It is likely that Brian is a swan. There is a better than even chance that Jessica is a cat. We doubt that Bernhard is yellow. It is impossible that if either 'Bernhard is yellow' or 'Jessica is a cat' but not both then Lily is a frog. There is little chance that if 'Jessica is a cat and Brian is a swan' then Mary went to the kitchen. Chances are about even that if 'Jessica is a cat and Brian is a swan' then John moved to the garden.
It is probable that either 'Mary went to the kitchen' or 'Brian is a swan' but not both.
It is probable that either 'Mary went to the kitchen' or 'Brian is a swan' but not both.
It is impossible that either 'Mary went to the kitchen' or 'Brian is a swan' 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.
  0.6::factB.
  0.2::factC.
  %hop1
  0.0::factX:-xor(factC,factB).
  0.1::factY:-and(factB,factA).
  0.5::factZ:-and(factB,factA).

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

  query(conclusion).
  
Either 'Mary went to the kitchen' or 'Brian is a swan' but not both.