We believe that John took the football. There is little chance that Julius is a rhino. We doubt that Lily is a frog. There is almost no chance that if 'Lily is a frog and John took the football' then Bernhard is gray. It is probably the case that if 'Julius is a rhino and John took the football' then Greg is white. There is a better than even chance that if 'Lily is a frog' or 'Julius is a rhino' or both then Mary left the football.
It is probably the case that either 'Greg is white' or 'Lily is a frog' but not both.
It is probably not the case that either 'Greg is white' or 'Lily is a frog' but not both.
It is probably the case that either 'Greg is white' or 'Lily is a frog' 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
  0.75::factA.
  0.1::factB.
  0.2::factC.
  %hop1
  0.02::factX:-and(factC,factA).
  0.7::factY:-and(factB,factA).
  0.6::factZ:-or(factC,factB).

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

  query(conclusion).
  
Either 'Greg is white' or 'Lily is a frog' but not both.