context: There is little chance that Jessica is a sheep. There is little chance that Greg is a frog. It is highly unlikely that Mary discarded the milk. It is probably not the case that if 'Mary discarded the milk and Greg is a frog' then John took the apple. It is certain that if either 'Greg is a frog' or 'Jessica is a sheep' but not both then Bernhard is green. Chances are about even that if either 'Greg is a frog' or 'Mary discarded the milk' but not both then Fred dropped the milk.
hypothesis: It is highly unlikely that either 'John took the apple' or 'Fred dropped the milk' but not both.
valid_hypothesis: It is highly unlikely that either 'John took the apple' or 'Fred dropped the milk' but not both.
invalid_hypothesis: Chances are about even that either 'John took the apple' or 'Fred dropped the milk' but not 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.
    0.1::factB.
    0.05::factC.
    %hop1
    0.25::factX:-and(factC,factB).
    1.0::factY:-xor(factB,factA).
    0.5::factZ:-xor(factB,factC).
  
    %hop2
    conclusion:-xor(factX,factZ).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John took the apple' or 'Fred dropped the milk' but not both.