Automated Model Building

Preface On the history of the book: In the early 1990s several new methods and perspectives in automated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last field which brought the authors of this book together. In 1994 they met at the Conference on Automated Deduction (CADE-12) in Nancy and agreed upon the general point of view, that semantics and, in particular, construction of models should play a central role in the field of automated deduction. In the following years the deduction groups of the laboratory LEIBNIZ at IMAG Grenoble and the University of Technology in Vienna organized several bilateral projects promoting this topic. This book emerged as a main result of this cooperation. The authors are aware of the fact, that the book does not cover all relevant methods of automated model building (also called model construction or model generation); instead the book focusses on deduction-based symbolic methods for the construction of Herbrand models developed in the last 12 years. Other methods of automated model building, in particular also finite model building, are mainly treated in the final chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of different approaches. The chapters 3 (resolution based methods) and 4 (constraint-based methods), which are largely based on former scientific work of the authors, can be considered as the core of the book; they depend on each other and should be read in this order. Chapter 2 (preliminaries), which should be read by need only, gives the basic concepts and makes the book accessible to graduate students without a firm background in first-order logic and automated deduction. Chapter 5 (on model representation and evaluation) essentially depends on the chapters 3 and 4. Chapter 6 on finite model building in largely independent of the former chapters and gives a broader view on the topic as a whole. 2 Acknowledgments We would like to thank Chris Fermüller for several substantial and fruitful discussions in the early stage of the book; important parts of the book are based on his research carried out together with one of the authors. Our special thanks go to Joseph Goguen for his encouragement and his constructive criticism; his remarks on the history, the general methodology and the philosophical background helped to improve the conceptual level …