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Books > Science & Mathematics > Mathematics > Mathematical foundations > General
This book provides a systematic survey of classical and recent
results on hyperbolic cross approximation. Motivated by numerous
applications, the last two decades have seen great success in
studying multivariate approximation. Multivariate problems have
proven to be considerably more difficult than their univariate
counterparts, and recent findings have established that
multivariate mixed smoothness classes play a fundamental role in
high-dimensional approximation. The book presents essential
findings on and discussions of linear and nonlinear approximations
of the mixed smoothness classes. Many of the important open
problems explored here will provide both students and professionals
with inspirations for further research.
This monograph provides a modern introduction to the theory of
quantales. First coined by C.J. Mulvey in 1986, quantales have
since developed into a significant topic at the crossroads of
algebra and logic, of notable interest to theoretical computer
science. This book recasts the subject within the powerful
framework of categorical algebra, showcasing its versatility
through applications to C*- and MV-algebras, fuzzy sets and
automata. With exercises and historical remarks at the end of each
chapter, this self-contained book provides readers with a valuable
source of references and hints for future research. This book will
appeal to researchers across mathematics and computer science with
an interest in category theory, lattice theory, and many-valued
logic.
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Computer Science Logic
- 22nd International Workshop, CSL 2008, 17th Annual Conference of the EACSL, Bertinoro, Italy, September 16-19, 2008, Proceedings
(Paperback, 2008 ed.)
Michael Kaminski, Simone Martini
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R2,429
Discovery Miles 24 290
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Out of stock
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This book constitutes the refereed proceedings of the 22nd
International Workshop on Computer Science Logic, CSL 2008, held as
the 17th Annual Conference of the EACSL in Bertinoro, Italy, in
September 2008.
The 31 revised full papers presented together with 4 invited
lectures were carefully reviewed and selected from 102 submissions.
All current aspects of logic in computer science are addressed,
ranging from foundational and methodological issues to application
issues of practical relevance. The book concludes with a
presentation of this year's Ackermann award.
This book presents a collection of recent research on topics
related to Pythagorean fuzzy set, dealing with dynamic and complex
decision-making problems. It discusses a wide range of theoretical
and practical information to the latest research on Pythagorean
fuzzy sets, allowing readers to gain an extensive understanding of
both fundamentals and applications. It aims at solving various
decision-making problems such as medical diagnosis, pattern
recognition, construction problems, technology selection, and more,
under the Pythagorean fuzzy environment, making it of much value to
students, researchers, and professionals associated with the field.
This book creates a conceptual schema that acts as a correlation
between Epistemology and Epistemic Logic. It connects both fields
and offers a proper theoretical foundation for the contemporary
developments of Epistemic Logic regarding the dynamics of
information. It builds a bridge between the view of Awareness
Justification Internalism, and a dynamic approach to Awareness
Logic. The book starts with an introduction to the main topics in
Epistemic Logic and Epistemology and reviews the disconnection
between the two fields. It analyses three core notions representing
the basic structure of the conceptual schema: "Epistemic
Awareness", "Knowledge" and "Justification". Next, it presents the
Explicit Aware Knowledge (EAK) Schema, using a diagram of three
ellipses to illustrate the schema, and a formal model based on a
neighbourhood-model structure, that shows one concrete application
of the EAK-Schema into a logical structure. The book ends by
presenting conclusions and final remarks about the uses and
applications of the EAK-Schema. It shows that the most important
feature of the schema is that it serves both as a theoretical
correlate to the dynamic extensions of Awareness Logic, providing
it with a philosophical background, and as an abstract conceptual
structure for a re-interpretation of Epistemology.
This first part presents chapters on models of computation,
complexity theory, data structures, and efficient computation in
many recognized sub-disciplines of Theoretical Computer Science.
Studies in Logic and the Foundations of Mathematics, Volume 123:
Constructivism in Mathematics: An Introduction, Vol. II focuses on
various studies in mathematics and logic, including metric spaces,
polynomial rings, and Heyting algebras. The publication first takes
a look at the topology of metric spaces, algebra, and finite-type
arithmetic and theories of operators. Discussions focus on
intuitionistic finite-type arithmetic, theories of operators and
classes, rings and modules, linear algebra, polynomial rings,
fields and local rings, complete separable metric spaces, and
located sets. The text then examines proof theory of intuitionistic
logic, theory of types and constructive set theory, and choice
sequences. The book elaborates on semantical completeness, sheaves,
sites, and higher-order logic, and applications of sheaf models.
Topics include a derived rule of local continuity, axiom of
countable choice, forcing over sites, sheaf models for higher-order
logic, and complete Heyting algebras. The publication is a valuable
reference for mathematicians and researchers interested in
mathematics and logic.
A significant number of works have set forth, over the past
decades, the emphasis laid by seventeenth-century mathematicians
and philosophers on motion and kinematic notions in geometry. These
works demonstrated the crucial role attributed in this context to
genetic definitions, which state the mode of generation of
geometrical objects instead of their essential properties. While
the growing importance of genetic definitions in sixteenth-century
commentaries on Euclid's Elements has been underlined, the place,
uses and status of motion in this geometrical tradition has however
never been thoroughly and comprehensively studied. This book
therefore undertakes to fill a gap in the history of early modern
geometry and philosophy of mathematics by investigating the
different treatments of motion and genetic definitions by seven
major sixteenth-century commentators on Euclid's Elements, from
Oronce Fine (1494-1555) to Christoph Clavius (1538-1612), including
Jacques Peletier (1517-1582), John Dee (1527-1608/1609) and Henry
Billingsley (d. 1606), among others. By investigating the
ontological and epistemological conceptions underlying the
introduction and uses of kinematic notions in their interpretation
of Euclidean geometry, this study displays the richness of the
conceptual framework, philosophical and mathematical, inherent to
the sixteenth-century Euclidean tradition and shows how it
contributed to a more generalised acceptance and promotion of
kinematic approaches to geometry in the early modern period.
The two notions of proofs and calculations are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. This volume explores this key relationship and introduces simple type theory. Starting from the familiar propositional calculus, the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system that codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. An appendix contains complete solutions of these exercises.
This book features more than 20 papers that celebrate the work of
Hajnal Andreka and Istvan Nemeti. It illustrates an interaction
between developing and applying mathematical logic. The papers
offer new results as well as surveys in areas influenced by these
two outstanding researchers. They also provide details on the
after-life of some of their initiatives. Computer science connects
the papers in the first part of the book. The second part
concentrates on algebraic logic. It features a range of papers that
hint at the intricate many-way connections between logic, algebra,
and geometry. The third part explores novel applications of logic
in relativity theory, philosophy of logic, philosophy of physics
and spacetime, and methodology of science. They include such
exciting subjects as time travelling in emergent spacetime. The
short autobiographies of Hajnal Andreka and Istvan Nemeti at the
end of the book describe an adventurous journey from electric
engineering and Maxwell's equations to a complex system of computer
programs for designing Hungary's electric power system, to
exploring and contributing deep results to Tarskian algebraic logic
as the deepest core theory of such questions, then on to
applications of the results in such exciting new areas as
relativity theory in order to rejuvenate logic itself.
This textbook introduces the representation theory of algebras by
focusing on two of its most important aspects: the Auslander-Reiten
theory and the study of the radical of a module category. It starts
by introducing and describing several characterisations of the
radical of a module category, then presents the central concepts of
irreducible morphisms and almost split sequences, before providing
the definition of the Auslander-Reiten quiver, which encodes much
of the information on the module category. It then turns to the
study of endomorphism algebras, leading on one hand to the
definition of the Auslander algebra and on the other to tilting
theory. The book ends with selected properties of
representation-finite algebras, which are now the best understood
class of algebras. Intended for graduate students in representation
theory, this book is also of interest to any mathematician wanting
to learn the fundamentals of this rapidly growing field. A graduate
course in non-commutative or homological algebra, which is standard
in most universities, is a prerequisite for readers of this book.
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