There is a better than even chance that Brian is gray. It is improbable that Yann is tired. It is unlikely that Bernhard is white. It is probable that if 'Bernhard is white' or 'Brian is gray' or both then Greg is a lion. It is probably the case that if 'Bernhard is white' or 'Yann is tired' or both then Mary picked up the milk. It is highly likely that if 'Bernhard is white and Yann is tired' then John went to the kitchen.
We doubt that either 'Yann is tired' or 'Mary picked up the milk' but not both.
We doubt that either 'Yann is tired' or 'Mary picked up the milk' but not both.
It is highly likely that either 'Yann is tired' or 'Mary 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.
  0.1::factB.
  0.2::factC.
  %hop1
  0.7::factX:-or(factC,factA).
  0.7::factY:-or(factC,factB).
  0.9::factZ:-and(factC,factB).

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

  query(conclusion).
  
Either 'Yann is tired' or 'Mary picked up the milk' but not both.