Specifying the Problem:

Now next here furtherly we now use to look at how you mentally constructed your decision tree where deciding what to do at the weekend. But if one way would be to require some background information as axioms and deduce then what to do. If we look an example here you might know that your parents in reality like going to the cinema or that your parents are in town and therefore as using something like Modus Ponens then you would decide to go to the cinema of course. 

Now next here instantly one way such you might have made up your mind was by generalising from previous experiences. Visualize like you remembered all the times where you had a really good weekend. Means a few weeks back there it was sunny and your parents were not visiting or you played tennis so and it was good for you. Thus a month ago if it was raining instantly you were penniless then a trip to the cinema cheered you up like so on. Hence information of this type could have guided your decision making then if this was the case as you would have used an inductive so deductive method to construct your decision tree. Now next here instantly we considered humans reason to solve decisions by utilising both inductive and deductive processes. 

Furthermore we have a set of examples correctly categorised with categories as decisions. So here we have a set of attributes describing the examples also and each attribute has a finite set of values that it can possibly take. However we want to utilise the examples to learn the structure of a decision tree that can be required to decide the category of an unseen. 

By supposing that there are no inconsistencies in the data as where two examples have exactly the same values for the attributes and are categorised differently and it is obvious that we can always construct a decision tree to correctly decide for the training cases with 100% accuracy. Thus all we have to do is make sure every situation is catered for down some branch of the decision tree. Obviously there 100% accuracy may indicate overfitting.