There is little chance that John grabbed the apple. It is probably not the case that if 'Greg is white and Bernhard is a frog' then Bill went to the kitchen. There is little chance that if 'John grabbed the apple and Bernhard is a frog' then Jeff left the apple. We doubt that if either 'John grabbed the apple' or 'Bernhard is a frog' but not both then Daniel dropped the milk.
We believe that either 'Daniel dropped the milk' or 'Bernhard is a frog' but not both.
We believe that either 'Daniel dropped the milk' or 'Bernhard is a frog' but not both.
It is improbable that either 'Daniel dropped the milk' or 'Bernhard is a frog' 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
  0.2::factA.
  0.9::factB.
  0.1::factC.
  %hop1
  0.25::factX:-and(factA,factB).
  0.1::factY:-and(factC,factB).
  0.2::factZ:-xor(factC,factB).

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

  query(conclusion).
  
Either 'Daniel dropped the milk' or 'Bernhard is a frog' but not both.