What exactly is a symbolic classifier? What exactly is a symbolic classifier? What does the input data look like? I understand decision trees and kNN classifier are considered as symbolic classifiers.
EDIT: This presentation gives a brief overview on the topic in question: https://www.rocq.inria.fr/axis/modulad/Workshop_Franco_Bresilien/programme/diday-slides.pdf
 A: Pages 6 and 7 of the slides you link describe what symbolic data is.
Here is page 7:

A typical classifier will be trained with labeled data. These labels are simplistic, there is one correct label. The training data has many possible outcomes for the labels but there is no implied relationship between them. For example you may have individual labels for birds "Hawk", "Eagle", "Chicken"; these are three unique labels and we know that they are strongly related to each other but the data doesn't indicate that. The classifier can't learn a general idea of "bird" because it is only told about "Hawk", "Eagle", and "Chicken".
On the other hand, a symbolic classifier deals with concepts. Instead of labeling images with exact descriptions we can label them with general concepts which describe them. 
Imagine if you had images of hawks, eagles, hyenas, chickens and cows. The labeling might be like this:


*

*hawk: bird, predator

*eagle: bird, predator

*hyena: dog, predator

*chicken: bird, farm

*cow: mammal, farm
When you train a classifier with this data it can create an idea of "predator", "bird", "dog" and "farm". Once the symbolic classifier has been trained it might identify a sheep-dog as a mix of "farm" and "dog" even though you never trained it with images of domestic dogs.
Another feature of this classifier is that hawks and eagles are labeled exactly the same. In one way this makes sense because we are rarely interested in what makes eagles different from hawks.
