context: It is highly likely that Brian is white. There is almost no chance that Mary went to the kitchen. We doubt that Jessica is a cat. It is probably the case that if either 'Jessica is a cat' or 'Mary went to the kitchen' but not both then John put down the milk. It is impossible that if either 'Mary went to the kitchen' or 'Jessica is a cat' but not both then Sandra got the football. It is improbable that if either 'Mary went to the kitchen' or 'Jessica is a cat' but not both then Julius is a swan.
hypothesis: It is probable that either 'John put down the milk' or 'Mary went to the kitchen' but not both.
valid_hypothesis: There is little chance that either 'John put down the milk' or 'Mary went to the kitchen' but not both.
invalid_hypothesis: It is probable that either 'John put down the milk' or 'Mary went to the kitchen' 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
    0.9::factA.
    0.02::factB.
    0.2::factC.
    %hop1
    0.7::factX:-xor(factC,factB).
    0.0::factY:-xor(factB,factC).
    0.1::factZ:-xor(factB,factC).
  
    %hop2
    conclusion:-xor(factX,factB).
  
    query(conclusion).
    
hypothesis_assertion: Either 'John put down the milk' or 'Mary went to the kitchen' but not both.