Chances are slight that Brian is gray. Chances are slight that Daniel got the apple. It is improbable that Sumit is bored. It is highly likely that if 'Brian is gray' or 'Sumit is bored' or both then Greg is a swan. It is unlikely that if either 'Daniel got the apple' or 'Sumit is bored' but not both then Mary picked up the milk. It is likely that if either 'Sumit is bored' or 'Brian is gray' but not both then Bernhard is a lion.
We doubt that either 'Brian is gray' or 'Sumit is bored' but not both.
We doubt that either 'Brian is gray' or 'Sumit is bored' but not both.
It is highly likely that either 'Brian is gray' or 'Sumit is bored' 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.
  0.1::factB.
  0.1::factC.
  %hop1
  0.9::factX:-or(factA,factC).
  0.2::factY:-xor(factB,factC).
  0.7::factZ:-xor(factC,factA).

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

  query(conclusion).
  
Either 'Brian is gray' or 'Sumit is bored' but not both.