Mathematical logic Books
Cambridge University Press Topological Duality for Distributive Lattices
Book SynopsisThis introduction to StonePriestley duality theory brings modern tools in the area together in textbook format for the first time and covers applications to logic and theoretical computer science. This book is for undergraduates, graduate students, and researchers in lattice theory, algebra, topology, logic, and theoretical computer science.
£64.99
Cambridge University Press Equivalents of the Riemann Hypothesis Volume 3 Further Steps towards Resolving the Riemann Hypothesis
Book SynopsisThis three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.Table of Contents1. Nicolas' π(x) < li(θ(x)) equivalence; 2. Nicolas' number of divisors function equivalence; 3. An aspect of the zeta function zero gap estimates; 4. The Rogers–Tao equivalence; 5. The Dirichlet series of Dobner; 6. An upper bound for the deBruijn–Newman constant; 7. The Pólya–Jensen equivalence; 8. Ono et al. and Jensen polynomials; 9. Gonek–Bagchi universality and Bagchi's equivalence; 10. A selection of undecidable propositions; 11. Equivalences and decidability for Riemann's zeta; A. Imports for Gonek's theorems; B. Imports for Nicolas' theorems; C. Hyperbolic polynomials; D. Absolute continuity; E. Montel and Hurwitz's theorems; F. Markov and Gronwall's inequalities; G. Characterizing Riemann's zeta function; H. Bohr's theorem; I. Zeta and L-functions; J. de Reyna's expansion for the Hardy contour; K. Stirling's approximation for the gamma function; L. Propositional calculus $\mathscr{P}_0$; M. First order predicate calculus $\mathscr{P}_1$; N. Recursive functions; O. Ordinal numbers and analysis; References; Index
£999.99
Cambridge University Press Philosophical Uses of Categoricity Arguments
Book SynopsisThis Element addresses the categoricity arguments that have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.Table of Contents1. Introduction; 2. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 3. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 4. Kreisel in 'Informal rigor and incompleteness proofs' (1967) and 'Two notes on the foundations of set theory'(1969); 5. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 6. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 7. Conclusion; References.
£58.12
Cambridge University Press Polygraphs From Rewriting to Higher Categories
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£85.50
LEGARE STREET PR The Cloud of Unknowing
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£13.95
LEGARE STREET PR An Investigation Of The Laws Of Thought On Which Are Founded The Mathematical Theories Of Logic And Probabilities
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£28.45
LEGARE STREET PR An Investigation Of The Laws Of Thought On Which Are Founded The Mathematical Theories Of Logic And Probabilities
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£19.90
LEGARE STREET PR The The Elements of Logic
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£25.60
Legare Street Press Outline of the Laws of Thought
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£28.45
LEGARE STREET PR Treatise
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£25.60
Legare Street Press A A Letter to Augustus De Morgan
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£21.80
Cambridge University Press Descriptive Complexity Canonisation and Definable Graph Structure Theory 47 Lecture Notes in Logic Series Number 47
Book SynopsisThis groundbreaking, yet accessible book contains original results on the interaction between graph theory and computational complexity using methods from finite model theory. As well as a wealth of new, previously unpublished results, the author also gives an account of the established results in the area.Trade Review'The book is divided evenly into two parts. Part I gives background and definitions of the main notions, and makes the book self-contained. Many results from descriptive complexity theory, and the author's earlier results, are clearly presented. Part II is devoted to the main theorem about graphs with excluded minors. The book ends with a symbol index and an index.' Pascal Michel, Mathematical ReviewsTable of Contents1. Introduction; Part I. The Basic Theory: 2. Background from graph theory and logic; 3. Descriptive complexity; 4. Treelike decompositions; 5. Definable decompositions; 6. Graphs of bounded tree width; 7. Ordered treelike decompositions; 8. 3-Connected components; 9. Graphs embeddable in a surface; Part II. Definable Decompositions of Graphs with Excluded Minors: 10. Quasi-4-connected components; 11. K5-minor free graphs; 12. Completions of pre-decompositions; 13. Almost planar graphs; 14. Almost planar completions; 15. Almost embeddable graphs; 16. Decompositions of almost embeddable graphs; 17. Graphs with excluded minors; 18. Bits and pieces; Appendix. Robertson and Seymour's version of the local structure theorem; References; Symbol index; Index.
£155.00
Springer International Publishing AG Combinatorial Set Theory: With a Gentle Introduction to Forcing
Book SynopsisThis 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.Trade Review“Each chapter ends with Notes that often add historical information, offer further remarks on the chapter’s contents … . Halbheisen’s Combinatorial Set Theory is an excellent source for the intermediate or advanced student of set theory … Because of its wealth of material, it should also serve as an excellent resource for those designing advanced courses or searching for seminar assignments for students.” (J. M. Plotkin, zbMATH 06755662, 2018)Table of ContentsThe 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.
£999.99
Creative Media Partners, LLC Lectures On the Logic of Arithmetic
£16.20
Creative Media Partners, LLC The SETL Project Master Catalog. A Comprehensive Listing of Reports Working Papers and Computer Readable Document and Program Files Pertaining to Work at NYU on the SETL Settheoretic Programming Language
£21.80
Creative Media Partners, LLC The SETL Project Master Catalog. A Comprehensive Listing of Reports Working Papers and Computer Readable Document and Program Files Pertaining to Work at NYU on the SETL Settheoretic Programming Language
£13.22
Creative Media Partners, LLC Studies on the Logic of Automatic Computation
£22.75
Creative Media Partners, LLC Polymorphic Type Inference and Semiunification
£22.75
Creative Media Partners, LLC A Hierarchical Technique for Mechanical Theorem Proving and its Application to Programming Language Design
£13.95
Creative Media Partners, LLC Specimen Logicae Universaliter Demonstratae
£999.99
Creative Media Partners, LLC Automating Security Protocol Analysis
£22.75
Creative Media Partners, LLC Automating Security Protocol Analysis
£14.96
Creative Media Partners, LLC An Application of Automated Theorem Provers to Computer System Security
£22.75
Creative Media Partners, LLC An Application of Automated Theorem Provers to Computer System Security
£14.96
Creative Media Partners, LLC Generating Test Templates via Automated Theorem Proving
£22.75
Creative Media Partners, LLC Generating Test Templates via Automated Theorem Proving
£14.09
McGraw-Hill Education - Europe Schaums Outline of Boolean Algebra and Switching
Book SynopsisConfusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.Table of ContentsThe Algebra of LogicThe Algebra of SetsBoolean AlgebrasSwitching Circuits and Logic CircuitsTopics in the Theory of Boolean AlgebrasAppendix
£23.39
Cambridge University Press The Joy of Abstraction
Book SynopsisJourney through the world of abstract mathematics into category theory with popular science author Eugenia Cheng. Featuring humanizing examples and demystification of mathematical thought processes, this book is for fans of How to Bake Pi who want to dig deeper into mathematical concepts and build their mathematical background.Trade Review'This book is an educational tour de force that presents mathematical thinking as a right-brained activity. Most 'left brain/right brain' education-talk is at best a crude metaphor; but by putting the main focus on the process of (mathematical) abstraction, Eugenia Cheng supplies the reader (whatever their 'brain-type') with the mental tools to make that distinction precise and potentially useful. The book takes the reader along in small steps; but make no mistake, this is a major intellectual journey. Starting not with numbers, but everyday experiences, it develops what is regarded as a very advanced branch of abstract mathematics (category theory, though Cheng really uses this as a proxy for mathematical thinking generally). This is not watered-down math; it's the real thing. And it challenges the reader to think-deeply at times. We 'left-brainers' can learn plenty from it too.' Keith Devlin, Stanford University (Emeritus), author of The Joy of Sets'Eugenia Cheng loves mathematics—not the ordinary sort that most people encounter, but the most abstract sort that she calls 'the mathematics of mathematics.' And in this lovely excursion through her abstract world of Category Theory, she aims to give those who are willing to join her a glimpse of that world. The journey will change how they view mathematics. Cheng is a brilliant writer, with prose that feels like poetry. Her contagious enthusiasm makes her the perfect guide.' John Ewing, President, Math for America'Eugenia Cheng's singular contribution is in making abstract mathematics relevant to all through her great ingenuity in developing novel connections between logic and life. Her latest book, The Joy of Abstraction, provides a long awaited fully rigorous yet gentle introduction to the 'mathematics of mathematics,' allowing anyone to experience the joy of learning to think categorically.' Emily Riehl, Johns Hopkins University, author of Category Theory in Context'Archimedes is quoted as having said once: 'Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.' In this fascinating book, Eugenia Cheng approaches the abstract mathematical area of Category Theory with pure love, to reveal its beauty to anybody interested in learning something about contemporary mathematics.' Mario Livio, astrophysicist, author of The Golden Ratio and Brilliant Blunders'Eugenia Cheng's latest book will appeal to a remarkably broad and diverse audience, from non-mathematicians who would like to get a sense of what mathematics is really about, to experienced mathematicians who are not category theorists but would like a basic understanding of category theory. Speaking as one of the latter, I found it a real pleasure to be able to read the book without constantly having to stop and puzzle over the details. I have learnt a lot from it already, including what the famous Yoneda lemma is all about, and I look forward to learning more from it in the future.' Sir Timothy Gowers, Collège de France, Fields Medalist, main editor of The Princeton Companion to Mathematics'At last: a book that makes category theory as simple as it really is. Cheng explains the subject in a clear and friendly way, in detail, not relying on material that only mathematics majors learn. Category theory – indeed, mathematics as a whole – has been waiting for a book like this.' John Baez, University of California, Riverside'Many people speak derisively of category theory as the most abstract area of mathematics, but Eugenia Cheng succeeds in redeeming the word 'abstract'. This book is loquacious, conversational, and inviting. Reading this book convinced me I could teach category theory as an introductory course, and that is a real marvel, since it is a subject most people leave for experts.' Francis Su, Harvey Mudd College, author of Mathematics for Human Flourishing'Finally, a book about category theory that doesn't assume you already know category theory! In this inviting but rigorous introduction to what she calls 'the mathematics of mathematics', Eugenia Cheng brings the subject to us with insight, wit, and a point of view. Her story of finding joy-and advantage-in abstraction will inspire you to find it, too.' Patrick Honner, award-winning high school math teacher, columnist for Quanta Magazine, author of Painless Statistics'This higher category theory is the mathematics of the twenty-first century (at least my corner of it). If you'd like a taste of it, I recommend Dr. Cheng's book. The first half is an accessible and thought-provoking insight into categorical thinking. The second half climbs into the rarified air of theoretic math, but it is worth a read to get a feel for what some parts of modern mathematics look like.' Jonathan Kujawa, 3 Quarks Daily'… a successful addition to the literature that I am sure students will use in the future and I would be happy to recommend.' Constanze Roitzheim, Mathematische SemesterberichteTable of ContentsPrologue; Part I. Building Up to Categories: 1. Categories: the idea; 2. Abstraction; 3. Patterns; 4. Context; 5. Relationships; 6. Formalism; 7. Equivalence relations; 8. Categories: the definition; Interlude: A Tour of Math: 9. Examples we've already seen, secretly; 10. Ordered sets; 11. Small mathematical structures; 12. Sets and functions; 13. Large worlds of mathematical structures; Part II. Doing Category Theory: 14. Isomorphisms; 15. Monics and epics; 16. Universal properties; 17. Duality; 18. Products and coproducts; 19. Pullbacks and pushouts; 20. Functors; 21. Categories of categories; 22. Natural transformations; 23. Yoneda; 24. Higher dimensions; 25. Epilogue: thinking categorically; Appendices: A. Background on alphabets; B. Background on basic logic; C. Background on set theory; D. Background on topological spaces; Glossary; Further reading; Acknowledgements; Index.
£23.52
Cambridge University Press An Invitation to Model Theory
Book SynopsisModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.Table of ContentsPreface; Part I. Languages and Structures: 1. Structures; 2. Terms; 3. Formulas; 4. Definable sets; 5. Substructures and quantifiers; Part II. Theories and Compactness: 6. Theories and axioms; 7. The complex and real fields; 8. Compactness and new constants; 9. Axiomatisable classes; 10. Cardinality considerations; 11. Constructing models from syntax; Part III. Changing Models: 12. Elementary substructures; 13. Elementary extensions; 14. Vector spaces and categoricity; 15. Linear orders; 16. The successor structure; Part IV. Characterising Definable Sets: 17. Quantifier elimination for DLO; 18. Substructure completeness; 19. Power sets and Boolean algebras; 20. The algebras of definable sets; 21. Real vector spaces and parameters; 22. Semi-algebraic sets; Part V. Types: 23. Realising types; 24. Omitting types; 25. Countable categoricity; 26. Large and small countable models; 27. Saturated models; Part VI. Algebraically Closed Fields: 28. Fields and their extensions; 29. Algebraic closures of fields; 30. Categoricity and completeness; 31. Definable sets and varieties; 32. Hilbert's Nullstellensatz; Bibliography; Index.
£30.44
Springer London Ltd Quaternions for Computer Graphics
Book SynopsisIf you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, diTable of Contents
£53.99
Clanrye International New Frontiers in Fuzzy Controllers
Book SynopsisAdvances in the sphere of fuzzy controllers have been rapid, giving rise to the need for literature that documents all the recent advances both in theory and in applications. This book has been published with an aim of serving the same purpose. It is a compilation of various research outcomes on diverse applications of fuzzy control systems. At the center of numerous engineering challenges is the question of controlling different systems. The wide spectrum of these structures includes a variety of systems varying from the inverted pendulum to auto-focusing system of a digital camera. Fuzzy control systems have displayed their improved output in all these areas. This book examines new areas of fuzzy applications such as a two-layered control system, cycle-to-cycle fuzzy logic control etc. It will be a good source of reference for researchers, engineers, and postgraduate students specializing in associated fields of fuzzy control systems.
£66.49
Atlantic Books Metamaths
Book SynopsisOne of the world's greatest mathematicians explains his revolutionary hypothesis about the enigma at the heart of maths: omega. 'Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken.' -- Peter Pesic, TLSMeta Maths is Gregory Chaitin's exuberant account of his discovery of 'omega': the infinitely long, exquisitely complex and utterly incalculable representation of randomness and unknowability in mathematics. From Euclid to Gödel to Turing, Chaitin's infectious narrative guides us on a spellbinding journey through the historical advances in maths and science that led to his breakthrough discovery. Once there he takes us further, to the very frontiers of scientific thinking. Meta Maths shows that mathematics is as much art form as logic, as much science as pure reasoning, and sheds light on what we can ultimately hope to know about the universe and the very nature of life.Trade ReviewMeta Maths is truly idiosyncratic. Informal, chatty and cerebral... it mixes mathematics with Chaitin's outlook on life and philosophy... Great fun. -- Alan Cane * Financial Times *
£16.19
College Publications Logic and Computation: Essays in Honour of
Book SynopsisThis volume celebrates Amílcar Sernadas' (1952--2017) highly significant and original scientific contributions, as well as his outstanding academic career. This compilation of articles by colleagues, former students and friends was prepared in the months that followed the Conference in Honour of Amílcar, which was held at the Instituto Superior Técnico in April 2016, to celebrate his 64th birthday.
£13.50
Springer Nature Switzerland AG Ludwig Wittgenstein: Dictating Philosophy: To
Book SynopsisIn this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein’s philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter’s role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein’s fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. This collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O’Mahony joined him in co-editing and bringing this book to publication. Trade Review“Gibson and O’Mahony have done a remarkable job and Dictating Philosophy will prove to be of tremendous importance to the field of Wittgenstein scholarship. … the new angles of approach and skillfully crafted examples from these dictations unquestionably provide real food for thought.” (Nuno Venturinha, PHILOSOPHY, The Journal of the Royal Institute of Philosophy, June 16, 2021)Table of ContentsPart 1. The Emergence of the Archive.- Chapter 1. Introduction.- Chapter 2. The Amanuensis Matters.- Part 2. The Transcriptions of the Wittgenstien Skinner Manuscripts.- Chapter 3. The Pink Book.- Chapter 4. Communication of Personal Experience.- Chapter 5. Philosophy.- Chapter 6. Visual Image in his Brain.- Chapter 7. Norwegian Notebook.- Chapter 8. Self Evidence and Logic.- Part 3. Calculations in the Hand of Francis Skinner.- Chapter 9. Mathematical Calculations in Skinner’s Hand.
£35.99
Springer Nature Switzerland AG Sequents and Trees: An Introduction to the Theory
Book SynopsisThis textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.Trade Review“Each chapter of the book is structured in a similar way and contains the basic definitions, facts and necessary discussion regarding the key notions, accompanied with new ideas and a wide reference list, followed by the author's clear and approachable style. This book is self-contained, presenting an extensive survey of the applications and usefulness of cut elimination, and seems to be an extremely interesting source not only for logicians and philosophers, but also for researchers in computer science.” (Branislav Boričić, Mathematical Reviews, May, 2022)Table of ContentsIntroduction.- Analytic Sequent Calculus for CPL.- Gentzen's Sequent Calculus LK.- Purely Logical Sequent Calculus.- Sequent Calculi for Modal Logics.- Alternatives to CPL.- Appendix.
£999.99
Springer Nature Switzerland AG Computability
Book SynopsisThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.Trade Review“This textbook is suited for self-study … . As a second reading however a reader interested in rigorous proofs and/or different approaches to known concepts will benefit from this wealth of material.” (Dieter Riebesehl, zbMATH 1507.03002, 2023)Table of ContentsMathematical Background; a Review.- A Theory of Computability.- Primitive Recursive Functions.- Loop Programs.-The Ackermann Function.- (Un)Computability via Church's Thesis.- Semi-Recursiveness.- Yet another number-theoretic characterisation of P.- Godel's Incompleteness Theorem via the Halting Problem.- The Recursion Theorem.- A Universal (non-PR) Function for PR.- Enumerations of Recursive and Semi-Recursive Sets.- Creative and Productive Sets Completeness.- Relativised Computability.- POSSIBILITY: Complexity of P Functions.- Complexity of PR Functions.- Turing Machines and NP-Completeness.
£71.99
Springer Nature Switzerland AG Computability
Book SynopsisThis survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.Trade Review“This textbook is suited for self-study … . As a second reading however a reader interested in rigorous proofs and/or different approaches to known concepts will benefit from this wealth of material.” (Dieter Riebesehl, zbMATH 1507.03002, 2023)Table of ContentsMathematical Background; a Review.- A Theory of Computability.- Primitive Recursive Functions.- Loop Programs.-The Ackermann Function.- (Un)Computability via Church's Thesis.- Semi-Recursiveness.- Yet another number-theoretic characterisation of P.- Godel's Incompleteness Theorem via the Halting Problem.- The Recursion Theorem.- A Universal (non-PR) Function for PR.- Enumerations of Recursive and Semi-Recursive Sets.- Creative and Productive Sets Completeness.- Relativised Computability.- POSSIBILITY: Complexity of P Functions.- Complexity of PR Functions.- Turing Machines and NP-Completeness.
£52.24
Springer Nature Switzerland AG The Logical Writings of Karl Popper
Book SynopsisThis open access book is the first ever collection of Karl Popper's writings on deductive logic.Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.Table of Contents Part I: Articles.- Chapter 1. Introduction to Popper’s Articles on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 2. Are Contradictions Embracing? (1943) (Karl R. Popper).- Chapter 3. Logic without Assumptions (1947) (Karl R. Popper).- Chapter 4. New Foundations for Logic (1947) (Karl R. Popper).- Chapter 5. Functional Logic without Axioms or Primitive Rules of Inference (1947)(Karl R. Popper).- Chapter 6. On the Theory of Deduction, Part I. Derivation and its Generalizations (1948) (Karl R. Popper).- Chapter 7. On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation (1948) (Karl R. Popper).- Chapter 8. The Trivialization of Mathematical Logic (1949) (Karl R. Popper).- Chapter 9. A Note on Tarski’s Definition of Truth (1955) (Karl R. Popper).-Chapter 10. On a Proposed Solution of the Paradox of the Liar (1955) (Karl R. Popper).- Chapter 11. On Subjunctive Conditionals with Impossible Antecedents (1959) (Karl R. Popper).- Chapter 12. Lejewski’s Axiomatization of My Theory of Deducibility (1974) (Karl R. Popper).- Chapter 13. Reviews of Popper’s Articles on Logic (Wilhelm Ackermann et.al).- Part II: Manuscripts.- Chapter 14. Introduction to Popper’s Manuscripts on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 15. On Systems of Rules of Inference (Karl R. Popper and Paul Bernays).- Chapter 16. A General Theory of Inference (Karl R. Popper).- Chapter 17. On the Logic of Negation (Karl R. Popper).- Chapter 18. A Note on the Classical Conditional (Karl R. Popper).- Part III: Correspondence.- Chapter 19. Introduction to Popper’s Correspondence on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 20. Popper’s Correspondence with Paul Bernays (Karl R. Popper and Paul Bernays).- Chapter 21. Popper’s Correspondence with Luitzen Egbertus Jan Brouwer (Karl R. Popper and Luitzen E. J. Brouwer).- Chapter 22. Popper’s Correspondence with Rudolf Carnap (Karl R. Popper and Rudolf Carnap).- Chapter 23. Popper’s Correspondence with Alonzo Church (Karl R. Popper and Alonzo Church).- Chapter 24. Popper’s Correspondence with Kalman Joseph Cohen (Karl R. Popper and Kalman J. Cohen).- Chapter 25. Popper’s Correspondence with Henry George Forder (Karl R. Popper and Henry George Forder).- Chapter 26. Popper’s Correspondence with Harold Jeffreys (Karl R. Popper and Harold Jeffreys).- Chapter 27. Popper’s Correspondence with Stephen Cole Kleene (Karl R. Popper and Stephen C. Kleene).- Chapter 28. Popper’s Correspondence with William Calvert Kneale (Karl R. Popper and William C. Kneale).- Chapter 29. Popper’s Correspondence with Willard Van Orman Quine (Karl R. Popper and Willard V. O. Quine).- Chapter 30. Popper’s Correspondence with Heinrich Scholz (Karl R. Popper and Heinrich Scholz).- Chapter 31. Popper’s Correspondence with Peter Schroeder-Heister (Karl R. Popper and Peter Schroeder-Heister).- Concordances.- Bibliography.- Index.
£40.49
Springer International Publishing AG Inquisitive Logic: Consequence and Inference in
Book SynopsisThis open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logician’s toolkit, including model-theoretic constructions and proof systems.After motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive—i.e., extended conservatively with questions—and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.Table of Contents1. Introduction.- 2. On the role of questions in logic.- 3. Questions in propositional logic.- 4. Reasoning with questions.- 5. Questions in first-order logic.- 6. Questions in modal logic.- 7. Connections with intuitionistic logic.- 8. Connections with dependence logic.- 9. Conclusion.
£40.49
Springer International Publishing AG Philosophy of Science for Scientists
Book SynopsisThis textbook offers an introduction to the philosophy of science. It helps undergraduate students from the natural, the human and social sciences to gain an understanding of what science is, how it has developed, what its core traits are, how to distinguish between science and pseudo-science and to discover what a scientific attitude is. It argues against the common assumption that there is fundamental difference between natural and human science, with natural science being concerned with testing hypotheses and discovering natural laws, and the aim of human and some social sciences being to understand the meanings of individual and social group actions. Instead examines the similarities between the sciences and shows how the testing of hypotheses and doing interpretation/hermeneutics are similar activities. The book makes clear that lessons from natural scientists are relevant to students and scholars within the social and human sciences, and vice versa. It teaches its readers how to effectively demarcate between science and pseudo-science and sets criteria for true scientific thinking. Divided into three parts, the book first examines the question What is Science? It describes the evolution of science, defines knowledge, and explains the use of and need for hypotheses and hypothesis testing. The second half of part I deals with scientific data and observation, qualitative data and methods, and ends with a discussion of theories on the development of science. Part II offers philosophical reflections on four of the most important concepts in science: causes, explanations, laws and models. Part III presents discussions on philosophy of mind, the relation between mind and body, value-free and value-related science, and reflections on actual trends in science.Trade Review“Target audience comprises ‘students of engineering, physics, biology, social science, medicine and nursing’ … this book allows readers from a global audience to grasp the ‘flavour’ of the long and rich Germanic and Scandinavian tradition.” (Agustín Adúriz-Bravo, Science and Education, Vol. 28, 2019)“The aim of Lars-Göran Johansson’s textbook Philosophy of Science for Scientists is … to provide an introduction to the philosophy of science for students in all fields of science. … the book is supposed to be suitable for an undergraduate level course in the philosophy of science for philosophy students.” (Amanda Thorell, Theoria, Vol. 83, 2017)“Lars-Göran Johansson’s recent book Philosophy of science for scientists is the only textbook in the philosophy of science that is addressed specifically to an audience consisting of scientists. … In its breadth of treated topics, the book can serve as a basic text to many different courses in the philosophy of science.” (Maarten Franssen, Metascience, Vol. 26, 2017)“Philosophy of Science for Scientists by Lars-Goran Johansson: a lovely textbook for undergraduates. It is a highly readable introduction to how one can view the practice of science. … this is an excellent introduction to understanding science in a general sense. Students and practitioners will find it worthwhile to read and discuss.” (David S. Mazel, MAA Reviews, maa.org, November, 2016)“This is an excellent book that can serve as a very appropriate textbook for the first course in Philosophy of Science. … it is a very well written book and is an enjoyable reading. … It is well written by a great authority in the field and I strongly recommend it to you if you are interested in to understand what science is and why science is important for knowledge and our understanding of reality.” (Philosophy, Religion and Science Book Reviews, Bookinspections.wordpress.com, July, 2016)Table of ContentsPreface and overview of the bookPart 1: What is science?.- 1. The Evolution of Science.- 2. Knowledge.- 3. Hypotheses and Hypothesis Testing.- 4. On Scientific Data.- 5. Qualitative Data and Methods.- 6. Theories about the Development of Science.- Part 2. Philosophical reflections on four core concepts in science: causes, explanations, laws and models.- 7. On Causes and Correlations.- 8. Explanations.- 9. Explanation in the Humanities and Social Sciences.- 10. Scientific Laws.- 11. Theories, Models and Reality.- Part 3. Some auxiliaries.- 12. The Mind-Body Problem.- 13. Science and Values.- 14. Some trends in science.- Appendix.- Logical Forms.- Index.
£61.74
Birkhauser Verlag AG Number Theory: An Introduction via the Density of
Book SynopsisNow in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.Trade Review“In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. … Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)“The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. … a good text for an introductory course … .” (Allen Stenger, MAA Reviews, maa.org, November, 2016)Table of ContentsIntroduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- The Fields Q_p of p-adic Numbers: Hensel's Lemma.- References.- Index.
£44.99
Springer International Publishing AG Don Pigozzi on Abstract Algebraic Logic,
Book SynopsisThis book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.Table of ContentsA Mathematical Life; Pigozzi, Don.- Assertional logics, truth-equational logics, and the hierarchiesof abstract algebraic logic; Albuquerque, Hugo, Font, Josep Maria, Jansana, Ramon, and Moraschini, Tommaso.- Deduction-Detachment Theorem and Gentzen-Style Deductive Systems; Babenyshev, Sergey.- Introducing Boolean Semilattices; Bergman, Clifford.- The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras; Czelakowski, Janusz.- A short overview of Hidden Logic; Ferreirim, Isabel and Martins, Manuel A.- Absorption and directed J´onsson terms; Kazda, Alexandr, Kozik, Marcin, McKenzie, Ralph and Moore, Matthew.- Relatively congruence modular quasivarieties of modules; Kearnes, Keith A. - The computational complexity of deciding whether a finite algebra generates a minimal variety; McNulty, George F.- Characterization of protoalgebraic k-deductive systems; Palasinska; Katarzyna.- Diagrammatic duality; Romanowska, Anna B. and Smith, Jonathan D.H.- Boolean product representations of algebras via binary polynomials; Salibra, Antonino, Ledda, Antonio, and Paoli, Francesco.- Paraconsistent constructive logic with strong negation as a contraction-free relevant logic; Spinks, Matthew and Veroff, Robert.- Possible classification of finite-dimensional compact Hausdorfftopological algebras; Taylor, Walter.- Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems; Voutsadakis; George.
£999.99
World Scientific Publishing Co Pte Ltd Relations: Concrete, Abstract, And Applied - An
Book SynopsisThe book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
£139.50
Springer Verlag, Singapore Sparse Estimation with Math and R: 100 Exercises
Book SynopsisThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building R programs. Each chapter introduces the notion of sparsity and provides procedures followed by mathematical derivations and source programs with examples of execution. To maximize readers’ insights into sparsity, mathematical proofs are presented for almost all propositions, and programs are described without depending on any packages. The book is carefully organized to provide the solutions to the exercises in each chapter so that readers can solve the total of 100 exercises by simply following the contents of each chapter.This textbook is suitable for an undergraduate or graduate course consisting of about 15 lectures (90 mins each). Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning by data scientists, machine learning engineers, and researchers interested in linear regression, generalized linear lasso, group lasso, fused lasso, graphical models, matrix decomposition, and multivariate analysis.This book is one of a series of textbooks in machine learning by the same author. Other titles are: - Statistical Learning with Math and R (https://www.springer.com/gp/book/9789811575679) - Statistical Learning with Math and Python (https://www.springer.com/gp/book/9789811578762) - Sparse Estimation with Math and PythonTable of ContentsChapter 1: Linear Regression.- Chapter 2: Generalized Linear Regression.- Chapter 3: Group Lasso.- Chapter 4: Fused Lasso.- Chapter 5: Graphical Model.- Chapter 6: Matrix Decomposition.- Chapter 7: Multivariate Analysis.
£26.99
Springer Verlag, Singapore Statistical Learning with Math and Python: 100
Book SynopsisThe most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building Python programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning. Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning.Table of ContentsChapter 1: Linear Algebra.- Chapter 2: Linear Regression.- Chapter 3: Classification.- Chapter 4: Resampling.- Chapter 5: Information Criteria.- Chapter 6: Regularization.- Chapter 7: Nonlinear Regression.- Chapter 8: Decision Trees.- Chapter 9: Support Vector Machine.- Chapter 10: Unsupervised Learning.
£26.99
John Wiley & Sons Inc Logic For Dummies
Book SynopsisLogic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies.Table of ContentsIntroduction. Part I: Overview of Logic. Chapter 1: What Is This Thing Called Logic? Chapter 2: Logical Developments from Aristotle to the Computer. Chapter 3: Just for the Sake of Argument. Part II: Formal Sentential Logic (SL). Chapter 4: Formal Affairs. Chapter 5: The Value of Evaluation. Chapter 6: Turning the Tables: Evaluating Statements with Truth Tables. Chapter 7: Taking the Easy Way Out: Creating Quick Tables. Chapter 8: Truth Grows on Trees. Part III: Proofs, Syntax, and Semantics in SL. Chapter 9: What Have You Got to Prove? Chapter 10: Equal Opportunities: Putting Equivalence Rules to Work. Chapter 11: Big Assumptions with Conditional and Indirect Proofs. Chapter 12: Putting It All Together: Strategic Moves to Polish Off Any Proof. Chapter 13: One for All and All for One. Chapter 14: Syntactical Maneuvers and Semantic Considerations. Part IV: Quantifier Logic (QL). Chapter 15: Expressing Quantity with Quality: Introducing Quantifier Logic. Chapter 16: QL Translations. Chapter 17: Proving Arguments with QL. Chapter 18: Good Relations and Positive Identities. Chapter 19: Planting a Quantity of Trees. Part V: Modern Developments in Logic. Chapter 20: Computer Logic. Chapter 21: Sporting Propositions: Non-Classical Logic. Chapter 22: Paradox and Axiomatic Systems. Part VI: The Part of Tens. Chapter 23: Ten Quotes about Logic. Chapter 24: Ten Big Names in Logic. Chapter 25: Ten Tips for Passing a Logic Exam. Index.
£17.09
Dover Publications Inc. Stewart I Game Set and Math
Book SynopsisThese pun-studded fables by a popular science writer make complicated mathematical concepts accessible and fun. Twelve essays take a playful approach to mathematics, investigating the topology of a warm blanket, the odds of beating a superior tennis player, and how to distinguish between fact and fallacy. 1991 edition.
£9.49
Princeton University Press AgentZero
Book SynopsisIntroduces a theoretical entity: Agent_Zero. This title weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others.Trade Review"Agent Zero offers a solution to some of social science's great puzzles. Its behavioral basis is the interplay of emotion, cognition, and network contagion effects. It elegantly explains why so many human actions are so manifestly dysfunctional, and why some are downright evil."—George Akerlof, Nobel Laureate in Economics"Rarely has a book stimulated me intellectually as much as this one. Particularly exciting is the incorporation of agents who feel (affect) and deliberate, as well as influence one another through social interaction. Epstein is a brilliantly creative scholar and the range of applications showcased here is stunning. In sum, this is a pathbreaking book."—Paul Slovic, University of Oregon"Joshua Epstein proposes a parsimonious but powerful model of individual behavior that can generate an extraordinary range of group behaviors, including mob violence, manias and financial panics, rebellions, network dynamics, and a host of other complex social phenomena. This is a highly original, beautifully conceived, and important book."—Peyton Young, University of Oxford"In social science generally and most notably in economics, the rational actor model has long been the benchmark for policy analysis and institutional design. Epstein now offers a worthy alternative: Agent_Zero, a mathematically and computationally tractable agent whose inner workings are grounded in neuroscience. Much like you and me, Agent_Zero is influenced by emotion, reason, and social pressures. Epstein demonstrates that collections of Agent Zeros perform amazingly like real groups, teams, and societies and can therefore serve as the fundamental building blocks for what he calls Generative Social Science. The rational actor now has a true competitor. Agent_Zero is a major advance."—Scott Page, University of Michigan"This is social science based on how our brains actually work. Epstein's computerized 'agents' can feel passion and fear, and can influence each other emotionally. And when they interact, we see many of the realities of social life, from the dynamics of juries to racist violence to Arab springs. A remarkable and original piece of work."—W. Brian Arthur, Santa Fe InstituteTable of ContentsForeword xi Preface xiii Acknowledgments xv INTRODUCTION 1 MOTIVATION 1 Generate Social Dynamics 2 A Core Target 2 THE MODEL COMPONENTS 5 Model Overview 6 Skeletal Equation 8 Specific Components 9 ORGANIZATION 10 Part I: Mathematical Model 10 Part II: Agent-Based Model 11 Part III: Extensions 13 Replicability and Research Resources on the Princeton University Press Website 16 Part IV: Future Research and Conclusions 17 PART 1. MATHEMATICAL MODEL 19 I.1. THE PASSIONS: FEAR CONDITIONING 19 Fear Circuitry and the Perils of Fitness 20 Nomenclature of Conditioning 29 The Rescorla-Wagner Model 33 Social Examples 37 Fear Extinction 41 I.2. REASON: THE COGNITIVE COMPONENT 46 I.3. THE SOCIAL COMPONENT 51 Simple Version of the Core Target 55 Examples of Fear Contagion 57 Mechanisms of Fear Contagion 59 Conformist Empirical Estimates 63 Generalizing Rescorla-Wagner 67 The Central Case 69 Tolstoy: The First Agent Modeler 71 A Mathematical Aside on Social Norms as Vector Fields 74 Extinction of Majorities 78 I.4. INTERIM CONCLUSIONS 80 PART II. AGENT-BASED COMPUTATIONAL MODEL 81 Affective Component 84 "Rational" Component 85 Social Component 88 Action 89 Pseudocode 89 II.1. COMPUTATIONAL PARABLES 90 Parable 1: The Slaughter of Innocents through Dispositional Contagion 90 Parable 2: Agent_Zero Initiates: Leadership as Susceptibility to Dispositional Contagion 94 Run 3. Information Cuts Both Ways 96 Run 4. A Day in the Life of Agent_Zero: How Affect and Probability Can Change on Different Time Scales 98 Run 5. Lesion Studies 102 PART III. EXTENSIONS 107 III.1. ENDOGENOUS DESTRUCTIVE RADIUS 107 III.2. AGE AND IMPULSE CONTROL 109 III.3. FIGHT VS. FLIGHT 110 Case 1: Fight 111 Case 2: Flight 112 Capital Flight 114 III.4. REPLICATING THE Latane-DARLEY EXPERIMENT 114 Threshold Imputation 115 The Dialogue 118 III.5. MEMORY 118 III.6. COUPLINGS: ENTANGLEMENT OF PASSION AND REASON 122 Mathematical Treatment 124 III.7.ENDOGENOUS DYNAMICS OF CONNECTION STRENGTH 128 Affective Homophily 128 General Setup 130 Agent-Based Model: Nonequlibrium Dynamics 135 III.8. GROWING THE 2011 ARAB SPRING 138 III.9. JURY PROCESSES 143 Phase 1. Public Phase 143 Phase 2. Courtroom Trial Phase 145 Phase 3. Jury Phase 147 III.10. EMERGENT DYNAMICS OF NETWORK STRUCTURE 152 Network Structure Dynamics as a Poincare Map 153 Relation to Literature 159 III.11. MULTIPLE SOCIAL LEVELS 160 Agent_Zero as Witness to History 161 III.12. THE 18TH BRUMAIRE OF AGENT_ZERO 165 III.13. INTRODUCTION OF PRICES AND SEASONAL ECONOMIC CYCLES 168 Prices 168 A Christmas Story 173 III.14. SPIRALS OF MUTUAL ESCALATION 176 PART IV. FUTURE RESEARCH AND CONCLUSION 181 IV.1. FUTURE RESEARCH 181 IV.2. CONCLUSION 187 Civil Violence 187 Economics 188 Health Behavior 189 Psychology 190 Jury Dynamics 191 The Formation and Dynamics of Networks 191 Mutual Escalation Dynamics 192 Birth and Intergenerational Transmission 192 IV.3. TOWARD NEW GENERATIVE FOUNDATIONS 192 Appendix I. Threshold Imputation Bounds 195 Appendix II. Mathematica Code 197 Appendix III. Agent_Zero NetLogo Source Code 213 Appendix IV. Parameter Settings for Model Runs 221 References 227 Index 243
£46.75
