Modal Logic

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Modal Logic

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Author : Patrick Blackburn
language : en
Publisher: Cambridge University Press
Release Date : 2001

Modal Logic written by Patrick Blackburn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.

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.

Modal Logic

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Author : Nino B. Cocchiarella
language : en
Publisher: Oxford University Press
Release Date : 2008-08-04

Modal Logic written by Nino B. Cocchiarella and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-04 with Philosophy categories.

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.

Handbook Of Modal Logic

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Author : Patrick Blackburn
language : en
Publisher: Elsevier
Release Date : 2006-11-03

Handbook Of Modal Logic written by Patrick Blackburn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-03 with Mathematics categories.

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

Modal Logic

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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2025-01-01

Modal Logic written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Technology & Engineering categories.

Unlock the full potential of modal logic in the context of robotics with Modal Logic, a comprehensive guide that seamlessly integrates complex logical systems with cuttingedge robotics applications. This book is designed for professionals, undergraduate and graduate students, and anyone fascinated by the powerful interplay of logic and robotics. Whether you're looking to advance your career or deepen your understanding, Modal Logic offers invaluable insights at an accessible price. Chapters Brief Overview: 1: Modal Logic: An introduction to the core principles of modal logic, establishing its foundational importance in robotics. 2: Saul Kripke: Examines Kripke's framework for modal logic, key to understanding roboticsrelated logical structures. 3: Intuitionistic Logic: Explores a nonclassical logic essential for designing algorithms with robotics' computational limitations. 4: Philosophical Logic: A discussion on the philosophical aspects that influence robotics, focusing on reasoning and decisionmaking. 5: Löb's theorem: Delve into Löb's theorem and its applications in artificial intelligence systems within robotics. 6: Normal Modal Logic: Covers normal modal logic's role in creating consistent, rational decisionmaking processes for robots. 7: Kripke Semantics: Analyzes Kripke semantics in depth, revealing its applications for modelbuilding in robotics. 8: Admissible Rule: Investigates admissible rules for logical systems, a fundamental tool in robotics' algorithmic development. 9: Accessibility Relation: Discusses the accessibility relation in modal logic and its critical role in robot decisionmaking models. 10: Epistemic Modal Logic: Analyzes epistemic modal logic, which is vital for robots in reasoning about knowledge and belief systems. 11: General Frame: Introduces the concept of general frames in logic, a building block for more advanced robotics algorithms. 12: Łukasiewicz Logic: Examines Łukasiewicz's multivalued logic, offering alternative perspectives to binary systems in robotics. 13: S5 (Modal Logic): Presents the S5 modal logic system, illustrating its practical applications in robotics and AI environments. 14: Interpretation (Logic): Explores logic interpretation methods and their significance in the design of robotic systems. 15: Dynamic Semantics: Provides insight into dynamic semantics, crucial for realtime decisionmaking and robotic adaptability. 16: Standard Translation: Discusses standard translations in logic, highlighting its impact on crossplatform robotic communication. 17: Modal Depth: Explores modal depth's role in providing complexity in logical systems for advanced robotics development. 18: Dynamic Logic (Modal Logic): Focuses on dynamic logic's application in robotics for modeling processes and actions over time. 19: Dynamic Epistemic Logic: Investigates how dynamic epistemic logic supports robots in adapting to changing environments. 20: Timed Propositional Temporal Logic: Introduces timed propositional temporal logic for handling timesensitive robotic tasks. 21: Nonnormal Modal Logic: Concludes with nonnormal modal logic, essential for enhancing the flexibility and reasoning of autonomous robots. This book provides a structured, clear, and indepth look at the concepts that underpin the integration of modal logic in robotics. Its detailed chapter breakdown not only enriches your understanding of robotics' logical foundations but also bridges the gap between theoretical logic and practical robotic applications.

Modal Logic For Philosophers

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Author : James W. Garson
language : en
Publisher: Cambridge University Press
Release Date : 2013-11-25

Modal Logic For Philosophers written by James W. Garson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-25 with Computers categories.

The second edition of an accessible yet technically sound treatment of modal logic and its philosophical applications.

Proof Theory Of Modal Logic

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Author : Heinrich Wansing
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Proof Theory Of Modal Logic written by Heinrich Wansing and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Modal Logic As Metaphysics

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Author : Timothy Williamson
language : en
Publisher: OUP Oxford
Release Date : 2013-03-28

Modal Logic As Metaphysics written by Timothy Williamson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-28 with Philosophy categories.

Are there such things as merely possible people, who would have lived if our ancestors had acted differently? Are there future people, who have not yet been conceived? Questions like those raise deep issues about both the nature of being and its logical relations with contingency and change. In Modal Logic as Metaphysics, Timothy Williamson argues for positive answers to those questions on the basis of an integrated approach to the issues, applying the technical resources of modal logic to provide structural cores for metaphysical theories. He rejects the search for a metaphysically neutral logic as futile. The book contains detailed historical discussion of how the metaphysical issues emerged in the twentieth century development of quantified modal logic, through the work of such figures as Rudolf Carnap, Ruth Barcan Marcus, Arthur Prior, and Saul Kripke. It proposes higher-order modal logic as a new setting in which to resolve such metaphysical questions scientifically, by the construction of systematic logical theories embodying rival answers and their comparison by normal scientific standards. Williamson provides both a rigorous introduction to the technical background needed to understand metaphysical questions in quantified modal logic and an extended argument for controversial, provocative answers to them. He gives original, precise treatments of topics including the relation between logic and metaphysics, the methodology of theory choice in philosophy, the nature of possible worlds and their role in semantics, plural quantification compared to quantification into predicate position, communication across metaphysical disagreement, and problems for truthmaker theory.

Saul Kripke On Modal Logic

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Author : Yale Weiss
language : en
Publisher: Springer Nature
Release Date : 2024-10-02

Saul Kripke On Modal Logic written by Yale Weiss and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-02 with Philosophy categories.

This edited volume brings together papers by both eminent and rising scholars to celebrate Saul Kripke’s singular contributions to modal logic. Kripke’s work on modal logic helped usher in a new semantic epoch for the field and made facility with modal logic indispensable not only to technically oriented philosophers but to theoretical computer scientists and others as well. This volume features previously unpublished work of Kripke’s as well as a brief intellectual biography recounting the story of how Kripke became interested in, and made his first contributions to, modal logic. However, the majority of the volume’s contributions are forward-looking, and produce new philosophical and technical insights by engaging with ideas tracing back to Kripke.

A New Introduction To Modal Logic

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Author : M.J. Cresswell
language : en
Publisher: Routledge
Release Date : 2012-08-06

A New Introduction To Modal Logic written by M.J. Cresswell and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-06 with Philosophy categories.

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic. A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.

Neighborhood Semantics For Modal Logic

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Author : Eric Pacuit
language : en
Publisher: Springer
Release Date : 2017-11-15

Neighborhood Semantics For Modal Logic written by Eric Pacuit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Philosophy categories.

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.