Prototypical Concept Learning Task

• Given:
  • Instances X: Possible days, each described by the attributes Sky, AirTemp, Humidity, Wind, Water, Forecast

  • Target function c: $EnjoySport: X \rightarrow \{0,1 \}$

  • Hypotheses H: Conjunctions of literals. E.g.
    
    $$\langle ?, Cold, High, ?, ?, ? \rangle.$$
    
    

  • Training examples D: Positive and negative examples of the target function
    
    $$\langle x_1, c(x_1) \rangle , \ldots \langle x_m, c(x_m) \rangle$$
    
    

• Determine: A hypothesis h in H such that h(x)=c(x) for all x in D.

The inductive learning hypothesis: Any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples.