syntactically distinct hypothesis within H.

[tahasozgen]

Hi There;
There is a term that I cannot get. Could you please help me with decoding?
The text has been taken from the cornerstone book, "Machine Learning" written by Tom Mitchell.

First of all, I want to give information about the domain. Assume that you have a friend and according to different weather situations, we try to guess your friend likes playing tennis or not. For example, when the sky is sunny, air temperature is dry, humidity is normal, the wind is strong, the water is warm, the forecast is the same, your friend likes playing tennis. In order to make the calculation simple, we limit the conditions as such:
sky: 3 possible values: {Sunny, Rainy, Cloudy}
air temperature: 2 possible values : {Warm, Cold}
humidity: 2 possible values : {Normal, High}
wind: 2 possible values: {Strong,Mild}
water: 2 possible values : {Warm, Cold}
forecast: 2 possible values : {Same, Change}

The instance space X contains exactly 3 x2 x2 x2x2x2 = 96 distinct instances. (My Note: 3 is the spectrum of the sky, 2 is the spectrum of the air temperature and so on..) A similar calculation shows that there are 5 x4x4x4x4x4 = 5120 syntactically distinct hypothesis within H. (My Note: 3 was the spectrum of the sky 1 is for ? , denotes "it does not matter" and null denotes "it does not matter what is the sky, your friend does not like tennis" ). Notice however, that every hypothesis containing one or more null symbol represents the empty set of instances ...

what is syntactically in this context? Thanks in advance.

 

[jutfrank]

syntactically comes from the word 'syntax'. Generally speaking, syntax is the order of elements in a string. So for example, in a string of values such as 1,2,3 there are three elements. Now if we take a different string, such as 2,1,3 you can identify the same three elements. The difference is that the order of the elements (the syntax) is different.

There are six syntactically distinct ways of ordering the digits 1,2 and 3.

1,2,3
1,3,2
2,1,3
2,3,1
3,1,2
3,2,1