It is probable that John discarded the apple. It is improbable that Bernhard is a frog. It is certain that Gertrude is a cat. There is little chance that if either 'John discarded the apple' or 'Gertrude is a cat' but not both then Julius is a rhino. Chances are slight that if 'Gertrude is a cat' or 'John discarded the apple' or both then Brian is white. Chances are about even that if either 'Gertrude is a cat' or 'Bernhard is a frog' but not both then Mary went to the hallway.
It is impossible that 'Gertrude is a cat' or 'Mary went to the hallway' or both.
It is certain that 'Gertrude is a cat' or 'Mary went to the hallway' or both.
It is impossible that 'Gertrude is a cat' or 'Mary went to the hallway' or 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.
  0.1::factB.
  1.0::factC.
  %hop1
  0.1::factX:-xor(factA,factC).
  0.1::factY:-or(factC,factA).
  0.5::factZ:-xor(factC,factB).

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

  query(conclusion).
  
'Gertrude is a cat' or 'Mary went to the hallway' or both.