Ricardo Caferra - Böcker

On the history of the book: In the early 1990s several new methods and perspectives in au- mated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last ?eld 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 ?eld 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 focuses 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 ?nite model building, are mainly treated in the ?nal chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of di?erent approaches. Howtoreadthisbook: In the introduction we give an overview of automated deduction in a historical context, taking into account its relationship with the human views on formal and informal proofs.

Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is problematic and logic as a topic benefits from a unified approach. Logic for Computer Science and Artificial Intelligence utilizes this format, surveying the tableaux, resolution, Davis and Putnam methods, logic programming, as well as for example unification and subsumption. For non-classical logics, the translation method is detailed.Logic for Computer Science and Artificial Intelligence is the classroom-tested result of several years of teaching at Grenoble INP (Ensimag). It is conceived to allow self-instruction for a beginner with basic knowledge in Mathematics and Computer Science, but is also highly suitable for use in traditional courses. The reader is guided by clearly motivated concepts, introductions, historical remarks, side notes concerning connections with other disciplines, and numerous exercises, complete with detailed solutions, The title provides the reader with the tools needed to arrive naturally at practical implementations of the concepts and techniques discussed, allowing for the design of algorithms to solve problems.

Thisvolumeisacollectionofpapers onautomateddeduction inclassical,modal, and many-valued logics, with an emphasis on rst-order theories. Some authors bridgethe gaptohigher-order logicbydealingwithsimpletype theory ina r- order setting, or by resolving shortcomings of r st-order logic with the help of higher-order notions. Most papers rely on resolution or tableaux methods, with a few exceptions choosing the equational paradigm. In its entirety the volume is a mirror of contemporary research in r st-order theorem proving. One trend to be observed is the interest in e ective decision procedures. The main aim of rs t-order theorem proving was and still is to demonstrate the validity or unsatisa bility of formulas, by more and more - phisticatedmethods. Withinthelastyears,however,theothersideofthemedal{ falsi abilityand satisab ility { has r eceived growing attention. Though in g- eral non-terminating, theorem provers sometimes act as decision procedures on subclasses ofrs t-order logic. Inparticularcases theiroutputcanevenbeused to extract n ite representations of models or counter-examples.Another devel- mentistheextension ofdeductiontechniquesfromclassicallogictomany-valued and modal logics. By suitably generalizing classical concepts many results carry over to non-classical logics. This line of research is stimulated by artici al int- ligence with its need for more expressive logics capable of modeling real-world reasoning. From a formal point of view this volume comprises two types of papers, invited and contributed ones. Gilles Dowek, Melvin Fitting, Deepak Kapur, Alexander Leitsch, and David Plaisted accepted our invitation to present recent developments in and their view of the e ld. Contributed papers on the other hand underwent a two-staged selection process.