diplomarbeit

Alexander Heußner
"Semantic Foundation of Digrammatical Modelling Languages — Applying the Pictorial Turn to Conceptual Modelling", Diplomarbeit, University of Leipzig, 2007,
(please see version tag at end of preface for history of minor changes)

abstract

The thesis investigates the applicability of the pictorial turn to diagrammatic conceptual modelling languages. At its heart lies the question how the «semantic» gap between the formal semantics of diagrams and the meaning as intended by the modelling engineer can be bridged. To this end, a pragmatic approach 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 notions of semiotics and semantics as required for the later investigation and formalization of conceptual modelling will be introduced. This will allow for the formalization of pictures as semiotic entities that have a strong cognitive foundation.

Part II will try to approach diagrams with the help of a novel game-based FCA 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 concept 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.

Part II will try to approach diagrams with the help of a novel game-based FCA 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 concept 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.

graphical overview

A more detailed overview of the thesis and the interrelation between the sections is presented in appendix A of the thesis and can here be accessed as either PNG or SVG (inkscape-format).