The Logical Legacy of Nikolai Vasiliev and Modern Logic
The Logical Legacy of Nikolai Vasiliev and Modern Logic

Author: Vladimir Markin

Publisher: Springer

Published: 2017-11-21

Total Pages: 221

ISBN-13: 3319661620

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This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights.

Thinking about Contradictions
Thinking about Contradictions

Author: Venanzio Raspa

Publisher: Springer

Published: 2017-12-04

Total Pages: 176

ISBN-13: 3319660861

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This volume examines the entire logical and philosophical production of Nicolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. This volume will appeal to graduate students and scholars interested not only in Vasil’ev’s work, but also in the history of non-classical logics.

Foundations of Artificial Intelligence and Robotics
Foundations of Artificial Intelligence and Robotics

Author: Wendell H. Chun

Publisher: CRC Press

Published: 2024-12-24

Total Pages: 335

ISBN-13: 1040116167

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Artificial intelligence (AI) is a complicated science that combines philosophy, cognitive psychology, neuroscience, mathematics and logic (logicism), economics, computer science, computability, and software. Meanwhile, robotics is an engineering field that compliments AI. There can be situations where AI can function without a robot (e.g., Turing Test) and robotics without AI (e.g., teleoperation), but in many cases, each technology requires each other to exhibit a complete system: having "smart" robots and AI being able to control its interactions (i.e., effectors) with its environment. This book provides a complete history of computing, AI, and robotics from its early development to state‐of‐the‐art technology, providing a roadmap of these complicated and constantly evolving subjects. Divided into two volumes covering the progress of symbolic logic and the explosion in learning/deep learning in natural language and perception, this first volume investigates the coming together of AI (the mind) and robotics (the body), and discusses the state of AI today. Key Features: Provides a complete overview of the topic of AI, starting with philosophy, psychology, neuroscience, and logicism, and extending to the action of the robots and AI needed for a futuristic society Provides a holistic view of AI, and touches on all the misconceptions and tangents to the technologies through taking a systematic approach Provides a glossary of terms, list of notable people, and extensive references Provides the interconnections and history of the progress of technology for over 100 years as both the hardware (Moore’s Law, GPUs) and software, i.e., generative AI, have advanced Intended as a complete reference, this book is useful to undergraduate and postgraduate students of computing, as well as the general reader. It can also be used as a textbook by course convenors. If you only had one book on AI and robotics, this set would be the first reference to acquire and learn about the theory and practice.

Language, Logic, and Mathematics in Schopenhauer
Language, Logic, and Mathematics in Schopenhauer

Author: Jens Lemanski

Publisher: Springer Nature

Published: 2020-06-08

Total Pages: 318

ISBN-13: 3030330907

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The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

The Road to Universal Logic
The Road to Universal Logic

Author: Arnold Koslow

Publisher: Birkhäuser

Published: 2015-06-10

Total Pages: 607

ISBN-13: 3319153684

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This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

The Many Roots of Medieval Logic
The Many Roots of Medieval Logic

Author: John Marenbon

Publisher: BRILL

Published: 2007

Total Pages: 269

ISBN-13: 9004164871

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The specialized essays in this collection study whether non-Aristotelian traditions of ancient logic had a role for medieval logicians. Special attention is given to Stoic logic and semantics, and to Neoplatonism.

Paraconsistent Logic: Consistency, Contradiction and Negation
Paraconsistent Logic: Consistency, Contradiction and Negation

Author: Walter Carnielli

Publisher: Springer

Published: 2016-06-14

Total Pages: 417

ISBN-13: 3319332058

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This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

Waiting for the End of the World
Waiting for the End of the World

Author: Tsvetelin Stepanov

Publisher: BRILL

Published: 2019-10-21

Total Pages: 382

ISBN-13: 9004409939

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The French president Charles de Gaulle spoke of a Europe “from the Atlantic to the Urals”. Europe was spatially formed with these topographic parameters from the late 10th century onwards, with the massive Christianization of its inhabitants. At that time, however, all three monotheistic religions already had a steady presence there. Could such a macro-space be thought-and-narrated from a macro-perspective, in view of its medieval past? This has already been done through common ʻdenominatorsʻ such as the Migration Period, wars, trade, spread of Christianity. Could it also be seen through a common religious-philosophical and spiritual phenomenon – the Anticipation of the End of the world among Christians, Muslims, and Jews? This book gives a positive answer to the last question.