Michael Winter

Rudolf Berghammer, Jules Desharnais, Michael Winter

Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of functions, weaken it to the classes of partial functions, total relations and general relations and also strengthen it to the class of permutations. Then we investigate the class of involutions and the subclass of proper involutions. Finally, we treat idempotent functions, partial idempotent functions and related concepts. We count relations, calculate corresponding probabilities and also calculate the limiting values of the latter in case that the cardinality of $X$ tends to infinity. All these results have been motivated and also supported by numerous experiments performed with the RelView tool.

Aljosha Köcher, Alexander Belyaev, Jesko Hermann et al.

In manufacturing, many use cases of Industry 4.0 require vendor-neutral and machine-readable information models to describe, implement and execute resource functions. Such models have been researched under the terms capabilities and skills. Standardization of such models is required, but currently not available. This paper presents a reference model developed jointly by members of various organizations in a working group of the Plattform Industrie 4.0. This model covers definitions of most important aspects of capabilities and skills. It can be seen as a basis for further standardization efforts.

Felipe S. Abrahão, Hector Zenil, Fabio Porto et al.

When mining large datasets in order to predict new data, limitations of the principles behind statistical machine learning pose a serious challenge not only to the Big Data deluge, but also to the traditional assumptions that data generating processes are biased toward low algorithmic complexity. Even when one assumes an underlying algorithmic-informational bias toward simplicity in finite dataset generators, we show that current approaches to machine learning (including deep learning, or any formal-theoretic hybrid mix of top-down AI and statistical machine learning approaches), can always be deceived, naturally or artificially, by sufficiently large datasets. In particular, we demonstrate that, for every learning algorithm (with or without access to a formal theory), there is a sufficiently large dataset size above which the algorithmic probability of an unpredictable deceiver is an upper bound (up to a multiplicative constant that only depends on the learning algorithm) for the algorithmic probability of any other larger dataset. In other words, very large and complex datasets can deceive learning algorithms into a ``simplicity bubble'' as likely as any other particular non-deceiving dataset. These deceiving datasets guarantee that any prediction effected by the learning algorithm will unpredictably diverge from the high-algorithmic-complexity globally optimal solution while converging toward the low-algorithmic-complexity locally optimal solution, although the latter is deemed a global one by the learning algorithm. We discuss the framework and additional empirical conditions to be met in order to circumvent this deceptive phenomenon, moving away from statistical machine learning towards a stronger type of machine learning based on, and motivated by, the intrinsic power of algorithmic information theory and computability theory.

Michael Winter, Heiko Neumann, Rüdiger Pryss et al.

Process models depict crucial artifacts for organizations regarding documentation, communication, and collaboration. The proper comprehension of such models is essential for an effective application. An important aspect in process model literacy constitutes the question how the information presented in process models is extracted and processed by the human visual system? For such visuospatial tasks, the visual system deploys a set of elemental operations, from whose compositions different visual routines are produced. This paper provides insights from an exploratory eye tracking study, in which visual routines during process model comprehension were contemplated. More specifically, n = 29 participants were asked to comprehend n = 18 process models expressed in the Business Process Model and Notation 2.0 reflecting diverse mappings (i.e., straight, upward, downward) and complexity levels. The performance measures indicated that even less complex process models pose a challenge regarding their comprehension. The upward mapping confronted participants' attention with more challenges, whereas the downward mapping was comprehended more effectively. Based on recorded eye movements, three gaze patterns applied during model comprehension were derived. Thereupon, we defined a general model which identifies visual routines and corresponding elemental operations during process model comprehension. Finally, implications for practice as well as research and directions for future work are discussed in this paper.

Michael Winter, Rüdiger Pryss, Thomas Probst et al.

The comprehension of business process models is crucial for enterprises. Prior research has shown that children as well as adolescents perceive and interpret graphical representations in a different manner compared to grown-ups. To evaluate this, observations in the context of business process models are presented in this paper obtained from a study on visual literacy in cultural education. We demonstrate that adolescents without expertise in process model comprehension are able to correctly interpret business process models expressed in terms of BPMN 2.0. In a comprehensive study, n = 205 learners (i.e., pupils at the age of 15) needed to answer questions related to process models they were confronted with, reflecting different levels of complexity. In addition, process models were created with varying styles of element labels. Study results indicate that an abstract description (i.e., using only alphabetic letters) of process models is understood more easily compared to concrete or pseudo} descriptions. As benchmark, results are compared with the ones of modeling experts (n = 40). Amongst others, study findings suggest using abstract descriptions in order to introduce novices to process modeling notations. With the obtained insights, we highlight that process models can be properly comprehended by novices.

Michael Winter, Rüdiger Pryss, Matthias Fink et al.

Process models constitute crucial artifacts in modern information systems and, hence, the proper comprehension of these models is of utmost importance in the utilization of such systems. Generally, process models are considered from two different perspectives: process modelers and readers. Both perspectives share similarities and differences in the comprehension of process models (e.g., diverse experiences when working with process models). The literature proposed many rules and guidelines to ensure a proper comprehension of process models for both perspectives. As a novel contribution in this context, this paper introduces the Process Model Comprehension Framework (PMCF) as a first step towards the measurement and quantification of the perspectives of process modelers and readers as well as the interaction of both regarding the comprehension of process models. Therefore, the PMCF describes an Evaluation Theory Tree based on the Communication Theory as well as the Conceptual Modeling Quality Framework and considers a total of 96 quality metrics in order to quantify process model comprehension. Furthermore, the PMCF was evaluated in a survey with 131 participants and has been implemented as well as applied successfully in a practical case study including 33 participants. To conclude, the PMCF allows for the identification of pitfalls and provides related information about how to assist process modelers as well as readers in order to foster and enable a proper comprehension of process models.