The normal, sound, use of modus ponens is to infer that 
is true given that 
and
are known. However Figure 2.12 shows the type of
unsound reasoning known as logical abduction.
For example with the facts ``Jeff can fly'' and ``ducks can fly'', logical abduction allows the conclusion ``Jeff is a duck'' to be inferred, which could obviously be incorrect.
Generally an effect can have many 
causes, and a method to choose the 'best' abductive proof is needed.
There exist several techniques for choosing between various explanations,
including probabilistic methods (which have the difficulty of defining
the space over which to calculate the probabilities, and calculate
them given the lack of training data) and heuristic methods which
use another evaluation method such as choosing the explanation with
the least number of assumptions. These methods are considered beyond
the scope of this paper and shall therefore not be discussed.
