Inverse Entailment Pros and Cons

Pros:

• Subsumes earlier idea of finding $h$ that “fits” training data
• Domain theory $B$ helps define meaning of “fit” the data \[ B \wedge h \wedge x_{i} \entails f(x_{i}) \]
• Suggests algorithms that search $H$ guided by $B$

Cons:

• Doesn't allow for noisy data. Consider \[ \forall_{\langle x_{i},f(x_{i}) \rangle \in D} (B \wedge h \wedge x_{i}) \entails f(x_{i}) \]
• First order logic gives a huge hypothesis space $H$. This leads to over-fitting and the intractability of calculating all acceptable $h$'s.
• The complexity of space search increases as the background knowledge B is increased.