There is a very good chance that Jason is tired. We doubt that Bernhard is white. There is almost no chance that Brian is green. It is highly unlikely that if either 'Bernhard is white' or 'Jason is tired' but not both then Greg is yellow. There is little chance that if 'Bernhard is white' or 'Brian is green' or both then Mary left the milk. It is improbable that if 'Jason is tired and Brian is green' then John put down the milk.
It is improbable that either 'Bernhard is white' or 'Jason is tired' but not both.
It is probably the case that either 'Bernhard is white' or 'Jason is tired' but not both.
It is improbable that either 'Bernhard is white' or 'Jason is tired' 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
  0.8::factA.
  0.2::factB.
  0.02::factC.
  %hop1
  0.05::factX:-xor(factB,factA).
  0.1::factY:-or(factB,factC).
  0.1::factZ:-and(factA,factC).

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

  query(conclusion).
  
Either 'Bernhard is white' or 'Jason is tired' but not both.