Author: Klaus Mainzer
Publisher: World Scientific Publishing Company
ISBN: 9789811268533
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 0
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Book Description
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.
Author: Klaus Mainzer
Publisher: World Scientific
ISBN: 981126855X
Category : Mathematics
Languages : en
Pages : 221
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Book Description
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.
Author: Klaus Mainzer
Publisher: Springer Nature
ISBN: 3662682907
Category :
Languages : en
Pages : 167
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Author:
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ISBN:
Category : Mathematics
Languages : en
Pages : 1092
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Book Description
Author: Valery Berthoud
Publisher: Anchor Academic Publishing
ISBN: 3960676948
Category : Philosophy
Languages : en
Pages : 82
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Book Description
The concept of possible worlds is useful because it defines the four modalities – possibility, necessity, contingency, and impossibility – but a challenge lies in defining it. David Lewis’ polemical hypothesis (“genuine modal realism” as it is called) succeeds in it. Lewis’ modal realism stirred controversy because he maintains that a plurality of worlds exists. Some philosophers suggest that the Lewisian view is a violation to the law of parsimony, also known as Ockham’s Razor, i.e. not multiply entities beyond necessity. While avoiding a circular definition, Lewis constructs an inflated ontology. Is it worth it, and if we do not want to assume too many Lewisian worlds, what alternatives remain? Actualist modal realism and modal antirealism are the most relevant alternatives because modal abstentionism simply will not progress in this direction. This study evaluates the theories of possible worlds.
Author: Paul Thagard
Publisher: MIT Press
ISBN: 9780262700481
Category : Philosophy
Languages : en
Pages : 260
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Book Description
By applying research in artificial intelligence to problems in the philosophy of science, Paul Thagard develops an exciting new approach to the study of scientific reasoning. This approach uses computational ideas to shed light on how scientific theories are discovered, evaluated, and used in explanations. Thagard describes a detailed computational model of problem solving and discovery that provides a conceptually rich yet rigorous alternative to accounts of scientific knowledge based on formal logic, and he uses it to illuminate such topics as the nature of concepts, hypothesis formation, analogy, and theory justification.
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Category : American literature
Languages : en
Pages : 2476
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Author: Michael Abraham
Publisher:
ISBN: 9781848900936
Category : Logic
Languages : en
Pages : 296
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Book Description
This book puts forward new logical systems suitable for modelling Talmudic and Biblical reasoning and argumentation. The Talmud is very logical. It is said that when God gave Moses the Ten Commandments, He also gave him additional laws and rules of logic to enable human beings to derive more laws. Together with colleagues the authors have already written 8 books on the logic of the Talmud and the project will involve 15-20 volumes. The authors have discovered principles which can be exported to current research in scientific communities, as well as human common sense reasoning and laws as tackled by religious thinking. Topics in this book include: 1 Non-deductive Inference in the Talmud: The book includes a new topological matrix method for analogical reasoning, completely new to existing AI methods which rely on metric distances. 2 The Textual Inference Rules Klal uPrat. How the Bible Defines Sets: Traditional set theoretic methods for defining sets are either by enumeration of its elements or by a predicate formula. The biblical way is a common sense combination of the two, approximating the set from above and from below by predicates, supplemented by a small number of typical members of the set. 3 Talmudic Deontic Logic: The Talmud has its own Deontic Logic, free of the traditional paradoxes. 4 Temporal Logic in the Talmud: The Talmud allows for special conditionals with antecedents depending on the future and consequents valid in the present. This new type of logic allows for backwards causality and connects with aspects of Quantum Logic. 5 Resolution of Conflicts and Normative Loops in the Talmud: The book deals with Talmudic loop checking methods that can be widely applied to handling loops in AI and logic. 6 Delegation and Representation in Talmudic Logic: Talmudic systems of delegation are innovative and apply to modern day to day computer delegation and access control. This book is of great interest to researchers in AI and Law, in Argumentation theory, and in Pure and Applied logical systems, as well as students of Talmudic reasoning and debate.
Author: Zoran Majkic
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111081672
Category : Computers
Languages : en
Pages : 436
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Book Description
This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory.
Author:
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ISBN:
Category : American literature
Languages : en
Pages : 2280
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Book Description
A world list of books in the English language.
