It is highly likely that Lily is a frog. Chances are slight that Mary went to the hallway. We believe that Brian is yellow. We doubt that if 'Brian is yellow and Lily is a frog' then Julius is a swan. It is likely that if either 'Brian is yellow' or 'Mary went to the hallway' but not both then Jessica is a cat. Chances are slight that if either 'Mary went to the hallway' or 'Brian is yellow' but not both then John picked up the milk.
It is highly unlikely that either 'Mary went to the hallway' or 'Jessica is a cat' but not both.
There is a better than even chance that either 'Mary went to the hallway' or 'Jessica is a cat' but not both.
It is highly unlikely that either 'Mary went to the hallway' or 'Jessica is a cat' 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
  0.9::factA.
  0.1::factB.
  0.75::factC.
  %hop1
  0.2::factX:-and(factC,factA).
  0.7::factY:-xor(factC,factB).
  0.1::factZ:-xor(factB,factC).

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

  query(conclusion).
  
Either 'Mary went to the hallway' or 'Jessica is a cat' but not both.