It is improbable that Gertrude is a mouse. Chances are about even that Greg is white. It is probably the case that Bill got the milk there. It is probably the case that if either 'Gertrude is a mouse' or 'Bill got the milk there' but not both then Fred discarded the apple. There is a better than even chance that if 'Greg is white' or 'Bill got the milk there' or both then Brian is yellow. We believe that if 'Gertrude is a mouse and Greg is white' then Julius is gray.
Chances are about even that either 'Brian is yellow' or 'Greg is white' but not both.
Chances are about even that either 'Brian is yellow' or 'Greg is white' but not both.
It is certain that either 'Brian is yellow' or 'Greg is white' 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.
  0.5::factB.
  0.7::factC.
  %hop1
  0.7::factX:-xor(factA,factC).
  0.6::factY:-or(factB,factC).
  0.75::factZ:-and(factA,factB).

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

  query(conclusion).
  
Either 'Brian is yellow' or 'Greg is white' but not both.