There is a very good chance that Gertrude is a mouse. Chances are slight that Winona is a cat. There is a better than even chance that Mary dropped the apple. There is little chance that if either 'Mary dropped the apple' or 'Winona is a cat' but not both then Greg is gray. It is improbable that if 'Winona is a cat' or 'Gertrude is a mouse' or both then Lily is white. There is almost no chance that if 'Winona is a cat and Gertrude is a mouse' then Daniel got the milk.
It is impossible that either 'Lily is white' or 'Gertrude is a mouse' but not both.
It is likely that either 'Lily is white' or 'Gertrude is a mouse' but not both.
It is impossible that either 'Lily is white' or 'Gertrude is a mouse' 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.
  0.1::factB.
  0.6::factC.
  %hop1
  0.1::factX:-xor(factC,factB).
  0.1::factY:-or(factB,factA).
  0.02::factZ:-and(factB,factA).

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

  query(conclusion).
  
Either 'Lily is white' or 'Gertrude is a mouse' but not both.