The Incomputable [[electronic resource] :] : journeys Beyond the Turing Barrier / / ed.: Cooper, S. Barry., Soskova, Mariya I. - 1st ed. 2017. - [S. l. : s. n.]. - X, 292 p. 10 illus. in color. - Б. ц. Зміст: Part I, Challenging Turing: Extended Models of Computation -- Ivan Soskov: A Life in Computability -- Physical Logic -- From Quantum Foundations via Natural Language Meaning to a Theory of Everything -- Part II, The Search for "Natural" Examples of Incomputable Objects -- Some Recent Research Directions in the Computably Enumerable Sets -- Uncomputability and Physical Law -- Algorithmic Economics: Incomputability, Undecidability and Unsolvability in Economics -- Part III, Mind, Matter and Computation -- Is Quantum Physics Relevant for Life? -- Trouble with Computation: A Refutation of Digital Ontology -- Part IV, The Nature of Information: Complexity and Randomness -- Complexity Barriers as Independence -- Quantum Randomness: From Practice to Theory and Back -- Calculus of Cost Functions -- Part V -- The Mathematics of Emergence and Morphogenesis -- Turing’s Theory of Morphogenesis: Where We Started, Where We Are and Where We Want to Go -- Construction Kits for Biological Evolution. Рубрики: Computers. Computer science—Mathematics. Mathematical logic. Theory of Computation. Mathematics of Computing. Mathematical Logic and Foundations. Анотація: This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy. Перейти: https://doi.org/10.1007/978-3-319-43669-2 Дод.точки доступу: Cooper, S. Barry. \ed.\; Soskova, Mariya I. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Gorrieri, Roberto. Process Algebras for Petri Nets [[electronic resource] :] : the Alphabetization of Distributed Systems / / Roberto. Gorrieri ; . - 1st ed. 2017. - [S. l. : s. n.]. - XIII, 302 p. 64 illus., 4 illus. in color. - Б. ц. Зміст: Introduction -- Transition Systems -- Petri Nets -- The Basic Calculus: SFM -- Adding Asynchronous Parallel Composition: CFM and BPP -- Adding Communication and Restriction: FNC -- Adding Multi-party Communication: FNM -- Adding Atomic Tests for Absence: NPL -- Generalizations and Conclusions. Рубрики: Computers. Mathematical logic. Software engineering. Theory of Computation. Mathematical Logic and Foundations. Software Engineering/Programming and Operating Systems. Анотація: This book deals with the problem of finding suitable languages that can represent specific classes of Petri nets, the most studied and widely accepted model for distributed systems. Hence, the contribution of this book amounts to the alphabetization of some classes of distributed systems. The book also suggests the need for a generalization of Turing computability theory. It is important for graduate students and researchers engaged with the concurrent semantics of distributed communicating systems. The author assumes some prior knowledge of formal languages and theoretical computer science. Перейти: https://doi.org/10.1007/978-3-319-55559-1 Дод.точки доступу: Gorrieri, Roberto. \.\; SpringerLink (Online service) Свободных экз. нет |
Logic, Rationality, and Interaction [[electronic resource] :] : 6th International Workshop, LORI 2017, Sapporo, Japan, September 11-14, 2017, Proceedings / / ed.: Baltag, Alexandru., Seligman, Jeremy., Yamada, Tomoyuki. - 1st ed. 2017. - [S. l. : s. n.]. - XII, 694 p. 67 illus. - Б. ц. Зміст: Agency -- Argumentation and Agreement -- Belief Revision and Belief Merging -- Belief Representation -- Cooperation, Decision Making and Planning -- Natural Language -- Philosophy and Philosophical Logic -- Strategic Reasoning. Рубрики: Mathematical logic. Computer science—Mathematics. Computer logic. Mathematical Logic and Formal Languages. Mathematical Logic and Foundations. Discrete Mathematics in Computer Science. Symbolic and Algebraic Manipulation. Logics and Meanings of Programs. Анотація: This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning. . Перейти: https://doi.org/10.1007/978-3-662-55665-8 Дод.точки доступу: Baltag, Alexandru. \ed.\; Seligman, Jeremy. \ed.\; Yamada, Tomoyuki. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Recent Trends in Algebraic Development Techniques [[electronic resource] :] : 23rd IFIP WG 1.3 International Workshop, WADT 2016, Gregynog, UK, September 21–24, 2016, Revised Selected Papers / / ed.: James, Phillip., Roggenbach, Markus. - 1st ed. 2017. - [S. l. : s. n.]. - X, 223 p. 28 illus. - Б. ц. Рубрики: Computer logic. Mathematical logic. Software engineering. Programming languages (Electronic computers). Computer simulation. Logics and Meanings of Programs. Mathematical Logic and Formal Languages. Software Engineering. Programming Languages, Compilers, Interpreters. Simulation and Modeling. Mathematical Logic and Foundations. Анотація: This book constitutes the thoroughly refereed post-conference proceedings of the 23rd IFIP WG 1.3 International Workshop on Algebraic Development Techniques, WADT 2016, held in September 2016 in Gregynog, UK. The 9 revised papers presented together with two invited talks, one invited paper and two survey papers were carefully reviewed and selected from numerous submissions and focus on foundations of algebraic specification; other approaches to formal specification, including process calculi and models of concurrent, distributed and mobile computing; specification languages, methods, and environments; semantics of conceptual modeling methods and techniques; model-driven development; graph transformations, term rewriting and proof systems; integration of formal specification techniques; formal testing and quality assurance, validation, and verification areas, broadly falling into three categories: multimedia content analysis; multimedia signal processing and communications; and multimedia applications and services. Перейти: https://doi.org/10.1007/978-3-319-72044-9 Дод.точки доступу: James, Phillip. \ed.\; Roggenbach, Markus. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Springer Handbook of Model-Based Science [[electronic resource] /] : монография / ed.: Magnani, Lorenzo., Bertolotti, Tommaso. - 1st ed. 2017. - [S. l. : s. n.]. - XXXIX, 1179 p. 263 illus. in color. - Б. ц. Зміст: Theoretical Issues in Models -- Theoretical and Cognitive Issues in Abduction and Scientific Inference -- The Logic of Hypothetical Reasoning, Abduction, and Models -- Model-Based Reasoning in Science and History of Science -- Models in Mathematics -- Model-Based Reasoning in Cognitive Science -- Modeling and Computational Issues -- Models in Physics, Chemistry, and Life Sciences -- Models in Engineering, Architecture, and Economical and Human Sciences. . Рубрики: Computational intelligence. Philosophy and science. Mathematical logic. Physics. Cognitive psychology. Artificial intelligence. Computational Intelligence. Philosophy of Science. Mathematical Logic and Foundations. History and Philosophical Foundations of Physics. Cognitive Psychology. Artificial Intelligence. Анотація: The handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning. It highlights the role of models as mediators between theory and experimentation, and as educational devices, as well as their relevance in testing hypotheses and explanatory functions. The Springer Handbook merges philosophical, cognitive and epistemological perspectives on models with the more practical needs related to the application of this tool across various disciplines and practices. The result is a unique, reliable source of information that guides readers toward an understanding of different aspects of model-based science, such as the theoretical and cognitive nature of models, as well as their practical and logical aspects. The inferential role of models in hypothetical reasoning, abduction and creativity once they are constructed, adopted, and manipulated for different scientific and technological purposes is also discussed. Written by a group of internationally renowned experts in philosophy, the history of science, general epistemology, mathematics, cognitive and computer science, physics and life sciences, as well as engineering, architecture, and economics, this Handbook uses numerous diagrams, schemes and other visual representations to promote a better understanding of the concepts. This also makes it highly accessible to an audience of scholars and students with different scientific backgrounds. All in all, the Springer Handbook of Model-Based Science represents the definitive application-oriented reference guide to the interdisciplinary field of model-based reasoning. Перейти: https://doi.org/10.1007/978-3-319-30526-4 Дод.точки доступу: Magnani, Lorenzo. \ed.\; Bertolotti, Tommaso. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Trillas, Enric. On the Logos: A Naive View on Ordinary Reasoning and Fuzzy Logic [[electronic resource] /] : монография / Enric. Trillas ; . - 1st ed. 2017. - [S. l. : s. n.]. - XIV, 213 p. - Б. ц. Зміст: Introduction -- Meaning as a Quantity -- Antonyms, Negation, and the Fuzzy Case -- ‘And’, and ‘Or’ in Language. The case with Fuzzy Sets -- A First Look at Conditional Statements -- Linguistic Qualification, and Synonymy -- Thinking, Analogy, and Reasoning -- A (Naive) Symbolic Model of Ordinary Reasoning -- A Glance at Analogy -- A Glance at Creative Reasoning -- Formal Reasoning with Precise Words -- Formal Reasoning with Imprecise Words -- A Few Questions on the Reasoning of Quantum Physics -- Questions on Uncertain, Possible, and Probable -- Questions on Domesticating and Controlling Analogy -- Questions on the Classical Schemes of Inference -- Questions on the Fuzzy Schemes of Inference -- Questions on Monotony -- Questions on ‘Not Covered by P’ -- Questions on ‘Sorites’ in Ordinary Reasoning -- A Few Questions on Naming Concepts -- Instead of a Conclusion -- To End Up. . Рубрики: Computational intelligence. Artificial intelligence. Mathematical logic. Cognitive psychology. Logic. Computational Intelligence. Artificial Intelligence. Mathematical Logic and Foundations. Cognitive Psychology. Logic. Анотація: This book offers an inspiring and naive view on language and reasoning. It presents a new approach to ordinary reasoning that follows the author’s former work on fuzzy logic. Starting from a pragmatic scientific view on meaning as a quantity, and the common sense reasoning from a primitive notion of inference, which is shared by both laypeople and experts, the book shows how this can evolve, through the addition of more and more suppositions, into various formal and specialized modes of precise, imprecise, and approximate reasoning. The logos are intended here as a synonym for rationality, which is usually shown by the processes of questioning, guessing, telling, and computing. Written in a discursive style and without too many technicalities, the book presents a number of reflections on the study of reasoning, together with a new perspective on fuzzy logic and Zadeh’s “computing with words” grounded in both language and reasoning. It also highlights some mathematical developments supporting this view. Lastly, it addresses a series of questions aimed at fostering new discussions and future research into this topic. All in all, this book represents an inspiring read for professors and researchers in computer science, and fuzzy logic in particular, as well as for psychologists, linguists and philosophers. Перейти: https://doi.org/10.1007/978-3-319-56053-3 Дод.точки доступу: Trillas, Enric. \.\; SpringerLink (Online service) Свободных экз. нет |
T. Atanassov, Atanassov, Krassimir. Intuitionistic Fuzzy Logics [[electronic resource] /] : монография / Atanassov, Krassimir. T. Atanassov ; . - 1st ed. 2017. - [S. l. : s. n.]. - IX, 138 p. 34 illus. - Б. ц. Зміст: Elements of Intuitionistic Fuzzy Propositional Calculus -- Intuitionistic Fuzzy Predicate Logic -- Intuitionistic Fuzzy Modal Logics -- Temporal and Multidimensional Intuitionistic Fuzzy Logics -- Conclusion. Рубрики: Computational intelligence. Mathematical logic. Artificial intelligence. Operations research. Management science. Computational Intelligence. Mathematical Logic and Foundations. Artificial Intelligence. Operations Research, Management Science. Анотація: The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike. Перейти: https://doi.org/10.1007/978-3-319-48953-7 Дод.точки доступу: T. Atanassov, Krassimir. \.\; SpringerLink (Online service) Свободных экз. нет |
Givant, Steven. Simple Relation Algebras [[electronic resource] /] : монография / Steven. Givant, Andreka, Hajnal. ; . - 1st ed. 2017. - [S. l. : s. n.]. - XXIV, 622 p. 52 illus., 35 illus. in color. - Б. ц. Зміст: Preface -- 1. Rectangular Semiproducts -- 2. Equivalence Semiproducts -- 3. Diagonal Semiproducts -- 4. Semipowers -- 5. Simple Closures -- 6. Quasi-bijective Relation Algebras -- 7. Quotient Relations Algebras and Equijections -- 8. Quotient Semiproducts -- 9. Group and Geometric Quotient Semiproducts -- 10. Insertion Semiproducts -- 11. Two-quasi-bijective Relation Algebras -- A. Relation Algebras -- B. Geometry -- C. Selected Hints to Exercises -- References. Рубрики: Mathematical logic. Algebra. Mathematical Logic and Foundations. Algebra. Анотація: This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017). Перейти: https://doi.org/10.1007/978-3-319-67696-8 Дод.точки доступу: Andreka, Hajnal.; Givant, Steven. \.\; SpringerLink (Online service) Свободных экз. нет |
Feferman on Foundations [[electronic resource] :] : logic, Mathematics, Philosophy / / ed.: Jager, Gerhard., Sieg, Wilfried. - 1st ed. 2017. - [S. l. : s. n.]. - LXXX, 551 p. 4 illus. - Б. ц. Зміст: Tentative TOC Table of contents Introduction: Perspective Feferman: Autobiography I. Mathematical Logic -- Model Theory -- Set Theory -- Proof Theory. - Computability Theory II. Conceptual Expansions . Predicativity -- Unfolding 2 -- Semi-constructive systems III. Axiomatic Foundations -- Explicit Mathematics and Operational Set Theory -- Theories of Truth -- Foundations of Category Theory IV. From Logic to Philosophy -- What is Logic? -- Foundational Ways -- Godel, Minds and Machines -- New Axioms and the Continuum Problem -- Conceptual Structuralism V. Responses Feferman: Bibliography Contributors: Short biographies -- Index. . Рубрики: Mathematical logic. Logic. Mathematical Logic and Foundations. Logic. Mathematical Logic and Formal Languages. Анотація: This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Godel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic. Перейти: https://doi.org/10.1007/978-3-319-63334-3 Дод.точки доступу: Jager, Gerhard. \ed.\; Sieg, Wilfried. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Soifer, Alexander. The Colorado Mathematical Olympiad: The Third Decade and Further Explorations [[electronic resource] :] : from the Mountains of Colorado to the Peaks of Mathematics / / Alexander. Soifer ; . - 1st ed. 2017. - [S. l. : s. n.]. - LII, 259 p. 126 illus., 47 illus. in color. - Б. ц. Зміст: Twenty-First Colorado Mathematical Olympiad: April 16, 2004 -- Twenty-Second Colorado Mathematical Olympiad: April 22, 2005 .-Twenty-Third Colorado Mathematical Olympiad: April 21, 2006 -- Twenty-Fourth Colorado Mathematical Olympiad: April 20, 2007 -- Twenty-Fifth Colorado Mathematical Olympiad: April 18, 2008 .-Twenty-Sixth Colorado Mathematical Olympiad: April 17, 2009 .-Twenty-Seventh Colorado Mathematical Olympiad: April 23, 2010 -- Twenty-Eighth Colorado Mathematical Olympiad: April 22, 2011 -- Twenty-Ninth Colorado Mathematical Olympiad: April 20, 2012 -- Thirtieth Colorado Mathematical Olympiad: April 26, 2013 -- A Round Table Discussion of the Olympiad,or Looking Back from a 30-Year Perspective -- E21. Cover-Up with John Conway, Mitya Karabash, and Ron Graham -- E22. Deep Roots of Uniqueness -- E23. More about Love and Death -- E24. One Amazing Problem and its Connections to Everything: A Conversation in Three Movements -- E25. The Story of One Erdos Problem -- E26. Mark Heim’s Proof -- E27. Coloring Integers – Entertainment of Mathematical Kind -E28. The Erdos Number and Hamiltonian Mysteries -- E29. One Old Erdos–Turan Problem -- E30. Birth of a Problem: The Story of Creation in Seven Stages -- Movement 1. The Colorado Mathematical Olympiad is mathematics; it is sport; it is art. And it is also community, by Matthew Kahle -- Movement 2. I've begun paying off my debt with new kids, by Aaron Parsons -- Movement 3. Aesthetic of Personal Mastery, by Hannah Alpert -- Movement 4. Colorado Mathematical Olympiad: Reminiscences by Robert Ewell. . Рубрики: Number theory. Algebra. Mathematical logic. Geometry. Number Theory. Algebra. Mathematical Logic and Foundations. Geometry. Анотація: Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004–2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to ‘real’ mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems, solutions, and event statistics — it tells a compelling story involving the lives of those who have been part of the Olympiad, their reminiscences of the past and successes of the present. I am almost speechless facing the ingenuity and inventiveness demonstrated in the problems proposed in the third decade of these Olympics. However, equally impressive is the drive and persistence of the originator and living soul of them. It is hard for me to imagine the enthusiasm and commitment needed to work singlehandedly on such an endeavor over several decades. —Branko Grunbaum, University of Washington After decades of hunting for Olympiad problems, and struggling to create Olympiad problems, he has become an extraordinary connoisseur and creator of Olympiad problems. The Olympiad problems were very good, from the beginning, but in the third decade the problems have become extraordinarily good. Every brace of 5 problems is a work of art. The harder individual problems range in quality from brilliant to work-of-genius… The same goes for the “Further Explorations” part of the book. Great mathematics and mathematical questions are immersed in a sauce of fascinating anecdote and reminiscence. If you could have only one book to enjoy while stranded on a desert island, this would be a good choice. —Peter D. Johnson, Jr., Auburn University Like Gauss, Alexander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden, he can transform a dispassionate exercise in logic into a compelling account of sudden insights and ultimate triumph. — Cecil Rousseau Chair, USA Mathematical Olympiad Committee A delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved. —Paul Erdos The book is a gold mine of brilliant reasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on all levels of expertise. —Martin Gardner. Перейти: https://doi.org/10.1007/978-3-319-52861-8 Дод.точки доступу: Soifer, Alexander. \.\; SpringerLink (Online service) Свободных экз. нет |
The Square of Opposition: A Cornerstone of Thought [[electronic resource] /] : монография / ed.: Beziau, Jean-Yves., Basti, Gianfranco. - 1st ed. 2017. - [S. l. : s. n.]. - VI, 337 p. 125 illus., 74 illus. in color. - Б. ц. Зміст: Part I Introduction -- Part II Historical Perspectives on the Square -- Part III Reinterpretations of the Square -- Part IV Philosophical Perspectives on the Square -- Part V Theoretical Investigations on the Square -- Part VI Expansions and Variations of the Square -- Part VII Applications of the Square. Рубрики: Logic. Mathematics—Philosophy. Mathematical logic. Logic. Philosophy of Mathematics. Mathematical Logic and Foundations. Анотація: This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic. Перейти: https://doi.org/10.1007/978-3-319-45062-9 Дод.точки доступу: Beziau, Jean-Yves. \ed.\; Basti, Gianfranco. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Givant, Steven. Advanced Topics in Relation Algebras [[electronic resource] :] : relation Algebras, Volume 2 / / Steven. Givant ; . - 1st ed. 2017. - [S. l. : s. n.]. - XIX, 605 p. - Б. ц. Зміст: Preface -- Introduction -- 14. Canonical Extensions -- 15. Completions -- 16. Representations -- 17. Representation Theorems -- 18. Varieties of Relation Algebras -- 19. Atom Structures -- Epilogue -- References -- Index. . Рубрики: Mathematical logic. Algebra. Mathematical Logic and Foundations. General Algebraic Systems. Анотація: The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research. Building on the foundations established in the preceding Introduction to Relation Algebras, this volume advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators. Arranged in a modular fashion, this text offers the opportunity to explore any of several areas in detail; topics include canonical extensions, completions, representations, varieties, and atom structures. Each chapter offers a complete account of one such avenue of development, including a historical section and substantial number of exercises. The clarity of exposition and comprehensive nature of each module make this an ideal text for the independent reader entering the field, while researchers will value it as a reference for years to come. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. Note that this volume contains numerous, essential references to the previous volume, Introduction to Relation Algebras. The reader is strongly encouraged to secure at least electronic access to the first book in order to make use of the second. . Перейти: https://doi.org/10.1007/978-3-319-65945-9 Дод.точки доступу: Givant, Steven. \.\; SpringerLink (Online service) Свободных экз. нет |
von Plato, Plato, Jan. Saved from the Cellar [[electronic resource] :] : gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics / / Plato, Jan. von Plato ; . - 1st ed. 2017. - [S. l. : s. n.]. - X, 315 p. 9 illus. - Б. ц. Зміст: Part I: A Sketch of Gentzen's Life and Work -- 1. Overture -- 2. Gentzen's years of study -- Dr. Gentzen's arduous years in Nazi Germany -- 4. The scientific accomplishments -- 5. Loose ends -- 6. Gentzen's genuis -- Part II: Overview of the Shorthand Notes -- 1. Gentzen's series of stenographic manuscripts -- 2. The items in this collection -- Practical remarks on the manuscripts -- Manuscript illustrations -- The German alphabet in Latin, Sutterlin, and Fraktur Type -- Bibliography for parts I and II -- Index of names for Parts I and II -- Part III: The Original Writings -- 1. Reduction of number-theoretic problems to predicate logic -- 2. Replacement of functions by predicates -- 3. The formation of abstract concepts -- 4. Five different forms of natural calculi -- 5. Formal conception of correctness in arithmetic I -- 6. Investigations into logical inferences -- 7. Reduction of classical to intuitionistic logic -- 8. CV of the candidate Gerhard Gentzen.-0 9. Letters to Heyting -- 10. Formal conception of correctness in arithmetic II -- 11. Proof theory of number theory -- 12. Consistency of artihmetic, for publication -- 13. Correspondence with Paul Bernays -- 14. Forms of type theory -- 15. Predicate logic -- 16. Propositional logic -- 17. Foundational research in mathematics -- Table of cross-references in the Gentzen papers -- Index of names in the Gentzen papers -- Index of subjects in the Gentzen papers. Рубрики: Mathematics. History. Mathematical logic. History of Mathematical Sciences. Mathematical Logic and Foundations. Анотація: Gerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Godel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a well-developed form, and other times as flashes into the anatomy of the workings of a unique mind. Перейти: https://doi.org/10.1007/978-3-319-42120-9 Дод.точки доступу: von Plato, Jan. \.\; SpringerLink (Online service) Свободных экз. нет |
Sarbadhikari, Haimanti. A Course on Basic Model Theory [[electronic resource] /] : монография / Haimanti. Sarbadhikari, Srivastava, Shashi Mohan. ; . - 1st ed. 2017. - [S. l. : s. n.]. - XIX, 291 p. - Б. ц. Зміст: Chapter 1. Basic Introductory Concepts -- Chapter 2. Basic Introductory Results -- Chapter 3. Spaces of Types -- Chapter 4. Good Structures and Good Theories -- Chapter 5. Morley Categoricity Theorem and Forking Independence -- Chapter 6. Model Theory of Valued Fields. Рубрики: Mathematical logic. Algebraic geometry. Number theory. Mathematical Logic and Foundations. Algebraic Geometry. Number Theory. Анотація: This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work. Перейти: https://doi.org/10.1007/978-981-10-5098-5 Дод.точки доступу: Srivastava, Shashi Mohan.; Sarbadhikari, Haimanti. \.\; SpringerLink (Online service) Свободных экз. нет |
Montagnini, Leone. Harmonies of Disorder [[electronic resource] :] : norbert Wiener: A Mathematician-Philosopher of Our Time / / Leone. Montagnini ; . - 1st ed. 2017. - [S. l. : s. n.]. - XX, 307 p. 1 illus. - Б. ц. Зміст: Introduction -- PART I 1894-1918 -- Chapter 1 – Roots -- Chapter 2 – Education -- Chapter 3 - A young Philosopher -- PART II 1919-1939 -- Chapter 4 - A Mathematician at work -- Chapter 5 - Reflections on Science and Technology -- PART III. 1940-1945 -- Chapter 6 - Military Research Projects -- PART IV - 1946-1964 -- Chapter 7 - After Hiroshima and Nagasaki -- Chapter 8 - The book Cybernetics -- Ch. 9 - After Cybernetics -- Conclusions -- References -- Index of names -- Subject index. Рубрики: Mathematics. History. Physics. Computers. Mathematical logic. Philosophy. Control engineering. Robotics. Mechatronics. History of Mathematical Sciences. History and Philosophical Foundations of Physics. History of Computing. Mathematical Logic and Foundations. Philosophy of Technology. Control, Robotics, Mechatronics. Анотація: This book presents the entire body of thought of Norbert Wiener (1894–1964), knowledge of which is essential if one wishes to understand and correctly interpret the age in which we live. The focus is in particular on the philosophical and sociological aspects of Wiener’s thought, but these aspects are carefully framed within the context of his scientific journey. Important biographical events, including some that were previously unknown, are also highlighted, but while the book has a biographical structure, it is not only a biography. The book is divided into four chronological sections, the first two of which explore Wiener’s development as a philosopher and logician and his brilliant interwar career as a mathematician, supported by his philosophical background. The third section considers his research during World War II, which drew upon his previous scientific work and reflections and led to the birth of cybernetics. Finally, the radical post-war shift in Wiener’s intellectual path is considered, examining how he came to abandon computer science projects and commenced ceaseless public reflections on the new sciences and technologies of information, their social effects, and the need for responsibility in science. . Перейти: https://doi.org/10.1007/978-3-319-50657-9 Дод.точки доступу: Montagnini, Leone. \.\; SpringerLink (Online service) Свободных экз. нет |
Hansson, Sven Ove. Descriptor Revision [[electronic resource] :] : belief Change through Direct Choice / / Sven Ove. Hansson ; . - 1st ed. 2017. - [S. l. : s. n.]. - XVIII, 239 p. 18 illus. - Б. ц. Рубрики: Logic. Mathematical logic. Database management. Epistemology. Logic. Mathematical Logic and Formal Languages. Database Management. Epistemology. Mathematical Logic and Foundations. Анотація: This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. Перейти: https://doi.org/10.1007/978-3-319-53061-1 Дод.точки доступу: Hansson, Sven Ove. \.\; SpringerLink (Online service) Свободных экз. нет |
Halbeisen, Lorenz J. Combinatorial Set Theory [[electronic resource] :] : with a Gentle Introduction to Forcing / / Lorenz J. Halbeisen ; . - 2nd ed. 2017. - [S. l. : s. n.]. - XVI, 594 p. 20 illus. - Б. ц. Зміст: The Setting -- First-Order Logic in a Nutshell -- Axioms of Set Theory -- Overture: Ramsey's Theorem -- Cardinal Relations in ZF Only -- Forms of Choice -- How to Make Two Balls from One -- Models of Set Theory with Atoms -- Thirteen Cardinals and Their Relations -- The Shattering Number Revisited -- Happy Families and Their Relatives -- Coda: A Dual Form of Ramsey’s Theorem -- The Idea of Forcing -- Martin's Axiom -- The Notion of Forcing -- Proving Unprovability -- Models in Which AC Fails -- Combining Forcing Notions -- Models in Which p=c -- Suslin’s Problem -- Properties of Forcing Extensions -- Cohen Forcing Revisited -- Sacks Forcing -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- How Many Ramsey Ultrafilters Exist? -- Combinatorial Properties of Sets of Partitions -- Suite. Рубрики: Mathematical logic. Combinatorics. Mathematical Logic and Foundations. Combinatorics. Анотація: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study. Перейти: https://doi.org/10.1007/978-3-319-60231-8 Дод.точки доступу: Halbeisen, Lorenz J. \.\; SpringerLink (Online service) Свободных экз. нет |
Givant, Steven. Introduction to Relation Algebras [[electronic resource] :] : relation Algebras, Volume 1 / / Steven. Givant ; . - 1st ed. 2017. - [S. l. : s. n.]. - XXXII, 572 p. 25 illus. - Б. ц. Зміст: Preface -- Introduction -- 1. The calculus of relations -- 2. Relation algebras -- 3. Examples of relation algebras -- 4. Arithmetic -- 5. Special elements -- 6. Subalgebras -- 7. Homomorphisms -- 8. Ideals and quotients -- 9. Simple algebras -- 10. Relativizations -- 11. Direct products -- 12. Subdirect products -- 13. Minimal relation algebras -- References -- Index. Рубрики: Mathematical logic. Algebra. Mathematical Logic and Foundations. General Algebraic Systems. Анотація: The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naive set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. Перейти: https://doi.org/10.1007/978-3-319-65235-1 Дод.точки доступу: Givant, Steven. \.\; SpringerLink (Online service) Свободных экз. нет |
The Logical Legacy of Nikolai Vasiliev and Modern Logic [[electronic resource] /] : монография / ed.: Markin, Vladimir., Zaitsev, Dmitry. - 1st ed. 2017. - [S. l. : s. n.]. - VIII, 221 p. 76 illus. - Б. ц. Зміст: Preface. D. Zaitsev, V. Markin -- Chapter 1. Nikolai A. Vasiliev, His Life and Imaginary Logic Legacy. Valentin A. Bazhanov -- Chapter 2. N.A. Vasiliev in the context of philosophical and methodological disputes of the early 20th century. Galina V. Sorina -- Chapter 3. Is Modern Logic Non-Aristotelian? Jean-Yves Beziau -- Chapter 4. Vasiliev and the Foundations of Logic. Otavio Bueno -- Chapter 5. Vasiliev's ideas for non-Aristotelian logics: insight towards paraconsistency. Itala Maria Loffredo D'Ottaviano, Evandro Luls Gomes -- Chapter 6. Epicurus, Vasil’ev and Aristotle on the law of the excluded third. Jose Verissimo Teixeira da Mata -- Chapter 7. Modern Reconstruction of Vasiliev's Logical Systems. Vladimir I. Markin -- Chapter 8. Nikolai Vasiliev's Imaginary Logic and Stable Meaning. Ivan B. Mikirtumov -- Chapter 9. Vasiliev and the Foundations of Logical Laws. Elena D. Smirnova -- Chapter 10. The Impact of N.A. Vasiliev's Imaginary Logic on Epistemic and Relevance Logic. Werner Stelzner -- Chapter 11. Generalized Vasiliev-style Propositions. Dmitry V. Zaitsev -- Chapter 12. Plurivalent Logics. Graham Priest -- Chapter 13. On sublogics in Vasil'ev fragment of the logic definable with A. Arruda's calculus V1. Vladimir M. Popov, Vasily O. Shangin -- Chapter 14. Vasiliev’s Clue to Mourdoukhay-Boltovskoy’s Hypersyllogistic. Vladimir L. Vasyukov -- Chapter 15. Experimenting with consistency. Juliana Bueno-Soler, Walter Carnielli. Рубрики: Epistemology. Mathematical logic. History. Epistemology. Mathematical Logic and Foundations. History of Science. Анотація: 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. Перейти: https://doi.org/10.1007/978-3-319-66162-9 Дод.точки доступу: Markin, Vladimir. \ed.\; Zaitsev, Dmitry. \ed.\; SpringerLink (Online service) Свободных экз. нет |
Craig, William Lane. God and Abstract Objects [[electronic resource] :] : the Coherence of Theism: Aseity / / William Lane. Craig ; . - 1st ed. 2017. - [S. l. : s. n.]. - XV, 540 p. 6 illus. - Б. ц. Зміст: Part 1. The Problematic -- Chapter 1. Introduction -- Chapter 2. Theology Proper and Abstract Objects -- Chapter 3. The Indispensability Argument for Platonism -- Part 2. Realist Solutions -- Chapter 4. Absolute Creationism -- Chapter 5. Non-Platonic Realism -- Part 3. Anti-Realist Solutions -- Chapter 6. Alternative Logics and Semantics -- Chapter 7. Fictionalism -- Chapter 8. Ultima Facie Interpretive Strategies -- Chapter 9. Pretense Theory -- Chapter 10. Neo-Meinongianism -- Chapter 11. Neutralism -- Part 4. Conclusion -- Chapter 12. Concluding Remarks. Рубрики: Religion—Philosophy. Theology. Mathematical logic. Metaphysics. Philosophy of Religion. Christian Theology. Mathematical Logic and Foundations. Metaphysics. Анотація: This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. Перейти: https://doi.org/10.1007/978-3-319-55384-9 Дод.точки доступу: Craig, William Lane. \.\; SpringerLink (Online service) Свободных экз. нет |