Tools And Techniques In Modal Logic
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Tools and Techniques in Modal Logic
Author | : M. Kracht |
Publisher | : North Holland |
Total Pages | : 584 |
Release | : 1999-06-17 |
Genre | : Computers |
ISBN | : |
This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.
Handbook of Modal Logic
Author | : Patrick Blackburn |
Publisher | : Elsevier |
Total Pages | : 1260 |
Release | : 2006-11-03 |
Genre | : Mathematics |
ISBN | : 9780080466668 |
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
Natural Deduction, Hybrid Systems and Modal Logics
Author | : Andrzej Indrzejczak |
Publisher | : Springer Science & Business Media |
Total Pages | : 515 |
Release | : 2010-07-03 |
Genre | : Philosophy |
ISBN | : 9048187850 |
This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
Modal Logic
Author | : Patrick Blackburn |
Publisher | : Cambridge University Press |
Total Pages | : 574 |
Release | : 2002-08-22 |
Genre | : Computers |
ISBN | : 1316101959 |
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 Logics and Philosophy, Second Edition
Author | : Rod Girle |
Publisher | : McGill-Queen's Press - MQUP |
Total Pages | : 248 |
Release | : 2017-01-01 |
Genre | : Philosophy |
ISBN | : 0773550755 |
The new edition of this widely used and respected textbook includes three new chapters on conditional logic. Other chapters have been revised and updated, making the second edition a fully comprehensive introduction to modal logics and their application. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, Modal Logics and Philosophy focuses on showing how useful modal logic can be as a tool for formal philosophical analysis. In Part 1, the reader is introduced to some standard systems of modal logic and provided with a series of exercises that encourage proficiency in manipulating these logics. Girle emphasizes possible world semantics for modal logics and its formal method, Jeffrey-style truth-trees, in which standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, and obligation and permission.
Modal Logic
Author | : Brian F. Chellas |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 1980-02-29 |
Genre | : Mathematics |
ISBN | : 9780521295154 |
An introductory textbook on modal logic the logic of necessity and possibility.
Proof Theory of Modal Logic
Author | : Heinrich Wansing |
Publisher | : Springer Science & Business Media |
Total Pages | : 317 |
Release | : 2013-06-29 |
Genre | : Philosophy |
ISBN | : 9401727988 |
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 Logics and Philosophy
Author | : Rod Girle |
Publisher | : Routledge |
Total Pages | : 248 |
Release | : 2009 |
Genre | : Philosophy |
ISBN | : 9781844652082 |
Offers a comprehensive introduction to modal logics and their application suitable for course use. This book places its emphasis on showing how useful modal logic can be as a tool for formal philosophical analysis. It explores the applications of modal logic to philosophical issues such as truth, time, processes, and knowledge and belief.
Many-Dimensional Modal Logics: Theory and Applications
Author | : A. Kurucz |
Publisher | : Elsevier |
Total Pages | : 767 |
Release | : 2003-10-21 |
Genre | : Computers |
ISBN | : 008053578X |
Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables