The tableau methodology, invented in the 1950's by Beth and Hintikka and later perfected by Smullyan and Fitting, is today one of the most popular proof theoretical methodologies. Firstly because it is a very intuitive tool, and secondly because it appears to bring together the proof-theoretical and the semantical approaches to the presentation of a logical system. The increasing demand for improved tableau methods for various logics is mainly prompted by extensive applications of logic in computer science, artificial intelligence and logic programming, as well as its use as a means of conceptual analysis in mathematics, philosophy, linguistics and in the social sciences. In the last few years the renewed interest in the method of analytic tableaux has generated a plethora of new results, in classical as well as non-classical logics. On the one hand, recent advances in tableau-based theorem proving have drawn attention to tableaux as a powerful deduction method for classical first-order logic, in particular for non-clausal formulas accommodating equality. On the other hand, there is a growing need for a diversity of non-classical logics which can serve various applications, and for algorithmic presentations of these logicas in a unifying framework which can support (or suggest) a meaningful semantic interpretation. From this point of view, the methodology of analytic tableaux seems to be most suitable. Therefore, renewed research activity is being devoted to investigating tableau systems for intuitionistic, modal, temporal and many-valued logics, as well as for new families of logics, such as non-monotonic and substructural logics. The results require systematisation. This Handbook isthe first to provide such a systematisation of this expanding field. It contains several chapters on the use of tableaux methods in classical logic, but also contains extensive discussions on: the uses of the methodology in intuitionistic logics modal and temporal logics substructural logics, nonmonotonic and many-valued logics the implementation of semantic tableaux a bibliography on analytic tableaux theorem proving. The result is a solid reference work to be used by students and researchers in Computer Science, Artificial Intelligence, Mathematics, Philosophy, Cognitive Sciences, Legal Studies, Linguistics, Engineering and all the areas, whether theoretical or applied, in which the algorithmic aspects of logical deduction play a role.

This volume contains a selection of revised papers that were presented at the Software Aspects of Robotic Systems, SARS 2011 Workshop and the Machine Learning for System Construction, MLSC 2011 Workshop, held during October 17-18 in Vienna, Austria, under the auspices of the International Symposium Series on Leveraging Applications of Formal Methods, Verification, and Validation, ISoLA. The topics covered by the papers of the SARS and the MLSC workshop demonstrate the breadth and the richness of the respective fields of the two workshops stretching from robot programming to languages and compilation techniques, to real-time and fault tolerance, to dependability, software architectures, computer vision, cognitive robotics, multi-robot-coordination, and simulation to bio-inspired algorithms, and from machine learning for anomaly detection, to model construction in software product lines to classification of web service interfaces. In addition the SARS workshop hosted a special session on the recently launched KOROS project on collaborating robot systems that is borne by a consortium of researchers of the faculties of architecture and planning, computer science, electrical engineering and information technology, and mechanical and industrial engineering at the Vienna University of Technology. The four papers devoted to this session highlight important research directions pursued in this interdisciplinary research project.

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area."

This volume contains the research papers, invited papers, and abstracts of - torials presented at the Second International Conference on Tests and Proofs (TAP 2008) held April 9-11, 2008 in Prato, Italy. TAP was the second conference devoted to the convergence of proofs and tests. It combines ideas from both areasfor the advancement of softwarequality. To provethe correctnessof a programis to demonstrate, through impeccable mathematical techniques, that it has no bugs; to test a programis to run it with the expectation of discovering bugs. On the surface, the two techniques seem contradictory: if you have proved your program, it is fruitless to comb it for bugs; and if you are testing it, that is surely a sign that you have given up on anyhope of proving its correctness.Accordingly, proofs and tests have, since the onset of software engineering research, been pursued by distinct communities using rather di?erent techniques and tools. And yet the development of both approaches leads to the discovery of c- mon issues and to the realization that each may need the other. The emergence of model checking has been one of the ?rst signs that contradiction may yield to complementarity, but in the past few years an increasing number of research e?orts have encountered the need for combining proofs and tests, dropping e- lier dogmatic views of their incompatibility and taking instead the best of what each of these software engineering domains has to o?e

The ultimate goal of program verification is not the theory behind the tools or the tools themselves, but the application of the theory and tools in the software engineering process. Our society relies on the correctness of a vast and growing amount of software. Improving the software engineering process is an important, long-term goal with many steps. Two of those steps are the KeY tool and this KeY book.

This volume constitutes the proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, TABLEAU '95, held at Schloss Rheinfels, St. Goar, Germany in May 1995.
Originally tableau calculi and their relatives were favored primarily as a pedagogical device because of their advantages at the presentation level. The 23 full revised papers in this book bear witness that these methods have now gained fundamental importance in theorem proving, particularly as competitors for resolution methods. The book is organized in sections on extensions, modal logic, intuitionistic logic, the connection method and model elimination, non-clausal proof procedures, linear logic, higher-order logic, and applications"

This book constitutes a self-contained and unified approach to automated reasoning in multiple-valued logics (MVL) developed by the author. Moreover, it contains a virtually complete account of other approaches to automated reasoning in MVL. This is the first overview of this subfield of automated reasoning ever given. Finally, a variety of applications of automated reasoning in MVL including several short case studies are listed. Automated reasoning in non-classical logics is an essential subtask of many AI applications. Applications of MVL in particular include, for instance, hardware and software verification, reasoning with incomplete or inconsistent knowledge, and natural language processing. Therefore, efficient theorem proving methods in MVL are essential. In the historical part of the book it is demonstrated why existing approaches are inadequate. In the original part a simple, but powerful, concept called 'sets-as-signs' is introduced in the context of semantic tableaux, and subsequently is applied to a variety of calculi including resolution and dissolution. It is shown that 'sets-as-signs' yields a many-valued extension of the well-known relationship between classical logic and integer programming. As a consequence, automated reasoning in infinitely-valued logics can be done uniformly and efficiently for the first time.

This book presents reflections on the occasion of 20 years on the KeY project that focuses on deductive software verification.Since the inception of the KeY project two decades ago, the area of deductive verification has evolved considerably. Support for real world programming languages by deductive program verification tools has become prevalent. This required to overcome significant theoretical and technical challenges to support advanced software engineering and programming concepts. The community became more interconnected with a competitive, but friendly and supportive environment. We took the 20-year anniversary of KeY as an opportunity to invite researchers, inside and outside of the project, to contribute to a book capturing some state-of-the-art developments in the field. We received thirteen contributions from recognized experts of the field addressing the latest challenges. The topics of the contributions range from tool development, effciency and usability considerations to novel specification and verification methods. This book should offer the reader an up-to-date impression of the current state of art in deductive verification, and we hope, inspire her to contribute to the field and to join forces. We are looking forward to meeting you at the next conference, to listen to your research talks and the resulting fruitful discussions and collaborations.

Machine learning of software artefacts is an emerging area of interaction between the machine learning and software analysis communities. Increased productivity in software engineering relies on the creation of new adaptive, scalable tools that can analyse large and continuously changing software systems. These require new software analysis techniques based on machine learning, such as learning-based software testing, invariant generation or code synthesis. Machine learning is a powerful paradigm that provides novel approaches to automating the generation of models and other essential software artifacts. This volume originates from a Dagstuhl Seminar entitled "Machine Learning for Dynamic Software Analysis: Potentials and Limits" held in April 2016. The seminar focused on fostering a spirit of collaboration in order to share insights and to expand and strengthen the cross-fertilisation between the machine learning and software analysis communities. The book provides an overview of the machine learning techniques that can be used for software analysis and presents example applications of their use. Besides an introductory chapter, the book is structured into three parts: testing and learning, extension of automata learning, and integrative approaches.

This book constitutes revised lectures from the 11th Symposium on Formal Methods for Components and Object, FMCO 2012, held in Bertinoro, Italy, in September 2012. The 8 lectures featured in this volume are by world-renowned experts within the area of formal models for objects and components. The book provides a unique combination of ideas on software engineering and formal methods which reflect the expanding body of knowledge on modern software systems.

This book is Open Access under a CC BY licence. This book constitutes the proceedings of the 22nd International Conference on Fundamental Approaches to Software Engineering, FASE 2019, which took place in Prague, Czech Republic in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019.The 24 papers presented in this volume were carefully reviewed and selected from 94 submissions. The papers are organized in topical sections named: software verification; model-driven development and model transformation; software evolution and requirements engineering; specification, design, and implementation of particular classes of systems; and software testing.

Static analysis of software with deductive methods is a highly dynamic field of research on the verge of becoming a mainstream technology in software engineering. It consists of a large portfolio of - mostly fully automated - analyses: formal verification, test generation, security analysis, visualization, and debugging. All of them are realized in the state-of-art deductive verification framework KeY. This book is the definitive guide to KeY that lets you explore the full potential of deductive software verification in practice. It contains the complete theory behind KeY for active researchers who want to understand it in depth or use it in their own work. But the book also features fully self-contained chapters on the Java Modeling Language and on Using KeY that require nothing else than familiarity with Java. All other chapters are accessible for graduate students (M.Sc. level and beyond). The KeY framework is free and open software, downloadable from the book companion website which contains also all code examples mentioned in this book.