This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.

As a consequence of the wide distribution of software and software infrastructure, information security and safety depend on the quality and excellent understanding of its functioning. Only if this functionality is guaranteed as safe, customer and information are protected against adversarial attacks and malfunction. A vast proportion of information exchange is dominated by computer systems. Due to the fact that technical systems are more or less interfaced with software systems, most information exchange is closely related to software and computer systems. Information safety and security of software systems depend on the quality and excellent understanding of its functioning. The last few years have shown a renewed interest in formally specifying and verifying software and its role in engineering methods. Within the last decade, interactive program verifiers have been applied to control software and other critical applications. Software model checking has made strides into industrial applications and a number of research tools for bug detection have been built using automatic program-verification technology. Such solutions are high-level programming methods which provide strategies to ensure information security in complex software systems by automatically verified correctness. Based on the specific needs in applications of software technology, models and formal methods must serve the needs and the quality of advanced software engineering methods. This book provides an in-depth presentation of state-of-the-art topics on how to meet such challenges covering both theoretical foundations and industrial practice.

This volume presents the refereed proceedings from the 14th International Symposium on Static Analysis. The papers address all aspects of static analysis, including abstract domains, abstract interpretation, abstract testing, compiler optimizations, control flow analysis, data flow analysis, model checking, program specialization, security analysis, theoretical analysis frameworks, type-based analysis, and verification systems.

This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics. The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the following ones discuss fundamental issues related to hyper-intensional semantics or develop hyper-intensional frameworks to address issues in modal, epistemic, deontic and action logic. Authors in this volume present original results on logical systems but also extend beyond this by offering philosophical considerations on the topic as well. This volume will appeal to students and researchers in the field of logic.

This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.

This book constitutes the refereed proceedings of the 11th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2008, held in Budapest, Hungary, in March/April 2008 as part of ETAPS 2008, the European Joint Conferences on Theory and Practice of Software. The 33 revised full papers presented together with the abstract of 1 invited talk were carefully reviewed and selected from 124 submissions. A broad variety of theories and methods to support analysis, synthesis, transformation and verification of programs and software systems are addressed, including the following topics: algebraic models, automata and language theory, behavioural equivalences, categorical models, computation processes over discrete and continuous data, infinite state systems, computational structures, logics of programs, modal, spatial, and temporal logics, models of concurrent, reactive, distributed, and mobile systems, process algebras and calculi, semantics of programming languages, software specification and refinement, type systems and type theory, fundamentals of security, semi-structured data, program correctness and verification.

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.

This book constitutes the refereed proceedings of the 4th International Conference on Typed Lambda Calculi and Applications, TLCA'99, held in L'Aquila, Italy in April 1999. The 25 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. Also included are two invited demonstrations. The volume reports research results on various aspects of typed lambda calculi. Among the topics addressed are noncommutative logics, type theory, algebraic data types, logical calculi, abstract data types, and subtyping.