The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth

This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts: worlds and modality essentialism, ontological dependence, and modality modal anti-realism epistemology of modality modality in science modality in logic and mathematics modality in the history of philosophy. Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity. The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.

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.

“Satisfiability (SAT) related topics have attracted researchers from various disciplines: logic, applied areas such as planning, scheduling, operations research and combinatorial optimization, but also theoretical issues on the theme of complexity and much more, they all are connected through SAT. My personal interest in SAT stems from actual solving: The increase in power of modern SAT solvers over the past 15 years has been phenomenal. It has become the key enabling technology in automated verification of both computer hardware and software. Bounded Model Checking (BMC) of computer hardware is now probably the most widely used model checking technique. The counterexamples that it finds are just satisfying instances of a Boolean formula obtained by unwinding to some fixed depth a sequential circuit and its specification in linear temporal logic. Extending model checking to software verification is a much more difficult problem on the frontier of current research. One promising approach for languages like C with finite word-length integers is to use the same idea as in BMC but with a decision procedure for the theory of bit-vectors instead of SAT. All decision procedures for bit-vectors that I am familiar with ultimately make use of a fast SAT solver to handle complex formulas. Decision procedures for more complicated theories, like linear real and integer arithmetic, are also used in program verification. Most of them use powerful SAT solvers in an essential way. Clearly, efficient SAT solving is a key technology for 21st century computer science. I expect this collection of papers on all theoretical and practical aspects of SAT solving will be extremely useful to both students and researchers and will lead to many further advances in the field.”--Edmund Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University, winner of the 2007 A.M. Turing Award)

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial press ure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

This book constitutes the refereed proceedings of the 18th Workshop on Logic, Language, Information and Communication, WoLLIC 2011, held in Philadelphia, PA, USA, in May 2011. The 21 revised full papers presented were carefully reviewed and selected from 35 submissions. Among the topics covered are various aspects of mathematical logic, computer science logics, philosophical logics, such as complexity theory, model theory, partial order, Hoare logics, hybrid logics, Turing machines, etc.

This book consists of seven chapters containing multiple questions of the global socially epistemological situation in science and higher education. Despite the progress of techno-sciences, we are facing blind flaws in leading systems of knowledge and perception. The global era, in a paradox way, connects the new knowledge of economics, postpolitics, postdemocracy, and biopolitical regulation of live and unpresentable forms of the global geo-located violence. Techno-optimism and techno-dictatorship in the twenty-first century coincide with the ideology of market, biopolitics of mandatory satisfaction, religious revivalism, and collapse of higher education. In order for sciences to recover, it is necessary to make a globally epistemological and moral turn toward the truth. The book shows that, when joint desires of the new economics of knowledge and technology erase epistemology (in a way to assign definitions of knowledge and rules and practices of the public usage of the mind), then the time for epistemology is on its way.

This open access book constitutes the proceedings of the proceedings of the 32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2023, held in Prague, Czech Republic, during September 18-21, 2023. The 20 full papers and 5 short papers included in this book together with 5 abstracts of invited talks were carefully reviewed and selected from 43 submissions. They present research on all aspects of the mechanization of reasoning with tableaux and related methods. The papers are organized in the following topical sections: tableau calculi; sequent calculi; theorem proving; non-wellfounded proofs; modal logics; linear logic and MV-algebras; separation logic; and first-order logics.

Essences have been assigned important but controversial explanatory roles in philosophical, scientific, and social theorizing. Is it possible for the same organism to be first a caterpillar and then a butterfly? Is it impossible for a human being to transform into an insect like Gregor Samsa does in Kafka’s The Metamorphosis? Is it impossible for Lot’s wife to survive being turned into a pillar of salt? Traditionally, essences (or natures) have been thought to help answer such central questions about existence, identity, persistence, and modality. These questions are not only of great philosophical interest, they also are of great interest to society at large. This Handbook surveys the state of the art on essence. Core issues about essence are discussed in 33 chapters, all of them written exclusively for this volume by leading experts. They are organized into the following four major parts, each with its own introduction that provides a summary and comparison of the part’s chapters: History Essence and Essentialisms: Themes and Variations Applications Anti-Essentialist Challenges. The volume is accessible enough for students while also providing enough details to make it a valuable reference for researchers. While the notion of essence has been targeted for sustained criticisms since antiquity, recent work has renewed interest in the topic. This Handbook explains and synthesizes much of this current interest, placing essence within its historical context and drawing connections to many contemporary areas of philosophy as well as to scholarly work in other disciplines. With cross-references in each chapter and a comprehensive index, The Routledge Handbook of Essence in Philosophy is a useful resource and essential reading for anyone, whether in or out of academic philosophy, seeking clarification on one of philosophy’s most distinctive and notorious notions.