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The quantum-logic inspired decision tree (QLDT) is based on quantum logic concepts and input values from the unit interval whereas the traditional decision tree is based on Boolean values. The logic behind the QLDT obeys the rules of a Boolean algebra. The QLDT is appropriate for classification problems where for a class decision several input values interact gradually with each other. The QLDT construction for a classification problem with n input attributes requires the computation of 2n minterms. The QLDT+ method, however, uses a heuristic for obtaining a QLDT with much smaller computational complexity. As result, the QLDT+ method can be applied to classification problems with a higher number of input attributes.

Das wesentliche Ziel dieses Lehrbuchs ist es, die mathematischen Werkzeuge zur Modellierung kognitiver Strukturen und Prozesse auf der Grundlage der klassischen Logik und der Quantenlogik zu entwickeln. Die dafür erforderlichen mathematischen Sachverhalte werden so dargestellt und anhand von Beispielen motiviert, dass sie für angehende Ingenieure und Informatiker verständlich sind.
- Kompakte logische Darstellung der mathematischen Werkzeuge zur Modellierung kognitiver Strukturen und Prozesse
- Beispiele erläutern die Anwendung im Engineering
Zielgruppen sind insbesondere Studierende der Ingenieurwissenschaften und der Informatik, aber auch Studierende der Mathematik oder der Physik können durch den anwendungsbezogenen Blick ihren Horizont erweitern.

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.

Besides a good prediction a classifier is to give an explanation how the input data is related to the classification result. There is a general agreement that logic expressions provide a better explanation than other methods like SVM, logistic regression, and neural networks. However, a classifier based on Boolean logic needs to map continuous data to Boolean values which can cause a loss of information. In contrast, we design a quantum-logic-inspired classifier where continuous data are directly processed and the laws of the Boolean algebra are maintained. As a result from our approach we obtain a CQQL condition which provides good insights into the relation of input features to the class decision. Furthermore, our experiment shows a good prediction accuracy.

Homogeneity of persons in a social network is based on the
similarity of their attributes. Traditional clustering algorithms like
hierarchical (agglomerative) clustering or DBSCAN take distances
between objects as input and find clusters of objects. Distance
functions need to satisfy the triangle inequality (TI) property, but
sometimes TI is violated and, in addition, not all attributes do have
the same influence on the network and thus may affect the network and
compromise the quality of resulting clusters. We present an adaptive
clustering-based quantitative weighting approach that is completely
embedded in logic. To facilitate the user interaction with the system,
we exploit the concept of relevance feedback. The approach takes user
feedback as input to improve the quality of clusters and finds
meaningful clusters where TI does not hold. In addition, it has the
capability of providing the user alternative possible feedbacks that
can be fulfilled. To test the approach, we evaluate a clustering
distance regarding an ideal solution. Experiments demonstrate the
benefits of our approach.

The concept of intelligent agents is—roughly speaking—based on an architecture and a set of behavioral programs that primarily serve to solve problems autonomously.
Increasing the degree of autonomy and improving cognitive performance, which can be assessed using cognitive and behavioral tests, are two important research trends. The degree of autonomy can be increased using higher-level psychological modules with which needs and motives are taken into account. In our approach we integrate these modules in architecture for an embodied, enactive multi-agent system, such that distributed problem solutions can be achieved. Furthermore, after uncovering some weaknesses in the cognitive performance of traditionally designed agents, we focus on two major aspects. On the one hand, the knowledge processing of cognitive agents is based on logical formalisms, which have deficiencies in the representation and processing of incomplete or uncertain knowledge. On the other hand, in order to fully understand the performance of cognitive agents, explanations at the symbolic and subsymbolic levels are required. Both aspects can be addressed by quantum-inspired cognitive agents. To investigate this approach, we consider two tasks in the sphere of Shannon's famous mouse-maze problem: namely classifying target objects and ontology inference. First, the classification of an unknown target object in the mouse-maze, such as cheese, water, and bacon, is based on sensory data that measure characteristics such as odor, color, shape, or nature. For an intelligent agent, we need a classifier with good prediction accuracy and explanatory power on a symbolic level. Boolean logic classifiers do work on a symbolic level but are not adequate for dealing with continuous data. Therefore, we demonstrate and evaluate a quantum-logic-inspired classifier in comparison to Boolean-logic-based classifiers. Second, ontology inference is iteratively achieved by a quantum-inspired agent through maze exploration. This requires the agent to be able to manipulate its own state by performing actions and by collecting sensory data during perception. We suggest an algebraic approach where both kinds of behaviors are uniquely described by quantum operators. The agent's state space is then iteratively constructed by carrying out unitary action operators, while Hermitian perception operators act as observables on quantum eigenstates. As a result, an ontology emerges as the simultaneous solution of the respective eigenvalue equations.
Tags: btuktqiai; btuktcogsys; btukttheseus; btuktqtheseus

Experts and crowds can work together to generate high-quality datasets, but such collaboration is limited to a large-scale pool of data. In other words, training on a large-scale dataset depends more on crowdsourced datasets with aggregated labels than expert intensively checked labels. However, the limited amount of high-quality dataset can be used as an objective test dataset to build a connection between disagreement and aggregated labels. In this paper, we claim that the disagreement behind an aggregated label indicates more semantics (e.g. ambiguity or difficulty) of an instance than just spam or error assessment. We attempt to take advantage of the informativeness of disagreement to assist learning neural networks by computing a series of disagreement measurements and incorporating disagreement with distinct mechanisms. Experiments on two datasets demonstrate that the consideration of disagreement, treating training instances differently, can promisingly result in improved performance.

To enable users to influence clusters of a social network by their external feedback, we present an adaptive clustering-based quantitative weighting approach. Intrinsically, Persons in a social network are connected and their homogeneity is reflected based on the similarity of their attributes. But all attributes do not have the same influence on the network and thus may affect to form the network and compromise the quality of resulting clusters. The introduced weighting approach is completely embedded in logic and has the capability of assigning query weights to atomic conditions in user interaction. Hence, the presented system supports users by offering an intuitive feedback formulation without deeper knowledge of the underlying attributes of objects. Experiments demonstrate the benefits of our approach.

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.

Traditional clustering algorithms like K-medoids and DBSCAN take distances between objects as input and find clusters of objects. Distance functions need to satisfy the triangle inequality (TI) property, but sometimes TI is violated and, thus, may compromise the quality of resulting clusters. However, there are scenarios, for example in the context of social networks, where TI does not hold but a meaningful clustering is still possible. This paper investigates the consequences of TI violation with respect to different traditional clustering techniques and presents instead a clique guided approach to find meaningful clusters. In this paper, we use the quantum logic-based query language (CQQL) to measure the similarity value between objects instead of a distance function. The contribution of this paper is to propose an approach of non-TI clustering in the context of social network scenario.