Andrzej Mostowski And Foundational Studies

Author : A. Ehrenfeucht,V.W. Marek,M. Srebrny
Publisher : IOS Press
Page : 460 pages
File Size : 51,7 Mb
Release : 2008-03-06
Category : Mathematics
ISBN : 9781607502722

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Andrzej Mostowski and Foundational Studies by A. Ehrenfeucht,V.W. Marek,M. Srebrny Pdf

Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and human. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of foundations of mathematics. He is best known of the Kleene-Mostowski and Davis-Mostowski hierarchies of properties of integers reflecting the complexity of their definitions, and of the very elegant concept of a generalized quantifier which inspired and keeps stimulating a stream of deep work on fundamental issues of logics, deduction and reasoning both in mathematics and in computer science, and also of the contributions and excellent lectures on undecidability, unprovability, consistency and independence of various statements in set theory and arithmetic following Gödel, Tarski and Cohen. The overall content of the volume is designed to cover the current main streams in the field. For many years after WWII, especially in the late sixties, till his untimely death in 1975, Warsaw - where he led the centre of foundational studies - was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.

Author : Andrzej Ehrenfeucht,Wiktor Marek,Marian Srebrny
Publisher : Unknown
Page : 447 pages
File Size : 52,6 Mb
Release : 2013
Category : Electronic
ISBN : 161499305X

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Andrzej Mostowski and Foundational Studies by Andrzej Ehrenfeucht,Wiktor Marek,Marian Srebrny Pdf

Author : Andrzej Mostowski,Kazimierz Kuratowski
Publisher : Elsevier
Page : 615 pages
File Size : 40,8 Mb
Release : 1979
Category : Logic, Symbolic and mathematical
ISBN : 9780444851031

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Foundational Studies by Andrzej Mostowski,Kazimierz Kuratowski Pdf

Provability, Computability and Reflection.

Author : Andrzej Ehrenfeucht,V. Wiktor Marek,Marian Srebrny
Publisher : Unknown
Page : 447 pages
File Size : 52,5 Mb
Release : 2008
Category : Logic, Symbolic and mathematical
ISBN : 1433712261

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Andrzej Mostowski and Foundational Studies by Andrzej Ehrenfeucht,V. Wiktor Marek,Marian Srebrny Pdf

Andrzej Mostowski was one of the leading 20th century logicians. This volume examines his legacy, devoted both to his scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. It includes the bibliography of Mostowski's writings.

Author : Andrzej Mostowski
Publisher : IOS Press
Page : 460 pages
File Size : 42,8 Mb
Release : 2008
Category : Biography & Autobiography
ISBN : 9781586037826

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Andrzej Mostowski and Foundational Studies by Andrzej Mostowski Pdf

Andrzej Mostowski was one of the leading 20th century logicians. This volume examines his legacy, devoted both to his scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. It includes the bibliography of Mostowski's writings.

Author : Andrzej Mostowski
Publisher : Unknown
Page : 190 pages
File Size : 46,5 Mb
Release : 1966
Category : Logic, Symbolic and mathematical
ISBN : UOM:39015038906957

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Thirty Years of Foundational Studies by Andrzej Mostowski Pdf

Author : Ángel Garrido,Urszula Wybraniec-Skardowska
Publisher : Birkhäuser
Page : 815 pages
File Size : 44,6 Mb
Release : 2018-06-12
Category : Mathematics
ISBN : 9783319654300

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The Lvov-Warsaw School. Past and Present by Ángel Garrido,Urszula Wybraniec-Skardowska Pdf

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

Author : Giovanni Sommaruga
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 42,7 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9789400704312

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Foundational Theories of Classical and Constructive Mathematics by Giovanni Sommaruga Pdf

The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
Page : 653 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662090589

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Ω-Bibliography of Mathematical Logic by Heinz-Dieter Ebbinghaus Pdf

Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.

Author : Ronald J. Brachman,Hector J. Levesque,Ray Reiter
Publisher : Morgan Kaufmann Publishers
Page : 542 pages
File Size : 55,9 Mb
Release : 1989
Category : Computers
ISBN : UOM:39015015494266

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Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning by Ronald J. Brachman,Hector J. Levesque,Ray Reiter Pdf

Proceedings held May 1989. Topics include temporal logic, hierarchical knowledge bases, default theories, nonmonotonic and analogical reasoning, formal theories of belief revision, and metareasoning. Annotation copyright Book News, Inc. Portland, Or.

Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 634 pages
File Size : 45,5 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080955002

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Provability, Computability and Reflection by Lev D. Beklemishev Pdf

Provability, Computability and Reflection

Author : Andrew McFarland,Joanna McFarland,James T. Smith
Publisher : Springer
Page : 499 pages
File Size : 49,8 Mb
Release : 2014-08-11
Category : Mathematics
ISBN : 9781493914746

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Alfred Tarski by Andrew McFarland,Joanna McFarland,James T. Smith Pdf

Alfred Tarski (1901–1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now. This self-contained book focuses on Tarski’s early contributions to geometry and mathematics education, including the famous Banach–Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski’s later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski’s years in Poland. Alfred Tarski: Early Work in Poland serves the mathematical, educational, philosophical and historical communities by publishing Tarski’s early writings in a broadly accessible form, providing background from archival work in Poland and updating Tarski’s bibliography. A list of errata can be found on the author Smith’s personal webpage.

Author : Gerhard Jäger,Wilfried Sieg
Publisher : Springer
Page : 551 pages
File Size : 54,8 Mb
Release : 2018-04-04
Category : Mathematics
ISBN : 9783319633343

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Feferman on Foundations by Gerhard Jäger,Wilfried Sieg Pdf

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

Author : Roman Murawski
Publisher : Springer
Page : 228 pages
File Size : 44,8 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9783034808316

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The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland by Roman Murawski Pdf

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm.

Author : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 50,8 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9783319062334

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.