It is probable that Lily is yellow. There is a very good chance that Mary went to the office. We believe that Bernhard is green. There is a better than even chance that if either 'Mary went to the office' or 'Bernhard is green' but not both then Greg is a rhino. It is highly likely that if 'Mary went to the office and Lily is yellow' then Brian is white. It is certain that if 'Mary went to the office' or 'Bernhard is green' or both then John discarded the milk.
It is highly unlikely that either 'Lily is yellow' or 'Bernhard is green' but not both.
Chances are about even that either 'Lily is yellow' or 'Bernhard is green' but not both.
It is highly unlikely that either 'Lily is yellow' or 'Bernhard is green' 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.
  0.8::factB.
  0.75::factC.
  %hop1
  0.6::factX:-xor(factB,factC).
  0.9::factY:-and(factB,factA).
  1.0::factZ:-or(factB,factC).

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

  query(conclusion).
  
Either 'Lily is yellow' or 'Bernhard is green' but not both.