This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

An introduction to many-sorted logic as an extension of first-order logic.

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.

This work presents a purely classical first-order logical approach to the field of study in theoretical computer science sometimes referred to as the theory of programs, or programming theory. This field essentially attempts to provide a precise mathematical basis for the common activities involved in reasoning about computer programs and programming languages, and it also attempts to find practical applications in the areas of program specification, verification and programming language design. Many different approaches with different mathematical frameworks have been proposed as a basis for programming theory. They differ in the mathe matical machinery they use to define and investigate programs and program properties and they also differ in the concepts they deal with to understand the programming paradigm. Different approaches use different tools and viewpoints to characterize the data environment of programs. Most of the approaches are related to mathe matical logic and they provide their own logic. These logics, however, are very eclectic since they use special entities to reflect a special world of programs, and also, they are usually incomparable with each other. This Babel's mess irritated us and we decided to peel off the eclectic com ponents and try to answer all the questions by using classical first-order logic.

This book constitutes the refereed proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2008, which took place in Doha, Qatar, during November 22-27, 2008. The 45 revised full papers presented together with 3 invited talks were carefully revised and selected from 153 submissions. The papers address all current issues in automated reasoning, computational logic, programming languages and their applications and are organized in topical sections on automata, linear arithmetic, verification knowledge representation, proof theory, quantified constraints, as well as modal and temporal logics.