It is almost certain that Brian is a frog. It is probable that Lily is yellow. There is a better than even chance that Sandra took the milk. There is a better than even chance that if 'Brian is a frog' or 'Lily is yellow' or both then John grabbed the apple. We believe that if 'Lily is yellow and Brian is a frog' then Mary dropped the apple. It is improbable that if 'Brian is a frog' or 'Lily is yellow' or both then Bernhard is white.
It is impossible that either 'Brian is a frog' or 'Sandra took the milk' but not both.
Chances are about even that either 'Brian is a frog' or 'Sandra took the milk' but not both.
It is impossible that either 'Brian is a frog' or 'Sandra took the milk' 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
  0.95::factA.
  0.7::factB.
  0.6::factC.
  %hop1
  0.6::factX:-or(factA,factB).
  0.75::factY:-and(factB,factA).
  0.1::factZ:-or(factA,factB).

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

  query(conclusion).
  
Either 'Brian is a frog' or 'Sandra took the milk' but not both.