Many Dimensional Modal Logics Theory And Applications

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Many-Dimensional Modal Logics: Theory and Applications

Author : A. Kurucz
Publisher : Elsevier
ISBN 13 : 008053578X
Total Pages : 767 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Many-Dimensional Modal Logics: Theory and Applications by : A. Kurucz

Download or read book Many-Dimensional Modal Logics: Theory and Applications written by A. Kurucz and published by Elsevier. This book was released on 2003-10-21 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Many-dimensional Modal Logics

Author :
Publisher :
ISBN 13 : 9780444508263
Total Pages : 747 pages
Book Rating : 4.5/5 (82 download)

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Book Synopsis Many-dimensional Modal Logics by :

Download or read book Many-dimensional Modal Logics written by and published by . This book was released on 2003 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multi-Dimensional Modal Logic

Author : Maarten Marx
Publisher : Springer Science & Business Media
ISBN 13 : 9401156948
Total Pages : 242 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Multi-Dimensional Modal Logic by : Maarten Marx

Download or read book Multi-Dimensional Modal Logic written by Maarten Marx and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.) This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.

Logic and Its Applications

Author : Kamal Lodaya
Publisher : Springer
ISBN 13 : 3642360394
Total Pages : 267 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Logic and Its Applications by : Kamal Lodaya

Download or read book Logic and Its Applications written by Kamal Lodaya and published by Springer. This book was released on 2012-12-22 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 5th Indian Conference on Logic and Its Applications, ICLA 2013, held in Chennai, India, in January 2013. The 15 revised full papers presented together with 7 invited talks were carefully reviewed and selected from numerous submissions. The papers cover the topics related to pure and applied logic, foundations and philosophy of mathematics and the sciences, set theory, model theory, proof theory, areas of theoretical computer science, artificial intelligence and other disciplines which are of direct interest to mathematical and philosophical logic.

Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9401014531
Total Pages : 311 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics by : Dov M. Gabbay

Download or read book Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.

Nonclassical Logics and Their Applications

Author : Shier Ju
Publisher : Springer Nature
ISBN 13 : 9811513422
Total Pages : 159 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Nonclassical Logics and Their Applications by : Shier Ju

Download or read book Nonclassical Logics and Their Applications written by Shier Ju and published by Springer Nature. This book was released on 2020-01-31 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com

Dynamic Logic. New Trends and Applications

Author : Nina Gierasimczuk
Publisher : Springer Nature
ISBN 13 : 3031517776
Total Pages : 147 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Dynamic Logic. New Trends and Applications by : Nina Gierasimczuk

Download or read book Dynamic Logic. New Trends and Applications written by Nina Gierasimczuk and published by Springer Nature. This book was released on 2024-02-13 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the revised selected papers of the 5th International Workshop on Dynamic Logic. New Trends and Applications, DaLí 2023, held in Tbilisi, Georgia, during September 15–16, 2023. The 8 full papers in this book were carefully reviewed and selected from 10 submissions. They deal with new trends and applications in the area of Dynamic Logic.

Finite Model Theory and Its Applications

Author : Erich Grädel
Publisher : Springer Science & Business Media
ISBN 13 : 3540688048
Total Pages : 440 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Finite Model Theory and Its Applications by : Erich Grädel

Download or read book Finite Model Theory and Its Applications written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.

Handbook of Modal Logic

Author : Patrick Blackburn
Publisher : Elsevier
ISBN 13 : 9780080466668
Total Pages : 1260 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Handbook of Modal Logic by : Patrick Blackburn

Download or read book Handbook of Modal Logic written by Patrick Blackburn and published by Elsevier. This book was released on 2006-11-03 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Patrick Blackburn
Publisher : Cambridge University Press
ISBN 13 : 9780521527149
Total Pages : 574 pages
Book Rating : 4.5/5 (271 download)

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Book Synopsis Modal Logic by : Patrick Blackburn

Download or read book Modal Logic written by Patrick Blackburn and published by Cambridge University Press. This book was released on 2001 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frontiers of Combining Systems

Author : Pascal Fontaine
Publisher : Springer
ISBN 13 : 3642408850
Total Pages : 370 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Frontiers of Combining Systems by : Pascal Fontaine

Download or read book Frontiers of Combining Systems written by Pascal Fontaine and published by Springer. This book was released on 2013-09-11 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Symposium on Frontiers of Combining Systems, FroCoS 2013, held in Nancy, France, in September 2013. The 20 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 33 submissions. FroCoS'13 seeks to offer a common forum for research in the general area of combination, modularization and integration of systems, with emphasis on logic-based ones, and of their practical use. Typical topics of interest include following subjects: combinations of logics such as combined predicate, temporal, modal or epistemic logics, combinations and modularity in ontologies, combination of decision, procedures, of satisfiability, procedures and of constraint solving techniques, combinations and modularity in term rewriting, integration of equational and other theories into deductive systems, combination of deduction systems and computer algebra, integration of data structures into constraint logic programming and deduction, and modularizing programs and specifications.

Natural Deduction, Hybrid Systems and Modal Logics

Author : Andrzej Indrzejczak
Publisher : Springer Science & Business Media
ISBN 13 : 9048187850
Total Pages : 515 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Natural Deduction, Hybrid Systems and Modal Logics by : Andrzej Indrzejczak

Download or read book Natural Deduction, Hybrid Systems and Modal Logics written by Andrzej Indrzejczak and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Logic in Multi-Agent Systems

Author : João Leite
Publisher : Springer Science & Business Media
ISBN 13 : 354028060X
Total Pages : 292 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Computational Logic in Multi-Agent Systems by : João Leite

Download or read book Computational Logic in Multi-Agent Systems written by João Leite and published by Springer Science & Business Media. This book was released on 2005-07-20 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the strictly refereed post-proceedings of the 5th International Workshop on Computational Logic for Multi-Agent Systems, CLIMA V, held in Lisbon, Portugal, in September 2004 as a joint event in federation with the Ninth European Conference on Logics in Artificial Intelligence (JELIA’04) to promote the CLIMA research topics in the broader community of logics in AI. The 16 revised full papers presented were carefully selected from 35 submissions and are devoted to techniques from computational logic for representing, programming, and reasoning about multi-agent systems. The papers are organized in topical sections on foundations, architectures, interaction, and planning and applications.

Frontiers of Combining Systems

Author : Silvio Ghilardi
Publisher : Springer Science & Business Media
ISBN 13 : 364204221X
Total Pages : 392 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Frontiers of Combining Systems by : Silvio Ghilardi

Download or read book Frontiers of Combining Systems written by Silvio Ghilardi and published by Springer Science & Business Media. This book was released on 2009-09-07 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 7th International Symposium of Frontiers of Combining Systems (FroCoS 2009) held during September 16-18, 2009 in Trento, Italy. Previous FroCoS meetings were organized in Munich (1996), Amsterdam (1998), Nancy (2000), Santa Margherita Ligure (2002), - enna (2005), and Liverpool (2007). In 2004, 2006, and 2008 FroCoS joined IJCAR, the International Joint Conference on Automated Reasoning. Like its predecessors, FroCoS 2009 o?ered a forum for the presentation and discussion of research activities on the combination, integration, analysis, m- ularization and interaction of formally de?ned systems, with an emphasis on logic-based ones. These issues are important in many areas of computer science such as logic, computation, program development and veri?cation, arti?cial - telligence, automated reasoning, constraint solving, declarative programming, and symbolic computation. There were 35 submissions to FroCoS 2009. Each submission was reviewed by at least three Program Committee members. After a careful evaluation, the committee decided to accept the 19 papers which are published in this volume. The volume also includes four invited contributions by Alessandro Armando (DIST Genova), Thomas Eiter (TU Wien), Boris Motik (OUCL Oxford), and Ashish Tiwari (SRI Stanford).

Model and Proof Theory of Constructive ALC

Author : Stephan Scheele
Publisher : University of Bamberg Press
ISBN 13 : 3863093208
Total Pages : 348 pages
Book Rating : 4.8/5 (63 download)

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Book Synopsis Model and Proof Theory of Constructive ALC by : Stephan Scheele

Download or read book Model and Proof Theory of Constructive ALC written by Stephan Scheele and published by University of Bamberg Press. This book was released on 2015-07-02 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Spatial Logics

Author : Marco Aiello
Publisher : Springer Science & Business Media
ISBN 13 : 1402055870
Total Pages : 1072 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Spatial Logics by : Marco Aiello

Download or read book Handbook of Spatial Logics written by Marco Aiello and published by Springer Science & Business Media. This book was released on 2007-09-04 with total page 1072 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.

Leo Esakia on Duality in Modal and Intuitionistic Logics

Author : Guram Bezhanishvili
Publisher : Springer
ISBN 13 : 940178860X
Total Pages : 340 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Leo Esakia on Duality in Modal and Intuitionistic Logics by : Guram Bezhanishvili

Download or read book Leo Esakia on Duality in Modal and Intuitionistic Logics written by Guram Bezhanishvili and published by Springer. This book was released on 2014-06-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.