Many-dimensional modal logics: theory and applications
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier North Holland
2003
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Studies in logic and the foundations of mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Includes bibliographical references (pages 685-723) and index 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: & bull; Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science & bull; Written by internationally leading researchers in the field of pure and applied logic & bull; Combines mathematical theory of modal logic and applications in artificial intelligence and computer science & bull; Numerous open problems for further research & bull; Well illustrated with pictures and tables |
| Beschreibung: | 1 Online-Ressource (xviii, 747 pages) |
| ISBN: | 9780444508263 0444508260 9780080535784 008053578X 1281048518 9781281048516 |
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| 245 | 1 | 0 | |a Many-dimensional modal logics |b theory and applications |c D.M. Gabbay [and others] |
| 250 | |a 1st ed | ||
| 264 | 1 | |a Amsterdam |b Elsevier North Holland |c 2003 | |
| 300 | |a 1 Online-Ressource (xviii, 747 pages) | ||
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| 490 | 1 | |a Studies in logic and the foundations of mathematics |v v. 148 | |
| 500 | |a Includes bibliographical references (pages 685-723) and index | ||
| 500 | |a 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. | ||
| 500 | |a 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. | ||
| 500 | |a 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. | ||
| 500 | |a 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: & bull; Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science & bull; Written by internationally leading researchers in the field of pure and applied logic & bull; Combines mathematical theory of modal logic and applications in artificial intelligence and computer science & bull; Numerous open problems for further research & bull; Well illustrated with pictures and tables | ||
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Datensatz im Suchindex
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| any_adam_object | |
| building | Verbundindex |
| bvnumber | BV042317284 |
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| dewey-full | 160 511.3 |
| dewey-hundreds | 100 - Philosophy & psychology 500 - Natural sciences and mathematics |
| dewey-ones | 160 - Philosophical logic 511 - General principles of mathematics |
| dewey-raw | 160 511.3 |
| dewey-search | 160 511.3 |
| dewey-sort | 3160 |
| dewey-tens | 160 - Philosophical logic 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1st ed |
| format | Electronic eBook |
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| id | DE-604.BV042317284 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444508263 0444508260 9780080535784 008053578X 1281048518 9781281048516 |
| language | English |
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| physical | 1 Online-Ressource (xviii, 747 pages) |
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| series2 | Studies in logic and the foundations of mathematics |
| spelling | Many-dimensional modal logics theory and applications D.M. Gabbay [and others] 1st ed Amsterdam Elsevier North Holland 2003 1 Online-Ressource (xviii, 747 pages) txt rdacontent c rdamedia cr rdacarrier Studies in logic and the foundations of mathematics v. 148 Includes bibliographical references (pages 685-723) and index 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: & bull; Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science & bull; Written by internationally leading researchers in the field of pure and applied logic & bull; Combines mathematical theory of modal logic and applications in artificial intelligence and computer science & bull; Numerous open problems for further research & bull; Well illustrated with pictures and tables PHILOSOPHY / Logic bisacsh Modality (Logic) fast Modale logica gtt Universele algebra gtt Algebraïsche logica gtt Modality (Logic) Modallogik (DE-588)4074914-9 gnd rswk-swf Modallogik (DE-588)4074914-9 s 1\p DE-604 Gabbay, Dov M. Sonstige oth Studies in logic and the foundations of mathematics 148 (DE-604)BV000893472 148 http://www.sciencedirect.com/science/book/9780444508263 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Many-dimensional modal logics theory and applications Studies in logic and the foundations of mathematics PHILOSOPHY / Logic bisacsh Modality (Logic) fast Modale logica gtt Universele algebra gtt Algebraïsche logica gtt Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| subject_GND | (DE-588)4074914-9 |
| title | Many-dimensional modal logics theory and applications |
| title_auth | Many-dimensional modal logics theory and applications |
| title_exact_search | Many-dimensional modal logics theory and applications |
| title_full | Many-dimensional modal logics theory and applications D.M. Gabbay [and others] |
| title_fullStr | Many-dimensional modal logics theory and applications D.M. Gabbay [and others] |
| title_full_unstemmed | Many-dimensional modal logics theory and applications D.M. Gabbay [and others] |
| title_short | Many-dimensional modal logics |
| title_sort | many dimensional modal logics theory and applications |
| title_sub | theory and applications |
| topic | PHILOSOPHY / Logic bisacsh Modality (Logic) fast Modale logica gtt Universele algebra gtt Algebraïsche logica gtt Modality (Logic) Modallogik (DE-588)4074914-9 gnd |
| topic_facet | PHILOSOPHY / Logic Modality (Logic) Modale logica Universele algebra Algebraïsche logica Modallogik |
| url | http://www.sciencedirect.com/science/book/9780444508263 |
| volume_link | (DE-604)BV000893472 |
| work_keys_str_mv | AT gabbaydovm manydimensionalmodallogicstheoryandapplications |