We believe that Lily is a frog. There is little chance that John discarded the apple. It is unlikely that Brian is white. We doubt that if 'Lily is a frog and John discarded the apple' then Greg is a swan. It is unlikely that if 'Lily is a frog' or 'Brian is white' or both then Mary got the milk. It is impossible that if 'John discarded the apple' or 'Lily is a frog' or both then Bill went to the garden.
We believe that either 'Bill went to the garden' or 'Lily is a frog' but not both.
We believe that either 'Bill went to the garden' or 'Lily is a frog' but not both.
It is highly unlikely that either 'Bill went to the garden' 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
  0.2::factX:-and(factA,factB).
  0.2::factY:-or(factA,factC).
  0.0::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'Bill went to the garden' or 'Lily is a frog' but not both.