Logic / Computer Science / Mathematical Philosophy : upso
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Games User Research
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198794844.jpg" alt="Games User Research"/><br/></td><td><dl><dt>Author:</dt><dd>AndersDrachenAnders DrachenVeteran Data Scientist, University of YorkPejmanMirza-BabaeiPejman Mirza-BabaeiAssistant Professor, University of Ontario Institute of TechnologyLennartNackeLennart NackeAssociate Professor, HCI Games Group, University of Waterloo</dd><dt>ISBN:</dt><dd>9780198794844</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy, Computational Mathematics / Optimization</dd><dt>DOI:</dt><dd>10.1093/oso/9780198794844.001.0001</dd><dt>Published in print:</dt><dd>2018</dd><dt>Published Online:</dt><dd>2018-03-22</dd></dl></td></tr></table><p>Today, Games User Research forms an integral component of the development of any kind of interactive entertainment. User research stands as the primary source of business intelligence in the incredibly competitive game industry. This book aims to provide the foundational, accessible, go-to resource for people interested in GUR. It is a community-driven effort—it is written by passionate professionals and researchers in the GUR community as a handbook and guide for everyone interested in user research and games. The book bridges the current gaps of knowledge in Game User Research, building the go-to volume for everyone working with games, with an emphasis on those new to the field.</p>Anders Drachen, Pejman Mirza-Babaei, and Lennart Nacke2018-03-22Lectures on Inductive Logic
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199666478.jpg" alt="Lectures on Inductive Logic"/><br/></td><td><dl><dt>Author:</dt><dd>Jon Williamson</dd><dt>ISBN:</dt><dd>9780199666478</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199666478.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2017-03-23</dd></dl></td></tr></table><p>Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of inductive logic and develops a new Bayesian inductive logic. Chapter 1 introduces perhaps the simplest and most natural account of inductive logic, classical inductive logic, which is attributable to Ludwig Wittgenstein. Classical inductive logic is seen to fail in a crucial way, so there is a need to develop more sophisticated inductive logics. Chapter 2 presents enough logic and probability theory for the reader to begin to study inductive logic, while Chapter 3 introduces the ways in which logic and probability can be combined in an inductive logic. Chapter 4 analyses the most influential approach to inductive logic, due to W.E. Johnson and Rudolf Carnap. Again, this logic is seen to be inadequate. Chapter 5 shows how an alternative approach to inductive logic follows naturally from the philosophical theory of objective Bayesian epistemology. This approach preserves the inferences that classical inductive logic gets right (Chapter 6). On the other hand, it also offers a way out of the problems that beset classical inductive logic (Chapter 7). Chapter 8 defends the approach by tackling several key criticisms that are often levelled at inductive logic. Chapter 9 presents a formal justification of the version of objective Bayesianism which underpins the approach. Chapter 10 explains what has been achieved and poses some open questions.</p>Jon Williamson2017-03-23Noncooperative Game Theory
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691175218.jpg" alt="Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists"/><br/></td><td><dl><dt>Author:</dt><dd>João P. Hespanha</dd><dt>ISBN:</dt><dd>9780691175218</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691175218.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2018-05-24</dd></dl></td></tr></table><p>This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.</p>João P. Hespanha2018-05-24Interpolation and Definability
//www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198511748.001.0001/acprof-9780198511748
<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198511748.jpg" alt="Interpolation and DefinabilityModal and Intuitionistic Logics"/><br/></td><td><dl><dt>Author:</dt><dd>Dov M. Gabbay, Larisa Maksimova</dd><dt>ISBN:</dt><dd>9780198511748</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198511748.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book focuses on interpolation and definability. This notion is not only central in pure logic, but has significant meaning and applicability in all areas where logic itself is applied, especially in computer science, artificial intelligence, logic programming, philosophy of science, and natural language. The book provides basic knowledge on interpolation and definability in logic, and contains a systematic account of material which has been presented in many papers. A variety of methods and results are presented beginning with the famous Beth's and Craig's theorems in classical predicate logic (1953-57), and to the most valuable achievements in non-classical topics on logic, mainly intuitionistic and modal logic. Together with semantical and proof-theoretic methods, close interrelations between logic and universal algebra are established and exploited.</p>Dov M. Gabbay and Larisa Maksimova2007-09-01Bolzano's Logical System
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198788294.jpg" alt="Bolzano's Logical System"/><br/></td><td><dl><dt>Author:</dt><dd>Ettore Casari</dd><dt>ISBN:</dt><dd>9780198788294</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198788294.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2017-01-19</dd></dl></td></tr></table><p>A starting point of Bolzano’s logical reflection was the conviction that among truths there is a connection, according to which some truths are grounds of others, and these in turn are consequences of the former, and that such a connection is objective, i.e. subsisting independently of every cognitive activity of the subject. In the attempt to account for the distinction between subjective and objective levels of knowledge, Bolzano gradually gained the conviction that the reference of the subject to the object is mediated by a realm of entities without existence that, recalling the Stoic lectà, are here called ‘lectological’. Moreover, of the two main ways through which that reference takes place—psychic activity and linguistic activity—Bolzano favoured the first and traced back to it the problems of the second; i.e. he considered those intermediate entities first as possible content of psychic phenomena and only subordinately, on the basis of a complex theory of signs, as meanings of linguistic phenomena. This book follows this schema and treats, in great detail, first, lectological entities (ideas and propositions in themselves), second, cognitive psychic phenomena (subjective ideas and judgements), and, finally, linguistic phenomena. Moreover, it tries to bring to light the extraordinary systematic character of Bolzano’s logical thought and it does this showing that the main logical ideas developed principally in the first three parts of the Theory of Science, published in 1837, can be effortlessly formally presented within the well-known Hilbertian epsilon-calculus.</p>Ettore Casari2017-01-19Computational Interaction
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198799603.jpg" alt="Computational Interaction"/><br/></td><td><dl><dt>Author:</dt><dd>AnttiOulasvirtaAntti OulasvirtaAssociate Professor, Aalto UniversityPer OlaKristenssonPer Ola KristenssonUniversity Reader in Interactive Systems Engineering, University of CambridgeXiaojunBiXiaojun BiAssistant Professor, Stony Brook UniversityAndrewHowesAndrew HowesProfessor and Head of School at the School of Computer Science, University of Birmingham</dd><dt>ISBN:</dt><dd>9780198799603</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/oso/9780198799603.001.0001</dd><dt>Published in print:</dt><dd>2018</dd><dt>Published Online:</dt><dd>2018-03-22</dd></dl></td></tr></table><p>This book presents computational interaction as an approach to explaining and enhancing the interaction between humans and information technology. Computational interaction applies abstraction, automation, and analysis to inform our understanding of the structure of interaction and also to inform the design of the software that drives new and exciting human-computer interfaces. The methods of computational interaction allow, for example, designers to identify user interfaces that are optimal against some objective criteria. They also allow software engineers to build interactive systems that adapt their behaviour to better suit individual capacities and preferences. Embedded in an iterative design process, computational interaction has the potential to complement human strengths and provide methods for generating inspiring and elegant designs. Computational interaction does not exclude the messy and complicated behaviour of humans, rather it embraces it by, for example, using models that are sensitive to uncertainty and that capture subtle variations between individual users. It also promotes the idea that there are many aspects of interaction that can be augmented by algorithms. This book introduces computational interaction design to the reader by exploring a wide range of computational interaction techniques, strategies and methods. It explains how techniques such as optimisation, economic modelling, machine learning, control theory, formal methods, cognitive models and statistical language processing can be used to model interaction and design more expressive, efficient and versatile interaction.</p>Antti Oulasvirta, Per Ola Kristensson, Xiaojun Bi, and Andrew Howes2018-03-22Gödel's Disjunction
//www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198759591.001.0001/acprof-9780198759591
<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198759591.jpg" alt="Gödel's DisjunctionThe scope and limits of mathematical knowledge"/><br/></td><td><dl><dt>Author:</dt><dd>LeonHorstenLeon HorstenProfessor of Philosophy, University of BristolPhilipWelchPhilip WelchProfessor of Mathematical Logic, University of Bristol</dd><dt>ISBN:</dt><dd>9780198759591</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198759591.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2016-11-17</dd></dl></td></tr></table><p>The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer) or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematicalmind ismore powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency of rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel’s disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.</p>Leon Horsten and Philip Welch2016-11-17Set Theory
//www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198568520.001.0001/acprof-9780198568520
<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198568520.jpg" alt="Set TheoryBoolean-Valued Models and Independence Proofs"/><br/></td><td><dl><dt>Author:</dt><dd>John L. Bell</dd><dt>ISBN:</dt><dd>9780198568520</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198568520.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated exposition of the theory of Boolean-valued models as developed by Scott and Solovay in the 1960s, deriving along the way the central set theoretic independence proofs of Cohen and others in the particularly elegant form that the Boolean-valued approach enables them to assume. In this edition, the background material has been augmented to include an introduction to Heyting algebras. It includes chapters on Boolean-valued analysis and Heyting-algebra-valued models of intuitionistic set theory.</p>John L. Bell2007-09-01The Structure of Models of Peano Arithmetic
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198568278.jpg" alt="The Structure of Models of Peano Arithmetic"/><br/></td><td><dl><dt>Author:</dt><dd>Roman Kossak, James Schmerl</dd><dt>ISBN:</dt><dd>9780198568278</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198568278.001.0001</dd><dt>Published in print:</dt><dd>2006</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem. There are also chapters discussing ω1-like models with interesting second order properties, and a chapter on order types of nonstandard models.</p>Roman Kossak and James Schmerl2007-09-01In Defence of Objective Bayesianism
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199228003.jpg" alt="In Defence of Objective Bayesianism"/><br/></td><td><dl><dt>Author:</dt><dd>Jon Williamson</dd><dt>ISBN:</dt><dd>9780199228003</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199228003.001.0001</dd><dt>Published in print:</dt><dd>2010</dd><dt>Published Online:</dt><dd>2010-09-01</dd></dl></td></tr></table><p>Bayesian epistemology aims to answer the following question: How strongly should an agent believe the various propositions expressible in her language? Subjective Bayesians hold that.it is largely (though not entirely) up to the agent as to which degrees of belief to adopt. Objective Bayesians, on the other hand, maintain that appropriate degrees of belief are largely (though not entirely) determined by the agent's evidence. This book states and defends a version of objective Bayesian epistemology. According to this version, objective Bayesianism is characterized by three norms: (i) Probability: degrees of belief should be probabilities; (ii) Calibration: they should be calibrated with evidence; and (iii) Equivocation: they should otherwise equivocate between basic outcomes. Objective Bayesianism has been challenged on a number of different fronts: for example, it has been accused of being poorly motivated, of failing to handle qualitative evidence, of yielding counter‐intuitive degrees of belief after updating, of suffering from a failure to learn from experience, of being computationally intractable, of being susceptible to paradox, of being language dependent, and of not being objective enough. The book argues that these criticisms can be met and that objective Bayesianism is a promising theory with an exciting agenda for further research.</p>Jon Williamson2010-09-01Simplicity Theory
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198567387.jpg" alt="Simplicity Theory"/><br/></td><td><dl><dt>Author:</dt><dd>Byunghan Kim</dd><dt>ISBN:</dt><dd>9780198567387</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198567387.001.0001</dd><dt>Published in print:</dt><dd>2013</dd><dt>Published Online:</dt><dd>2014-01-23</dd></dl></td></tr></table><p>This book is about simple first-order theories. The class of simple theories was introduced by S. Shelah in the early 1980s. Then several specific algebraic structures having simple theories have been studied by leading researchers, notably by E. Hrushovski. In the mid-1990s the author established in his thesis the symmetry and transitivity of non-forking for simple theories and, with A. Pillay, type-amalgamation for Lascar strong types. Since then a great deal of research work on simplicity theory, the study of simple theories and structures has been produced. This book starts with the introduction of the fundamental notions of dividing and forking, and covers up to the hyperdefinable group configuration theorem for simple theories.</p>Byunghan Kim2014-01-23Bayesian Nets and Causality
//www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198530794.001.0001/acprof-9780198530794
<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198530794.jpg" alt="Bayesian Nets and CausalityPhilosophical and Computational Foundations"/><br/></td><td><dl><dt>Author:</dt><dd>Jon Williamson</dd><dt>ISBN:</dt><dd>9780198530794</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198530794.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book provides an introduction to, and analysis of, the use of Bayesian nets in causal modelling. It puts forward new conceptual foundations for causal network modelling: The book argues that probability and causality need to be interpreted as epistemic notions in order for the key assumptions behind causal models to hold. Under the epistemic view, probability and causality are understood in terms of the beliefs an agent ought to adopt. The book develops an objective Bayesian notion of probability and a corresponding epistemic theory of causality. This yields a general framework for causal modelling, which is extended to cope with recursive causal relations, logically complex beliefs and changes in an agent's language.</p>Jon Williamson2007-09-01Everyday Cryptography
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198788003.jpg" alt="Everyday CryptographyFundamental Principles and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Keith Martin</dd><dt>ISBN:</dt><dd>9780198788003</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/oso/9780198788003.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2017-07-20</dd></dl></td></tr></table><p>Cryptography is a vital technology that underpins the security of information in computer networks. This book presents a comprehensive introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient technologies and overwhelming theoretical research. The first part of the book provides essential background, identifying the core security services provided by cryptography. The next part introduces the main cryptographic mechanisms that deliver these security services such as encryption, hash functions, and digital signatures, discussing why they work and how to deploy them, without delving into any significant mathematical detail. In the third part, the important practical aspects of key management are introduced, which is essential for making cryptography work in real systems. The last part considers the application of cryptography. A range of application case studies is presented, alongside a discussion of the wider societal issues arising from use of cryptography to support contemporary cyber security.</p>Keith Martin2017-07-20Here Be Dragons
//www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198723547.001.0001/acprof-9780198723547
<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198723547.jpg" alt="Here Be DragonsScience, Technology and the Future of Humanity"/><br/></td><td><dl><dt>Author:</dt><dd>Olle Häggström</dd><dt>ISBN:</dt><dd>9780198723547</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198723547.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2016-01-21</dd></dl></td></tr></table><p>This book challenges the widely held but oversimplified and even dangerous conception that progress in science and technology is our salvation, and the more of it, the better. The future will offer huge changes due to such progress, but it is not certain that all changes will be for the better. The unprecedented rate of technological development that the 20th century witnessed has made our lives today vastly different from those in 1900. No slowdown is in sight, and the 21st century will most likely see even more revolutionary changes than the 20th, due to advances in science, technology and medicine. Areas where extraordinary and perhaps disruptive advances can be expected include biotechnology, nanotechnology and machine intelligence. We may also look forward to various ways to enhance human cognitive and other abilities using pharmaceuticals, genetic engineering or machine–brain interfaces—perhaps to the extent of changing human nature beyond what we currently think of as human, and into a posthuman era. The potential benefits of all these technologies are enormous, but so are the risks, including the possibility of human extinction. The currently dominant attitude towards scientific and technological advances is tantamount to running blindfold and at full speed into a minefield. This book is a passionate plea for doing our best to map the territories ahead of us, and for acting with foresight, so as to maximize our chances of reaping the benefits of the new technologies while avoiding the dangers.</p>Olle Häggström2016-01-21Mathematical Knowledge and the Interplay of Practices
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691167510.jpg" alt="Mathematical Knowledge and the Interplay of Practices"/><br/></td><td><dl><dt>Author:</dt><dd>José Ferreirós</dd><dt>ISBN:</dt><dd>9780691167510</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691167510.001.0001</dd><dt>Published in print:</dt><dd>2015</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.</p>José Ferreirós2017-10-19Reductive Logic and Proof-search
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198526339.jpg" alt="Reductive Logic and Proof-searchProof Theory, Semantics, and Control"/><br/></td><td><dl><dt>Author:</dt><dd>David J. Pym, Eike Ritter</dd><dt>ISBN:</dt><dd>9780198526339</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198526339.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This a research study about logic. Logic is both part of and has roles in many disciplines, including inter alia, mathematics, computing, and philosophy. The topic covered here — the mathematical theory of reductive logic and proof-search — draws upon the techniques and cultures of all three disciplines, but is mainly about mathematics and computation. Since its earliest presentations, mathematical logic has been formulated as a formalization of deductive reasoning: given a collection of hypotheses, a conclusion is derived. However, the advent of computational logic has emphasized the significance of reductive reasoning: given a putative conclusion, what are sufficient premises? Whilst deductive systems typically have a well-developed semantics of proofs, reductive systems are typically well-understood only operationally. Typically, a deductive system can be read as a corresponding reductive system. The process of calculating a proof of a given putative conclusion, for which non-deterministic choices between premises must be resolved, is called proof-search and is an essential enabling technology throughout the computational sciences. This study suggests that the reductive view of logic is as fundamental as the deductive view, and discusses some of the problems that must be addressed in order to provide a semantics of proof-searches of comparable value to the corresponding semantics of proofs. Just as the semantics of proofs is intimately related to the model theory of the underlying logic, so too should be the semantics of reductions and of proof-search. The study discusses how to solve the problem of providing a semantics for proof-searches in intuitionistic logic, which adequately models both not only the logical but also via an embedding of intuitionistic reductive logic into classical reductive logic, the operational aspects, i.e., control of proof-search, of the reductive system. It concludes with a naturally motivated example of our semantics of proof-search: a class of games.</p>David J. Pym and Eike Ritter2007-09-01Mathematics without Apologies
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691175836.jpg" alt="Mathematics without ApologiesPortrait of a Problematic Vocation"/><br/></td><td><dl><dt>Author:</dt><dd>Michael Harris</dd><dt>ISBN:</dt><dd>9780691175836</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691175836.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2018-05-24</dd></dl></td></tr></table><p>What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers, this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on the author's personal experiences as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, the book reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, the book touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? The book takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.</p>Michael Harris2018-05-24From Sets and Types to Topology and Analysis
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198566519.jpg" alt="From Sets and Types to Topology and AnalysisTowards practicable foundations for constructive mathematics"/><br/></td><td><dl><dt>Author:</dt><dd>LauraCrosillaLaura CrosillaUniversite di FirenzePeterSchusterPeter SchusterMathematical Institut, Universitaet Munich</dd><dt>ISBN:</dt><dd>9780198566519</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198566519.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Constructive mathematics is a vital area of research which has gained special attention in recent years due to the distinctive presence of computational content in its theorems. This characteristic had been already stressed by Bishop in his fundamental contribution to the subject, Foundations of Constructive Analysis (1967). Following Bishop's new approach to mathematics based on intuitionistic logic, various formal systems were introduced in the early 1970s with the intent to clarify the notion of set theory underlying his work. This book addresses the relationship between foundations and practice of constructive mathematics Bishop-style, by presenting on the one hand some very recent contributions to constructive analysis and formal topology, and on the other hand studies which underline the capabilities and expressiveness of various formal systems which have been introduced as foundations for constructive mathematics, like constructive set and type theories. The book aims to provide a point of reference by pesenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions. The book also aims at further promoting awareness and discussion on the issue of bridging foundations and practice of constructive mathematics, thus filling the apparent distance that has emerged between them in recent years.</p>Laura Crosilla and Peter Schuster2007-09-01Computability and Randomness
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199230761.jpg" alt="Computability and Randomness"/><br/></td><td><dl><dt>Author:</dt><dd>André Nies</dd><dt>ISBN:</dt><dd>9780199230761</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199230761.001.0001</dd><dt>Published in print:</dt><dd>2009</dd><dt>Published Online:</dt><dd>2009-05-01</dd></dl></td></tr></table><p>The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book is about these two aspects of sets of natural numbers and about their interplay. For the first aspect, lowness and highness properties of sets are introduced. For the second aspect, firstly randomness of finite objects are studied, and then randomness of sets of natural numbers. A hierarchy of mathematical randomness notions is established. Each notion matches the intuition idea of randomness to some extent. The advantages and drawbacks of notions weaker and stronger than Martin-Löf randomness are discussed. The main topic is the interplay of the computability and randomness aspects. Research on this interplay has advanced rapidly in recent years. One chapter focuses on injury-free solutions to Post's problem. A core chapter contains a comprehensible treatment of lowness properties below the halting problem, and how they relate to K triviality. Each chapter exposes how the complexity properties are related to randomness. The book also contains analogs in the area of higher computability theory of results from the preceding chapters, reflecting very recent research.</p>André Nies2009-05-01The New ABCs of Research
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198758839.jpg" alt="The New ABCs of ResearchAchieving Breakthrough Collaborations"/><br/></td><td><dl><dt>Author:</dt><dd>Ben Shneiderman</dd><dt>ISBN:</dt><dd>9780198758839</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198758839.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2016-03-24</dd></dl></td></tr></table><p>The immense problems of the twenty-first century invite innovative thinking from students, academic researchers, business research managers, and government policymakers. Hopes for raising quality in healthcare delivery, securing community safety, expanding food production, improving environmental sustainability, and much more depend on pervasive application of research solutions. This book recognizes the unbounded nature of human creativity, the multiplicative power of teamwork, and the catalytic effects of innovation. Contemporary science, engineering, and design research teams get a further boost from fresh ways of using the Web, social media, and visual communications tools that amplify collaborations. The applied and basic research heroes who take on the immense problems of the present time face bigger-than-ever challenges, but if they adopt potent guiding principles and effective research life cycle strategies, they can produce the advances that will enhance the lives of many people. These inspirational research leaders will break free from traditional thinking, disciplinary boundaries, and narrow aspirations. They will be bold innovators and engaged collaborators who are ready to lead yet open to new ideas, and self-confident yet empathetic to others. This book reports on the growing number of initiatives to promote integrated approaches to research and the expansion of these efforts. </p>Ben Shneiderman2016-03-24