We doubt that Julius is green. We believe that Jeff dropped the apple. It is certain that Brian is white. It is probably not the case that if 'Jeff dropped the apple and Julius is green' then Greg is a frog. It is probably the case that if either 'Brian is white' or 'Julius is green' but not both then John took the football. There is almost no chance that if either 'Julius is green' or 'Brian is white' but not both then Mary discarded the milk.
Chances are about even that either 'John took the football' or 'Brian is white' but not both.
Chances are about even that either 'John took the football' or 'Brian is white' but not both.
It is impossible that either 'John took the football' or 'Brian 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
  0.2::factA.
  0.75::factB.
  1.0::factC.
  %hop1
  0.25::factX:-and(factB,factA).
  0.7::factY:-xor(factC,factA).
  0.02::factZ:-xor(factA,factC).

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

  query(conclusion).
  
Either 'John took the football' or 'Brian is white' but not both.