Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification
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Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
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 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.
Grenzen Künstlicher Intelligenz
Die aktuellen Entwicklungen Künstlicher Intelligenz vermitteln den Eindruck grenzenloser Möglichkeiten. Sie strahlen dabei in alle gesellschaftlichen Bereiche aus und bestimmen unsere lebensweltlichen Praxen maßgeblich mit. Wie bei allen großen technologischen Transformationen stellt sich dabei die Frage nach deren zukünftigen Potentialen, umgekehrt aber auch nach ihren prinzipiellen Grenzen. In diesem Spannungsverhältnis kann philosophische Reflexion durch begriffliche Klarheit für Orientierung sorgen und einen (auf-)klärenden Beitrag leisten, welcher dabei hilft ernstzunehmende technische Möglichkeiten von unvernünftigen Spekulationen sinnvoll unterscheiden zu können. Der vorliegende Band trägt damit zu einem übergreifenden Diskurs über die Beurteilung von Möglichkeiten und Grenzen Künstlicher Intelligenz bei.