Temporal logic: from philosophy and proof theory to artificial intelligence and quantum computing
"Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ
World Scientific Publishing Co. Pte. Ltd.
[2023]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science. The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy"-- |
| Beschreibung: | xii, 208 Seiten Illustrationen 24 cm |
| ISBN: | 9789811268533 |
Internformat
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| 520 | 3 | |a "Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science. The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy"-- | |
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Datensatz im Suchindex
| _version_ | 1804186144582139904 |
|---|---|
| adam_text | Contents Preface v About the Authors 1. 2. 3. ix Philosophical Roots of Temporal Logic 1 1.1 The Concept of Time.................................................... 1.2 Toward Formal Systems of Temporal Logic................ 1 8 Computational Foundations of Temporal Logic 27 2.1 2.2 2.3 2.4 29 32 36 41 Basic Modal Logic........................................................... Linear-Time Temporal Logic........................................ Computation Tree Logic .............................................. Full Computation Tree Logic........................................ Proof-Theoretical Foundations of Temporal Logic 3.1 3.2 3.3 3.4 3.5 45 Gentzen Calculus and Temporal Logic............................. 46 Tableaux-Based Calculus and Temporal Logic .... 67 Automata-Based Calculus and Temporal Logic .... 77 Game-Based Calculus and Temporal Logic............... 84 Dialogue-Based Constructive Temporal Logic............ 95 xi
xii 4. Temporal Logic: From Philosophy and Proof Theory Applications and Outlook of Temporal Logic 111 4.1 Temporal Logic in Artificial Intelligence and Machine Learning.................................................... Ill 4.2 Temporal Logic in Relativistic Physics ....................... 131 4.3 Temporal Logic in Quantum Computing.................... 152 4.4 Societal Impact of Temporal Logic................................ 180 References 191 Index 201
|
| adam_txt |
Contents Preface v About the Authors 1. 2. 3. ' ix Philosophical Roots of Temporal Logic 1 1.1 The Concept of Time. 1.2 Toward Formal Systems of Temporal Logic. 1 8 Computational Foundations of Temporal Logic 27 2.1 2.2 2.3 2.4 29 32 36 41 Basic Modal Logic. Linear-Time Temporal Logic. Computation Tree Logic . Full Computation Tree Logic. Proof-Theoretical Foundations of Temporal Logic 3.1 3.2 3.3 3.4 3.5 45 Gentzen Calculus and Temporal Logic. 46 Tableaux-Based Calculus and Temporal Logic . 67 Automata-Based Calculus and Temporal Logic . 77 Game-Based Calculus and Temporal Logic. 84 Dialogue-Based Constructive Temporal Logic. 95 xi
xii 4. Temporal Logic: From Philosophy and Proof Theory Applications and Outlook of Temporal Logic 111 4.1 Temporal Logic in Artificial Intelligence and Machine Learning. Ill 4.2 Temporal Logic in Relativistic Physics . 131 4.3 Temporal Logic in Quantum Computing. 152 4.4 Societal Impact of Temporal Logic. 180 References 191 Index 201 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Centrone, Stefania 1975- Mainzer, Klaus 1947- |
| author_GND | (DE-588)1024682536 (DE-588)120140071 |
| author_facet | Centrone, Stefania 1975- Mainzer, Klaus 1947- |
| author_role | aut aut |
| author_sort | Centrone, Stefania 1975- |
| author_variant | s c sc k m km |
| building | Verbundindex |
| bvnumber | BV049414588 |
| classification_rvk | SK 130 |
| classification_tum | DAT 700 DAT 503 |
| ctrlnum | (OCoLC)1407831995 (DE-599)BVBBV049414588 |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| isbn | 9789811268533 |
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| spelling | Centrone, Stefania 1975- Verfasser (DE-588)1024682536 aut Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing Stefania Centrone, Klaus Mainzer (Technical University of Munich, Germany) Singapore ; Hackensack, NJ World Scientific Publishing Co. Pte. Ltd. [2023] © 2023 xii, 208 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier "Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators. Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science. The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy"-- Quantencomputer (DE-588)4533372-5 gnd rswk-swf Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Temporale Logik (DE-588)4137542-7 gnd rswk-swf Temporal automata Logic, Symbolic and mathematical Automates temporels Logique symbolique et mathématique Temporale Logik (DE-588)4137542-7 s Künstliche Intelligenz (DE-588)4033447-8 s Maschinelles Lernen (DE-588)4193754-5 s Quantencomputer (DE-588)4533372-5 s DE-604 Mainzer, Klaus 1947- Verfasser (DE-588)120140071 aut Erscheint auch als Online-Ausgabe 9789811268540 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034741581&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Centrone, Stefania 1975- Mainzer, Klaus 1947- Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing Quantencomputer (DE-588)4533372-5 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Temporale Logik (DE-588)4137542-7 gnd |
| subject_GND | (DE-588)4533372-5 (DE-588)4033447-8 (DE-588)4193754-5 (DE-588)4137542-7 |
| title | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing |
| title_auth | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing |
| title_exact_search | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing |
| title_exact_search_txtP | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing |
| title_full | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing Stefania Centrone, Klaus Mainzer (Technical University of Munich, Germany) |
| title_fullStr | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing Stefania Centrone, Klaus Mainzer (Technical University of Munich, Germany) |
| title_full_unstemmed | Temporal logic from philosophy and proof theory to artificial intelligence and quantum computing Stefania Centrone, Klaus Mainzer (Technical University of Munich, Germany) |
| title_short | Temporal logic |
| title_sort | temporal logic from philosophy and proof theory to artificial intelligence and quantum computing |
| title_sub | from philosophy and proof theory to artificial intelligence and quantum computing |
| topic | Quantencomputer (DE-588)4533372-5 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Temporale Logik (DE-588)4137542-7 gnd |
| topic_facet | Quantencomputer Künstliche Intelligenz Maschinelles Lernen Temporale Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034741581&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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