Ockham Algebras

Author : Varlet Blyth,Thomas Scott Blyth,J. Varlet (prof.)
Publisher : Clarendon Press
Page : 241 pages
File Size : 50,7 Mb
Release : 1994
Category : Language Arts & Disciplines
ISBN : 0198599382

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Ockham Algebras by Varlet Blyth,Thomas Scott Blyth,J. Varlet (prof.) Pdf

An Ockham algebra is a natural generalization of a well known and important notion of a boolean algebra. Regarding the latter as a bounded distributive lattice with complementation (a dual automorphism of period 2) by a dual endomorphism that satisfies the de Morgan laws, this seeminglymodest generalization turns out to be extemely wide. The variety of Ockham algebras has infinitely many subvarieties including those of de Morgan algebras, Stone algebras, and Kleene algebras. Folowing pioneering work by Berman in 1977, many papers have appeared in this area oflattice theory towhich several important results in the theory of universal algebra are highly applicable. This is the first unified account of some of this research. Particular emphasis is placed on Priestly's topological duality, which invloves working with ordered sets and order-reversing maps, hereby involvingmany problems of a combinatorial nature. Written with the graduate student in mind, this book provides an ideal overview of this are of increasing interest.

Author : Thomas Scott Blyth
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 1994
Category : Ockham algebras
ISBN : 138303107X

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Ockham Algebras by Thomas Scott Blyth Pdf

Author : Anonim
Publisher : American Mathematical Soc.
Page : 262 pages
File Size : 46,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821895885

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Ordered Sets and Lattices II by Anonim Pdf

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

Author : Jorge Almeida,Gabriela Bordalo,Philip Dwinger
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 55,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489926081

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Lattices, Semigroups, and Universal Algebra by Jorge Almeida,Gabriela Bordalo,Philip Dwinger Pdf

This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.

Author : Ivo Düntsch,Edwin Mares
Publisher : Springer Nature
Page : 591 pages
File Size : 41,9 Mb
Release : 2021-09-24
Category : Philosophy
ISBN : 9783030714307

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Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs by Ivo Düntsch,Edwin Mares Pdf

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

Author : Guojun Wang,Yongming Li,Bin Zhao
Publisher : World Scientific
Page : 724 pages
File Size : 50,7 Mb
Release : 2012
Category : Computers
ISBN : 9789814401524

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Quantitative Logic and Soft Computing by Guojun Wang,Yongming Li,Bin Zhao Pdf

The QL&SC 2012 is a major symposium for scientists, and practitioners all around the world to present their latest reseaches, results, ideas, developments and applications in such areas as quantitative logic, many-valued logic, fuzzy logic, quantification of software, artificial intelligence, fuzzy sets and systems and soft computing. This invaluable book provides a broad introduction to the fuzzy reasoning and soft computing. It is certain one should not go too far in approximation and optimization, and a certain degree must be kept in mind. This is the essential idea of quantitative logic and soft computing. The explanations in the book are complete to provide the necessary background material needed to go further into the subject and explore the research literature. It is suitable reading for graduate students. It provides a platform for mutual exchanges from top experts and scholars around the world in this field.

Author : Yongming Li
Publisher : World Scientific
Page : 724 pages
File Size : 49,6 Mb
Release : 2012
Category : Computers
ISBN : 9789814401531

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Quantitative Logic and Soft Computing by Yongming Li Pdf

The QL&SC 2012 is a major symposium for scientists, and practitioners all around the world to present their latest researches, results, ideas, developments and applications in such areas as quantitative logic, many-valued logic, fuzzy logic, quantification of software, artificial intelligence, fuzzy sets and systems and soft computing. This invaluable book provides a broad introduction to the fuzzy reasoning and soft computing. It is certain one should not go too far in approximation and optimization, and a certain degree must be kept in mind. This is the essential idea of quantitative logic and soft computing. The explanations in the book are complete to provide the necessary background material needed to go further into the subject and explore the research literature. It is suitable reading for graduate students. It provides a platform for mutual exchanges from top experts and scholars around the world in this field.

Author : Vladimir Kuchmei
Publisher : Unknown
Page : 99 pages
File Size : 48,5 Mb
Release : 2003
Category : Electronic
ISBN : 9985567420

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Affine Completeness of Some Ockham Algebras by Vladimir Kuchmei Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Author : L. Szabó,A. Szendrei
Publisher : Elsevier
Page : 657 pages
File Size : 45,5 Mb
Release : 2016-01-22
Category : Mathematics
ISBN : 9781483295404

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Lectures in Universal Algebra by L. Szabó,A. Szendrei Pdf

These 34 papers cover topics ranging from various problems on varieties and other classes of algebras including categorical aspects and duality theory to the structure of finite algebras and clones on finite (or infinite) sets.As well as survey articles by invited speakers, the papers contain full proofs of new results not published elsewhere. The volume ends with a list of problems.

Author : Balder D. ten Cate,Henk W. Zeevat
Publisher : Springer
Page : 282 pages
File Size : 54,5 Mb
Release : 2007-09-04
Category : Philosophy
ISBN : 9783540751441

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Logic, Language, and Computation by Balder D. ten Cate,Henk W. Zeevat Pdf

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book represents the thoroughly refereed post-proceedings of the 6th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2005, held in Batumi, Georgia. The 19 revised full papers presented were carefully reviewed and selected from numerous presentations at the symposium. The papers present current research in all aspects of linguistics, logic and computation.

Author : Anonim
Publisher : Unknown
Page : 390 pages
File Size : 42,8 Mb
Release : 2008
Category : Algebra
ISBN : UOM:39015072631461

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Algebra Colloquium by Anonim Pdf

Author : K. Denecke,M. Erné,S.L. Wismath
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 41,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781402018985

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Galois Connections and Applications by K. Denecke,M. Erné,S.L. Wismath Pdf

Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint situation" is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari eties, and conversely. Moreover, restriction to the "Galois-closed" or "Galois-open" objects (the fixed points of the composite maps) leads to a precise "duality between two maximal subworlds".

Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 688 pages
File Size : 44,8 Mb
Release : 2002-11-21
Category : Mathematics
ISBN : 3764369965

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General Lattice Theory by George Grätzer Pdf

"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS

Author : Ivo G. Rosenberg,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 565 pages
File Size : 46,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401706971

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Algebras and Orders by Ivo G. Rosenberg,Gert Sabidussi Pdf

In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.