It is likely that Bernhard is a frog. It is impossible that Yann is tired. It is impossible that Mary went to the kitchen. Chances are about even that if 'Bernhard is a frog' or 'Yann is tired' or both then Gertrude is a cat. Chances are slight that if 'Mary went to the kitchen and Bernhard is a frog' then Daniel took the apple. Chances are about even that if either 'Yann is tired' or 'Bernhard is a frog' but not both then Jason is bored.
It is likely that either 'Yann is tired' or 'Gertrude is a cat' but not both.
It is probably not the case that either 'Yann is tired' or 'Gertrude is a cat' but not both.
It is likely that either 'Yann is tired' or 'Gertrude 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
  0.7::factA.
  0.0::factB.
  0.0::factC.
  %hop1
  0.5::factX:-or(factA,factB).
  0.1::factY:-and(factC,factA).
  0.5::factZ:-xor(factB,factA).

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

  query(conclusion).
  
Either 'Yann is tired' or 'Gertrude is a cat' but not both.