There is a very good chance that Bernhard is gray. Chances are slight that Emily is a mouse. Chances are slight that Julius is gray. It is probably not the case that if either 'Emily is a mouse' or 'Bernhard is gray' but not both then John went to the garden. It is unlikely that if 'Bernhard is gray and Julius is gray' then Greg is a frog. We doubt that if 'Bernhard is gray and Emily is a mouse' then Gertrude is a sheep.
It is likely that either 'Gertrude is a sheep' or 'Julius is gray' but not both.
There is little chance that either 'Gertrude is a sheep' or 'Julius is gray' but not both.
It is likely that either 'Gertrude is a sheep' or 'Julius is gray' 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
  0.8::factA.
  0.1::factB.
  0.1::factC.
  %hop1
  0.25::factX:-xor(factB,factA).
  0.2::factY:-and(factA,factC).
  0.2::factZ:-and(factA,factB).

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

  query(conclusion).
  
Either 'Gertrude is a sheep' or 'Julius is gray' but not both.