Chances are slight that Mary left the apple. It is certain that Bernhard is a swan. It is highly likely that John discarded the milk. We doubt that if 'Bernhard is a swan' or 'Mary left the apple' or both then Julius is gray. We doubt that if 'Bernhard is a swan' or 'John discarded the milk' or both then Brian is a frog. We believe that if either 'Bernhard is a swan' or 'John discarded the milk' but not both then Bill went to the garden.
It is probably not the case that 'Julius is gray' or 'Mary left the apple' or both.
It is probably not the case that 'Julius is gray' or 'Mary left the apple' or both.
It is probable that 'Julius is gray' or 'Mary left the apple' or 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
  0.1::factA.
  1.0::factB.
  0.9::factC.
  %hop1
  0.2::factX:-or(factB,factA).
  0.2::factY:-or(factB,factC).
  0.75::factZ:-xor(factB,factC).

  %hop2
  conclusion:-or(factX,factA).

  query(conclusion).
  
'Julius is gray' or 'Mary left the apple' or both.