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This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics. The original results of this book are split into two parts. This division reflects the division of the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators (M(En)) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise:1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators (MK(En)), which can be easily extended onto other frame classes,2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames (MK(En)), MT(En), MD(En), MB(En), MK4(En) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames (MK5(En)), MS5(En). Results of the second type consist of designing concrete deductive (tableau and sequent) systems for standard and non-standard hybrid logics. More precisely, they include:1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule (?D),2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature,3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination. The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic. The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity.

Logic, Symbolic and mathematical.

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Semantics (Philosophy) --- Logic, Symbolic and mathematical.

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Separation logic is the twenty-first-century variant of Hoare logic that permits verification of pointer-manipulating programs. This book covers practical and theoretical aspects of separation logic at a level accessible to beginning graduate students interested in software verification. On the practical side it offers an introduction to verification in Hoare and separation logics, simple case studies for toy languages, and the Verifiable C program logic for the C programming language. On the theoretical side it presents separation algebras as models of separation logics; step-indexed models of higher-order logical features for higher-order programs; indirection theory for constructing step-indexed separation algebras; tree-shares as models for shared ownership; and the semantic construction (and soundness proof) of Verifiable C. In addition, the book covers several aspects of the CompCert verified C compiler, and its connection to foundationally verified software analysis tools. All constructions and proofs are made rigorous and accessible in the Coq developments of the open-source Verified Software Toolchain.

Computer software --- Logic, Symbolic and mathematical. --- Compilers (Computer programs) --- Verification.

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Knowledge, Theory of. --- Logic, Symbolic and mathematical. --- Philosophie.

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The logician Kurt Godel (1906-1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gdel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

Logique mathématique --- Mathématiques --- Logic, Symbolic and mathematical. --- Mathematics --- Philosophie --- Philosophy. --- Gödel, Kurt, --- Logic, symbolic and mathematical --- Philosophy --- Gödel, Kurt --- Logique mathématique. --- Philosophie.