It is probably the case that John left the apple. We doubt that Mary got the football. There is a better than even chance that Greg is gray. It is certain that if 'Greg is gray and John left the apple' then Lily is a frog. We believe that if either 'Greg is gray' or 'Mary got the football' but not both then Sandra dropped the milk. We doubt that if 'John left the apple and Greg is gray' then Bernhard is yellow.
It is certain that either 'Sandra dropped the milk' or 'Bernhard is yellow' but not both.
Chances are about even that either 'Sandra dropped the milk' or 'Bernhard is yellow' but not both.
It is certain that either 'Sandra dropped the milk' or 'Bernhard is yellow' 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
  0.7::factA.
  0.2::factB.
  0.6::factC.
  %hop1
  1.0::factX:-and(factC,factA).
  0.75::factY:-xor(factC,factB).
  0.2::factZ:-and(factA,factC).

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

  query(conclusion).
  
Either 'Sandra dropped the milk' or 'Bernhard is yellow' but not both.