Many Dimensional Modal Logics

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Multi Dimensional Modal Logic

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Author : Maarten Marx
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Multi Dimensional Modal Logic written by Maarten Marx 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 2012-12-06 with Philosophy categories.

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.

Many Dimensional Modal Logics Theory And Applications

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Author : A. Kurucz
language : en
Publisher: Elsevier
Release Date : 2003-10-21

Many Dimensional Modal Logics Theory And Applications written by A. Kurucz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-21 with Computers categories.

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 Logic

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Author : Yde Venema
language : en
Publisher:
Release Date : 1991

Many Dimensional Modal Logic written by Yde Venema and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Algebra categories.

Many Dimensional Modal Logics

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Author : Dov M. Gabbay
language : en
Publisher: North-Holland
Release Date : 2003

Many Dimensional Modal Logics written by Dov M. Gabbay and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computers categories.

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

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.

Cylindric Like Algebras And Algebraic Logic

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Author : Hajnal Andréka
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-27

Cylindric Like Algebras And Algebraic Logic written by Hajnal Andréka 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 2014-01-27 with Mathematics categories.

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.​

Handbook Of Spatial Logics

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Author : Marco Aiello
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-04

Handbook Of Spatial Logics written by Marco Aiello 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 2007-09-04 with Science categories.

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.

Logic Language Information And Computation

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Author : Alexandra Silva
language : en
Publisher: Springer Nature
Release Date : 2021-10-05

Logic Language Information And Computation written by Alexandra Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-05 with Philosophy categories.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.

Frontiers Of Combining Systems

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Author : Pascal Fontaine
language : en
Publisher: Springer
Release Date : 2013-09-11

Frontiers Of Combining Systems written by Pascal Fontaine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-11 with Computers categories.

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.

Logic And Metalogic

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Author :
language : en
Publisher: PediaPress
Release Date :

Logic And Metalogic written by and has been published by PediaPress this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.