Knowledge Base Verification Using Algebraic Graph Transformations

Memòria presentada per en Gabriel Alejandro Valiente Feruglio per op-tar al grau de Doctor en Informàtica. Dedicated to my mother Helda, to my brothers Willy and Nicky, and specially to my cousin Leo for his immense patience. i Preface Validation, verification and testing of knowledge-based systems has evolved in the last years from isolated, individual efforts to a whole field of active research and development in itself. As such, it differs from conventional software validation and verification not only in the nature of the specific kind of software under study, but also in the methods employed. The techniques used for verification of knowledge-based systems range from early graph-theoretical, static analyses to Petri net-based modeling and simulation and to logic-based analyses. This thesis presents new methods for the verification of knowledge-based systems, that are based on algebraic graph transformations. Both the intuitive appeal of graph transformations as a specification tool for complex problems, as well as the mathematical elegance of the algebraic approach to graph transformation, known as the Berlin school, have first attracted the author and later plugged him into a way of thinking in terms of graphs and graph transformations. This way of thinking has proved to be quite effective in extending current solutions of well-known verification problems, as well as in developing solutions to new verification problems. The purpose of this thesis is then threefold: To share the new verification methods with the research community, to encourage other researchers, from within the field of validation, verification, and testing of knowledge-based systems as well as from other fields of computer science, to step into the fascinating world of algebraic graph transformations, and last, but not least, to fulfill academic requirements to get the PhD degree in Computer Science. iii Acknowledgment The research presented in this thesis arose from an investigation of the application of algebraic graph transformation to the specification of knowledge-based systems, which took place at the Technical University of Berlin during the winter semester of 1991/92. have introduced me to the algebraic approach to graph transformation. Many of the ideas presented in this thesis evolved through discussions with Teszkiewicz have allowed me to give an early lecture entitled Llompart have encouraged further research on the theory and application of algebraic graph transformation, while I was supported by a visitor professor contract. Francesc Rosselló Llompart, Michael Löwe and Andrea Corradini have read previous drafts of this thesis, which …