New Learning Problem

Learning algorithm accepts explicit prior knowledge as an input, in addition to the training data.
Inverted deduction systems also use background knowledge, but they use it to augment the description of instances. \[\forall_{\langle x_{i}, f(x_i) \rangle \in D} B \wedge h \wedge x_{i} \entails f(x_{i}) \] This results in increasing the size of H.
In explanation-based learning the prior knowledge is used to reduce the size of H. EBL assumes that \[ \forall_{\langle x_{i}, f(x_i) \rangle \in D} B' \wedge x_{i} \entails f(x_{i}) \] and outputs $h$ such that \[ \forall_{\langle x_{i}, f(x_i) \rangle \in D} h \wedge x_{i} \entails f(x_{i}) \]\[ D \wedge B' \entails h \]