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.
Contents:
- Philosophical Roots of Temporal Logic:
- The Concept of Time
- Toward Formal Systems of Temporal Logic
- Computational Foundations of Temporal Logic:
- Basic Modal Logic
- Linear-Time Temporal Logic
- Computation Tree Logic
- Full Computation Tree Logic
- Proof-Theoretical Foundations of Temporal Logic:
- Gentzen Calculus and Temporal Logic
- Tableaux-Based Calculus and Temporal Logic
- Automata-Based Calculus and Temporal Logic
- Game-Based Calculus and Temporal Logic
- Dialogue-Based Constructive Temporal Logic
- Applications and Outlook of Temporal Logic:
- Temporal Logic in Artificial Intelligence and Machine Learning
- Temporal Logic in Relativistic Physics
- Temporal Logic in Quantum Computing
- Societal Impact of Temporal Logic
Readership: Researchers and students of mathematical logic and foundations, theoretical computer science, and philosophy. The level is graduate with introductions on the undergraduate level. The book can be used for courses on temporal logic in mathematical logic as well as in computer science. It is also of general interest for the general reader in philosophy, social science (e.g., security issues), and history of science.
Key Features:
- There are already monographs to special fields of temporal logic and calculi
- the first advantage of this book is the connection of proof-theoretical foundations of temporal logic with applications in computer science
- The second advantage is the integration of temporal concepts of modern physics which overcomes the traditional everyday understanding of time which is not sufficient for modern technology
- Thus, a main advantage of the book is its interdisciplinary approach of proof theory, computer science, physics, technology, and philosophy. These are all together very topical issues
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