It is probably not the case that Lily is white. Chances are slight that John grabbed the apple. It is unlikely that Mary went to the garden. It is impossible that if 'John grabbed the apple and Mary went to the garden' then Julius is yellow. We doubt that if either 'John grabbed the apple' or 'Mary went to the garden' but not both then Brian is a rhino. It is likely that if either 'Mary went to the garden' or 'John grabbed the apple' but not both then Sandra dropped the milk.
It is probable that either 'Mary went to the garden' or 'John grabbed the apple' but not both.
It is probably not the case that either 'Mary went to the garden' or 'John grabbed the apple' but not both.
It is probable that either 'Mary went to the garden' or 'John grabbed the apple' 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
  0.25::factA.
  0.1::factB.
  0.2::factC.
  %hop1
  0.0::factX:-and(factB,factC).
  0.2::factY:-xor(factB,factC).
  0.7::factZ:-xor(factC,factB).

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

  query(conclusion).
  
Either 'Mary went to the garden' or 'John grabbed the apple' but not both.