It is certain that Brian is white. There is little chance that Mary went to the kitchen. It is highly unlikely that Lily is green. There is a better than even chance that if 'Brian is white' or 'Lily is green' or both then Julius is green. There is a very good chance that if 'Mary went to the kitchen and Brian is white' then John dropped the apple. It is improbable that if either 'Mary went to the kitchen' or 'Lily is green' but not both then Greg is a frog.
There is almost no chance that 'Brian is white and Greg is a frog'.
There is almost no chance that 'Brian is white and Greg is a frog'.
We believe that 'Brian is white and Greg is a frog'.

  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
  1.0::factA.
  0.1::factB.
  0.05::factC.
  %hop1
  0.6::factX:-or(factA,factC).
  0.8::factY:-and(factB,factA).
  0.1::factZ:-xor(factB,factC).

  %hop2
  conclusion:-and(factA,factZ).

  query(conclusion).
  
'Brian is white and Greg is a frog'.