There is a better than even chance that Yann is tired. It is likely that John picked up the milk. We doubt that Fred is in the school. There is almost no chance that if 'Yann is tired and John picked up the milk' then Bernhard is a lion. Chances are slight that if 'Yann is tired' or 'Fred is in the school' or both then Lily is a frog. Chances are slight that if either 'Fred is in the school' or 'Yann is tired' but not both then Brian is white.
It is probably the case that either 'Brian is white' or 'John picked up the milk' but not both.
It is probably the case that either 'Brian is white' or 'John picked up the milk' but not both.
There is little chance that either 'Brian is white' or 'John picked up 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
  0.6::factA.
  0.7::factB.
  0.2::factC.
  %hop1
  0.02::factX:-and(factA,factB).
  0.1::factY:-or(factA,factC).
  0.1::factZ:-xor(factC,factA).

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

  query(conclusion).
  
Either 'Brian is white' or 'John picked up the milk' but not both.