Universität Leipzig Fakultät für Mathematik und Informatik Institut für Informatik Johannisgasse 26 04103 Leipzig Semantic Foundation of Diagrammatic Modelling Languages Applying the Pictorial Turn to Conceptual Modelling Diplomarbeit im Studienfach Informatik vorgelegt von cand. inf. Alexander Heußner Leipzig, August 2007 betreuender Hochschullehrer: Prof. Dr. habil. Heinrich Herre Institut für Medizininformatik, Statistik und Epidemologie (I) Härtelstrasse 16–18 04107 Leipzig Abstract The following thesis investigates the applicability of the picto- rial turn to diagrammatic conceptual modelling languages. At its heart lies the question how the “semantic gap” between the for- mal semantics of diagrams and the meaning as intended by the modelling engineer can be bridged. To this end, a pragmatic ap- proach to the domain of diagrams will be followed, starting from pictures as the more general notion. The thesis consists of three parts: In part I, a basic model of cognition will be proposed that is based on the idea of conceptual spaces. Moreover, the most central no- tions of semiotics and semantics as required for the later inves- tigation and formalization of conceptual modelling will be intro- duced. This will allow for the formalization of pictures as semi- otic entities that have a strong cognitive foundation. Part II will try to approach diagrams with the help of a novel game-based F technique. A prototypical modelling attempt will reveal basic shortcomings regarding the underlying formal foundation. It will even become clear that these problems are common to all current conceptualizations of the diagram domain. To circumvent these difficulties, a simple axiomatic model will be proposed that allows to link the findings of part I on conceptual modelling and formal languages with the newly developed con- cept of «abstract logical diagrams». As an outlook, the outline of a categorical model that adjusts the basic lack of a rigorous foundation will be presented. In the final part III, the discussion of conceptual graphs (C) as an example of diagrammatic conceptual modelling languages will demonstrate a pragmatic, hands-on approach to the seman- tic gap. Several alternative semantic foundations of conceptual graphs will be compared, and their relation to the basic ideas of diagrammatic semantics will be elaborated. The thesis concludes with a practical modelling example that reveals the limits of this graphical formalism. After a detailed metaphysical and formal ontological meta-analysis of a simple domain, an extension of C, in the form of conceptual graphs with relators, is proposed that allows to model the example. Nimic nu se explica,˘ nimic nu se dovede¸ste, totul se vede. Emil Cioran [Cioran 2001, p116] Nothing is explicated, nothing is derived, everything can be seen. Preface Over the recent years, the computer science community has become aware of pictorial representations as an important formalism and tool for everyday work. A first indication is the upsurge of diagrams in software engineering and the om- nipresence of U. (There are even attempts to directly translate U into executable code.) But why do software engineers prefer a graphic notion for object-oriented analysis and design? Even before the now ubiquitous semantic technologies entered the focus of soft- ware engineering, knowledge bases have been an integral part of large applications and theoretical research. In the majority of cases, the interface between a human user and the knowledge base has been a formal representation language like F or K. Today, knowledge bases have become reduced to an everyday item for the normal computer user. The simple question arises: How to avoid these formal languages from the stone age of computing, such that an average person, in his role as a do- main expert that completes his personal knowledge acquisition task, can manage a knowledge base without a PhD in logic? Sketches are the real lingua franca of science. They are used to visualize results in publications, explain novel outcomes to fellow researchers or students, and even play an important role in the creative act of drawing conclusions which lead to new results. The question, how to deal with these notions of diagrammatic creativity, especially regarding their opposition to the classical way of publicating in linear text, is still open. Further, an implementation of these creative processes in (software) tools for the scientist or engineer is still far ahead. These first, rather naïve, and hyperbolic approaches to the domain of diagram- matic representation reveal most of the basic demands which antecede this thesis. a practical implementation of diagrammatic techniques require a prior in-depth under- standing of the basic research object, which can be circumscribed as: the application of diagrams in the creative acts of humans and the importance of these diagrams as externalizations of internal mental models. Regarding the following mainly theoretical approach, creative acts will be restricted to conceptual modelling and the entire discussion of the interplay between mental representations and external objects will be limited to the perception of concepts. i Ontogenesis of this Research This thesis can be seen as the agglomerate of a variety of research topics that I en- countered during my course of studies. First and foremost, it combines the mathemat- ical rigour of (theoretical) computer science with the extensiveness of philosophical approaches (following Deleuze, philosophy as “the art of forming, inventing, and fab- ricating concepts”). Conversely, computer science heavily depends on results, ideas, and conceptualizations from other research areas; hence, doing research in computer science is inherently inter-, trans-, and multidisciplinary. This work originated from two fields of research: the ideas of Bildwissenschaft which I encountered as a member of the Scientific Visualization project in Halle/S., and the foundation of conceptual modelling languages with the help of formal ontolo- gies which formed part of my research in the Onto-Med group. I myself prefer sketches and diagrams as a way of approaching scientific research and (software) engineering as well as sharing ideas and explicating the crux of a matter – I am “thinking visually” and my creativity heavily depends on visual repre- sentations be it as an internal mental model or as an externalized diagram. The combination of these three pillars explains my wild enthusiasm for drawing interconnections between a theoretical approach towards pictures, and classical ques- tions of computer science and logic. Further, diagrams will not appear only as re- search objects, but constitute a central paradigm of the following research methodol- ogy. Acknowledgements Writing and science in general is – as is commonly known – a constant switching be- tween eremitic thinking and the discussion of results (not to forget the proofreading). I am indebted to all the people who supported this lifestyle. Above all I will thank the Research Group Onto-Med in Leipzig for supporting my thirst for knowledge in the last semesters of my studies. First and foremost, I am indebted to Heinrich Herre who offered me the chance to write this thesis and supported my investigations beyond the borders of classical computer science with encouragement, help, ideas, criticism, and advice. As representative of my fellow researchers, I will thank Frank Loebe for sharing his expertise in G, especially in relations and roles, as well as his support for the odds and ends of writing a thesis. Further, I am much obliged to Roland Strauß who introduced me to the importance of pictorial presentations and allowed me to make my first research experiences in the Scientific Visualization Project. ii And naturally, I am rejoicing at having a host of proofreaders, critical listeners to new, abstruse ideas, and people that kept my non-thesis activities on life support – or, in a single word, “friends”. Thanks, Dominic, Thorsten, Angelika, Katja, Karin, Kai, Teresa, Christine, Irmi, . ! “The most I can do for a friend is simply be his friend” [H. D. T.] – nevertheless, thank you, Silvio, for your continuous long-distance support and your motivating stimuli especially in the final phase of finishing this thesis. And, both obligatory and frankly, I am deeply indebted to my family for their support and for keeping me grounded. This version of the thesis is indentical to the Diplomarbeit that was submitted in mid August 2007 apart from minor typographic changes and corrections. version tag: 20070820 iii Contents Preface i 0 Introduction 1 0.1 Motivation: The Pictorial Turn in Computer Science ......... 1 0.2 Research Questions ........................... 2 0.3 Outline ................................. 3 0.4 Reading Guide ............................. 4 I Fundamental Notions 1 Cognitive Basics 9 1.1 Philosophical Preliminaries ....................... 9 1.2 Cognition in a Nutshell ......................... 10 1.3 Conceptual Spaces ........................... 11 1.4 Matching Percepts and Concepts .................... 14 1.5 Conceptual Space as Search Space ................... 15 1.6 “Closeness” Revisited .......................... 17 1.7 Conceptual Spaces vs. Image Schemata ∗ ............... 18 1.8 Modelling Perception with the Help of Category Theory ∗∗ ...... 20 1.8.1 Category of Artificial Perceptions ............... 20 1.8.2 Why Category Theory ? .................... 21 2 Semiotics, Semantics, and Semantology 23 2.1 A first Approach to Signs .......................