context: Chances are slight that John put down the apple. We doubt that Lily is yellow. Chances are slight that Bernhard is a frog. It is certain that if 'John put down the apple and Lily is yellow' then Greg is a rhino. We doubt that if 'Lily is yellow' or 'Bernhard is a frog' or both then Brian is white. We believe that if either 'Bernhard is a frog' or 'John put down the apple' but not both then Mary went to the office.
hypothesis: It is probably the case that 'Brian is white' or 'Bernhard is a frog' or both.
valid_hypothesis: It is improbable that 'Brian is white' or 'Bernhard is a frog' or both.
invalid_hypothesis: It is probably the case that 'Brian is white' or 'Bernhard is a frog' or both.
problog: 
    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
    0.1::factA.
    0.2::factB.
    0.1::factC.
    %hop1
    1.0::factX:-and(factA,factB).
    0.2::factY:-or(factB,factC).
    0.75::factZ:-xor(factC,factA).
  
    %hop2
    conclusion:-or(factY,factC).
  
    query(conclusion).
    
hypothesis_assertion: 'Brian is white' or 'Bernhard is a frog' or both.