ALT Page 3

 Learning Conjunctive Concepts

Humans are able to distinguish between different “things,” e.g., chair, table, sofa, book, newspaper, car, airplane, a.s.o. Also, there is no doubt that humans have to learn how to distinguish “things.” Therefore, we ask whether this particular learning problem allows an algorithmic solution, too. That is, we specify the learner to be an algorithm. Furthermore, we specify the learning domain to be the set of all things. However, since we aim to model learning, we have to convert “real things” into mathematical descriptions of things. This can be done as follows. We fix some language to express a finite list of properties. Afterwards, we decide which of these properties are relevant for the particular things we want to deal with, and which of them have to be fulfilled or not to be fulfilled, respectively. For example, the list of properties may be fixed as follows:

- possesses 4 legs, - possesses a rest, - has brown color, - possesses 4 wheels,
- it needs fuel, - possesses a seat,- possesses wings, ..., - has more than 100 pages.

“What is a chair?”

by deciding which of the properties are relevant for the concept “chair,” and which of them have to be fulfilled or not to be fulfilled, respectively.

Hence, we obtain:

[1] possesses 4 legs - yes
[2] possesses a rest - yes
[3] has brown color - irrelevant
[4] possesses 4 wheels - no
[5] it needs fuel - no
[6] possesses a seat - yes
[7] possesses wings - no
.
.
.
[n.] has more than 100 pages - no