It is improbable that John went to the hallway. There is a better than even chance that Lily is a frog. Chances are about even that Gertrude is a cat. It is unlikely that if 'John went to the hallway' or 'Lily is a frog' or both then Bernhard is a swan. It is probable that if 'Gertrude is a cat' or 'Lily is a frog' or both then Greg is green. It is probable that if either 'John went to the hallway' or 'Lily is a frog' but not both then Brian is gray.
It is probably not the case that either 'Lily is a frog' or 'Greg is green' but not both.
It is probably not the case that either 'Lily is a frog' or 'Greg is green' but not both.
We believe that either 'Lily is a frog' or 'Greg is green' 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
  0.1::factA.
  0.6::factB.
  0.5::factC.
  %hop1
  0.2::factX:-or(factA,factB).
  0.7::factY:-or(factC,factB).
  0.7::factZ:-xor(factA,factB).

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

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