Displaying Modal Logic
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Displaying Modal Logic
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Author : Heinrich Wansing
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Displaying 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 2013-03-14 with Philosophy categories.
The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.
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
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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.
Modal Logic
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Author : Brian F. Chellas
language : en
Publisher: Cambridge University Press
Release Date : 1980-02-29
Modal Logic written by Brian F. Chellas 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 1980-02-29 with Mathematics categories.
A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.
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.
First Steps In Modal Logic
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Author : Sally Popkorn
language : en
Publisher: Cambridge University Press
Release Date : 1994-12-08
First Steps In Modal Logic written by Sally Popkorn 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 1994-12-08 with Mathematics categories.
This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.
Modal Logic As Metaphysics
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Author : Timothy Williamson
language : en
Publisher: Oxford University Press
Release Date : 2013-03-28
Modal Logic As Metaphysics written by Timothy Williamson 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 2013-03-28 with Mathematics categories.
Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.
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.
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.
Temporal Logic And State Systems
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Author : Fred Kröger
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-27
Temporal Logic And State Systems written by Fred Kröger 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 2008-03-27 with Computers categories.
Temporal logic has developed over the last 30 years into a powerful formal setting for the specification and verification of state-based systems. Based on university lectures given by the authors, this book is a comprehensive, concise, uniform, up-to-date presentation of the theory and applications of linear and branching time temporal logic; TLA (Temporal Logic of Actions); automata theoretical connections; model checking; and related theories. All theoretical details and numerous application examples are elaborated carefully and with full formal rigor, and the book will serve as a basic source and reference for lecturers, graduate students and researchers.