FG Datenbank- und Informationssysteme
Besides a good prediction a classifier is to give an explanation how input data is related to the classification result. Decision trees are very popular classifiers and provide a good trade-off between accuracy and explainability for many scenarios. Its split decisions correspond to Boolean conditions on single attributes. In cases when for a class decision several attribute values interact gradually with each other, Boolean-logic-based decision trees are not appropriate. For such cases we propose a quantum-logic inspired decision tree (QLDT) which is based on sums and products on normalized attribute values. In contrast to decision trees based on fuzzy logic a QLDT obeys the rules of the Boolean algebra.
Convolutional neural networks are often successfully used for clas-
si cation problems. Usually, a huge number of weights need to be
learnt by use of training data. However, the learnt weights give no
insight how the cnn really works. Thus, a cnn can be seen as a black
box solution. In our approach we develop a method to generate a
commuting quantum query language (cqql) condition from a sample
derived from a given cnn or from training input. The query language
cqql is inspired by quantum logic and its conditions obey the rules of
a Boolean algebra. The evaluation of a cqql condition provides values
from the unit interval [0; 1] and establishes therefore an elegant bridge between logic and a cnn. The underlying assumption is that a condition (a logic expression) gives much more understanding than pure cnn weights. Furthermore, the rich theory of Boolean algebra can be used for manipulating logic expressions. After extracting a cqql condition from a cnn or its training data we can use logic as a way to predict classes alternatively to a cnn.