Petr Hajek's Books

Metamathematics of Fuzzy Logic

By: Petr Hájek

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Metamathematics of Fuzzy Logic

By: Petr Hájek

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

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304

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Springer Science & Business Media

Published Date

ISBN 10

9401153000

ISBN 13

9789401153003

Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

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Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

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Page Count

455

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475734808

ISBN 13

9781475734805

Uncertain Information Processing In Expert Systems

By: Petr Hajek,Tomas Havranek,Radim Jirousek

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Uncertain Information Processing In Expert Systems

By: Petr Hajek,Tomas Havranek,Radim Jirousek

Uncertain Information Processing in Expert Systems systematically and critically examines probabilistic and rule-based (compositional, MYCIN-like) systems, the two most important families of expert systems dealing with uncertainty. The book features a detailed introduction to probabilistic systems (including methods using graphical models and methods of knowledge integration), an analysis of compositional systems based on algebraic considerations, an application of graphical models, and the Dempster-Shafer theory of evidence and its use in expert systems. The book will be useful to anyone working in artificial intelligence, statistical computing, symbolic logic, and expert systems.

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Page Count

310

Publisher

CRC Press

Published Date

ISBN 10

0849363683

ISBN 13

9780849363689

Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

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Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

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820

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441975152

ISBN 13

9781441975157

Metamathematics of First-Order Arithmetic

By: Petr Hájek,Pavel Pudlák

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Metamathematics of First-Order Arithmetic

By: Petr Hájek,Pavel Pudlák

A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

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Page Count

475

Publisher

Cambridge University Press

Published Date

ISBN 10

1107168414

ISBN 13

9781107168411

Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

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Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

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352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038768915X

ISBN 13

9780387689159

Smooth Analysis in Banach Spaces

By: Petr Hájek,Michal Johanis

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Smooth Analysis in Banach Spaces

By: Petr Hájek,Michal Johanis

This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.

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Page Count

514

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110258994

ISBN 13

9783110258998

Logic and Implication

An Introduction to the General Algebraic Study of Non-classical Logics

By: Petr Cintula,Carles Noguera

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Logic and Implication

An Introduction to the General Algebraic Study of Non-classical Logics

By: Petr Cintula,Carles Noguera

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

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Page Count

465

Publisher

Springer Nature

Published Date

ISBN 10

3030856755

ISBN 13

9783030856755

The Comprehensive Guide to Brewing

From Raw Material to Packaging

By: Gabriela Basarová,Jan Savel,Petr Basar,Pavlína Basarová,Tomás Lejsek

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The Comprehensive Guide to Brewing

From Raw Material to Packaging

By: Gabriela Basarová,Jan Savel,Petr Basar,Pavlína Basarová,Tomás Lejsek

The Czech Republic is one of the motherlands of beer culture – beers of the pilsner brewing tradition and the aromatic Saaz hops are famous the world over. Brewing technicians and scientists from the Czech Republic have an excellent reputation and are constantly seeking an exchange and discussion of their research findings on the international scene. And the team of authors around Professor Basařová are all experienced technicians and scientists with a wealth of international experience. "The Comprehensive Guide to Brewing" is a unique groundwork for brewing technicians which deals with all subject areas, from the raw materials to packaging. It also conveys advanced knowledge of the fundamentals of brewing research. Compulsory reading for anyone who wishes to gain in-depth knowledge of brewing technology.

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Page Count

876

Publisher

Fachverlag Hans Carl

Published Date

ISBN 10

3418009247

ISBN 13

9783418009247

Yield Formation in the Main Field Crops

By: V. Cerný,L. Hruška,J. Petr

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Yield Formation in the Main Field Crops

By: V. Cerný,L. Hruška,J. Petr

This book gives a detailed overview of production processes and yield formation in field crops and permanent grasslands. Yield formation is discussed by the authors as a dynamic process, involving many factors at each stage. Knowledge of the optimum levels of individual yield components makes it possible to control this dynamic process. It is intended that this approach will help to point out gaps in the understanding of the production processes and indicate the direction for further research on this subject.The authors report on various aspects which are involved in yield formation, such as uptake of nutrients, root growth, water use, photosynthesis, transport, distribution and accumulation of photosynthates, etc. A separate chapter discusses the production process as seen from a genetic standpoint. It includes an analysis of phenotype and genotype with respect to production potential, also the heredity, variability of yield potential and new cultivation methods are mentioned. The main part of the book deals with the theory and practice of yield formation in cereals, maize, legumes, sugarbeet, potatoes, clovers and perennial grass stands.

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Page Count

337

Publisher

Elsevier

Published Date

ISBN 10

0444599509

ISBN 13

9780444599506

Mechanizing Hypothesis Formation

Principles and Case Studies

By: Jan Rauch,Milan Šimůnek,David Chudán,Petr Máša

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Mechanizing Hypothesis Formation

Principles and Case Studies

By: Jan Rauch,Milan Šimůnek,David Chudán,Petr Máša

Mechanizing hypothesis formation is an approach to exploratory data analysis. Its development started in the 1960s inspired by the question “can computers formulate and verify scientific hypotheses?”. The development resulted in a general theory of logic of discovery. It comprises theoretical calculi dealing with theoretical statements as well as observational calculi dealing with observational statements concerning finite results of observation. Both calculi are related through statistical hypotheses tests. A GUHA method is a tool of the logic of discovery. It uses a one-to-one relation between theoretical and observational statements to get all interesting theoretical statements. A GUHA procedure generates all interesting observational statements and verifies them in a given observational data. Output of the procedure consists of all observational statements true in the given data. Several GUHA procedures dealing with association rules, couples of association rules, action rules, histograms, couples of histograms, and patterns based on general contingency tables are involved in the LISp-Miner system developed at the Prague University of Economics and Business. Various results about observational calculi were achieved and applied together with the LISp-Miner system. The book covers a brief overview of logic of discovery. Many examples of applications of the GUHA procedures to solve real problems relevant to data mining and business intelligence are presented. An overview of recent research results relevant to dealing with domain knowledge in data mining and its automation is provided. Firsthand experiences with implementation of the GUHA method in the Python language are presented.

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Page Count

362

Publisher

CRC Press

Published Date

ISBN 10

100077774X

ISBN 13

9781000777741

New Infinitary Mathematics

By: Petr Vopěnka

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New Infinitary Mathematics

By: Petr Vopěnka

The dominant current of twentieth-century mathematics, which simultaneously explores and applies infinity (albeit in bizarre ideal worlds), relies on Cantor's classical theory of infinite sets. Cantor’s theory in turn relies on the problematic assumption of the existence of the set of all natural numbers, the only justification for which – a theological justification - is usually concealed and pushed into the collective unconscious. This book begins by surveying the theological background, emergence, and development of classical set theory. The author warns us about the dangers implicit in the construction of set theory, traceable in his own and other eminent mathematicians' seminal works on the subject. He then goes on to present an argument about the absurdity of the assumption of the existence of the set of all natural numbers. However, the author’s contribution is not just a negation of current views and assumptions. On the contrary, the new infinitary mathematics that he proceeds to propose and develop is driven by a cautious effort to transcend the horizon bounding the ancient geometric world and pre-set-theoretical mathematics, whilst allowing mathematics to correspond more closely to the natural real world surrounding us. The final parts are devoted to a discussion of real numbers and to demonstrating how, within the new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.

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Page Count

352

Publisher

Charles University in Prague, Karolinum Press

Published Date

ISBN 10

8024646633

ISBN 13

9788024646633

Metamathematics of Fuzzy Logic

By: Petr Hájek

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Metamathematics of Fuzzy Logic

By: Petr Hájek

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Page Count

304

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401153000

ISBN 13

9789401153003

Smooth Analysis in Banach Spaces

By: Petr Hájek,Michal Johanis

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Smooth Analysis in Banach Spaces

By: Petr Hájek,Michal Johanis

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Page Count

589

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110391996

ISBN 13

9783110391992

Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

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Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

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Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038768915X

ISBN 13

9780387689159

Uncertain Information Processing In Expert Systems

By: Petr Hajek,Tomas Havranek,Radim Jirousek

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Uncertain Information Processing In Expert Systems

By: Petr Hajek,Tomas Havranek,Radim Jirousek

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Page Count

310

Publisher

CRC Press

Published Date

ISBN 10

0849363683

ISBN 13

9780849363689

Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

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Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

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Page Count

820

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441975152

ISBN 13

9781441975157

Metamathematics of First-Order Arithmetic

By: Petr Hájek,Pavel Pudlák

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Metamathematics of First-Order Arithmetic

By: Petr Hájek,Pavel Pudlák

A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

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Page Count

475

Publisher

Cambridge University Press

Published Date

ISBN 10

1107168414

ISBN 13

9781107168411

Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

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Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

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Page Count

455

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475734808

ISBN 13

9781475734805

Mathematical Foundations of Computer Science 1995

20th International Symposium, MFCS'95, Prague, Czech Republic, August 28 - September 1, 1995. Proceedings

By: Juraj Wiedermann

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Mathematical Foundations of Computer Science 1995

20th International Symposium, MFCS'95, Prague, Czech Republic, August 28 - September 1, 1995. Proceedings

By: Juraj Wiedermann

This book presents the proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science, MFCS'95, held in Prague, Czech Republic in August/September 1995. The book contains eight invited papers and two abstracts of invited talks by outstanding scientists as well as 44 revised full research papers selected from a total of 104 submissions. All relevant aspects of theoretical computer science are addressed, particularly the mathematical foundations; the papers are organized in sections on structural complexity, algorithms, complexity theory, graphs in models of computation, lower bounds, formal languages, unification, rewriting and type theory, distributed computation, concurrency, semantics, model checking, and formal calculi.

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Page Count

614

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540602461

ISBN 13

9783540602460

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