Alasdair Urquhart On Nonclassical And Algebraic Logic And Complexity Of Proofs

Author : Ivo Düntsch,Edwin Mares
Publisher : Springer Nature
Page : 591 pages
File Size : 48,9 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 : Uli Fahrenberg,Mai Gehrke,Luigi Santocanale,Michael Winter
Publisher : Springer Nature
Page : 515 pages
File Size : 48,6 Mb
Release : 2021-10-22
Category : Computers
ISBN : 9783030887018

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Relational and Algebraic Methods in Computer Science by Uli Fahrenberg,Mai Gehrke,Luigi Santocanale,Michael Winter Pdf

This book constitutes the proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2021, which took place in Marseille, France, during November 2-5, 2021. The 29 papers presented in this book were carefully reviewed and selected from 35 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.

Author : Roland Glück,Luigi Santocanale,Michael Winter
Publisher : Springer Nature
Page : 309 pages
File Size : 53,8 Mb
Release : 2023-03-07
Category : Computers
ISBN : 9783031280832

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Relational and Algebraic Methods in Computer Science by Roland Glück,Luigi Santocanale,Michael Winter Pdf

This book constitutes the proceedings of the 20th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2023, which took place in Augsburg, Germany, during April 3–6, 2023. The 17 papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond. Apart from the submitted articles, this volume features the abstracts of the presentations of the three invited speakers.

Author : Varlet Blyth,Thomas Scott Blyth,J. Varlet (prof.)
Publisher : Clarendon Press
Page : 241 pages
File Size : 47,9 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 : J. Michael Dunn,Gary Hardegree
Publisher : OUP Oxford
Page : 490 pages
File Size : 40,7 Mb
Release : 2001-06-28
Category : Electronic
ISBN : 9780191589225

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Algebraic Methods in Philosophical Logic by J. Michael Dunn,Gary Hardegree Pdf

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.

Author : Anup Rao,Amir Yehudayoff
Publisher : Cambridge University Press
Page : 271 pages
File Size : 55,5 Mb
Release : 2020-02-20
Category : Computers
ISBN : 9781108497985

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Communication Complexity by Anup Rao,Amir Yehudayoff Pdf

Presents basic theory for graduate students and researchers with applications in circuit and proof complexity, streaming algorithms and distributed computing.

Author : Katalin Bimbo
Publisher : CRC Press
Page : 386 pages
File Size : 42,6 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9781466564688

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Proof Theory by Katalin Bimbo Pdf

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi

Author : Jan Krajíček
Publisher : Cambridge University Press
Page : 533 pages
File Size : 50,5 Mb
Release : 2019-03-28
Category : Computers
ISBN : 9781108416849

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Proof Complexity by Jan Krajíček Pdf

Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.

Author : Robert Dubin
Publisher : Unknown
Page : 328 pages
File Size : 52,9 Mb
Release : 1978
Category : Science
ISBN : UOM:39015002407040

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Theory Building by Robert Dubin Pdf

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 45,6 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824

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Conceptions of Set and the Foundations of Mathematics by Luca Incurvati Pdf

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author : M. D'Agostino,Dov M. Gabbay,Reiner Hähnle,J. Posegga
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401717540

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Handbook of Tableau Methods by M. D'Agostino,Dov M. Gabbay,Reiner Hähnle,J. Posegga Pdf

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.

Author : Graham Priest
Publisher : Cambridge University Press
Page : 268 pages
File Size : 46,6 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 052179434X

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An Introduction to Non-Classical Logic by Graham Priest Pdf

This book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. The material is unified by the underlying theme of world-semantics. All of the topics are explained clearly and accessibly, using devices such as tableaux proofs, and their relation to current philosophical issues and debates is discussed. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy, but which, until now, could be studied only through the research literature. It will interest those studying logic, those who need to know about non-classical logics because of their philosophical importance, and, more widely, readers working in mathematics and computer science.

Author : Christopher Cowley
Publisher : University of Chicago Press
Page : 249 pages
File Size : 45,8 Mb
Release : 2015-10-26
Category : Literary Criticism
ISBN : 9780226267920

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The Philosophy of Autobiography by Christopher Cowley Pdf

This book promises to be the first of its kind: a philosophical investigation of autobiographical writing. All of us are autobiographers at least some of the time, and all of us crave certain kinds of recognition and confirmation from others, just as we fear blame and reproach from those who know us well. The philosophy of autobiography examines this fundamental story-telling process and its place in our lives. As such it straddles a number of long-standing philosophical questions, having to do with the meaning of life, the problems of autonomy and responsibility and authenticity, the nature of self-deception and bad faith, the structure of the self and its existence through time, the question of the reliability and meaning of memory, and the problem of understanding another person and imaginatively identifying with him. The contributors to the volume are mostly philosophers, but many of them have interests outside philosophy and have been informed by research findings from literary theory and from psychiatry. Some of the contributors are also literary theorists, and one of them has even published autobiographical work. Contributors also examine specific autobiographies and diaries, of philosophers and non-philosophers, as well as fictional works using an autobiographical format, in order to explore the philosophical implications and presuppositions of the genre. The result is a most useful and productive interdisciplinary exchange.

Author : Alex Citkin,Ioannis M. Vandoulakis
Publisher : Springer
Page : 0 pages
File Size : 55,8 Mb
Release : 2023-11-10
Category : Mathematics
ISBN : 3031068459

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V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics by Alex Citkin,Ioannis M. Vandoulakis Pdf

This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Author : Ofer Arieli,Anna Zamansky
Publisher : Springer Nature
Page : 369 pages
File Size : 40,5 Mb
Release : 2021-07-30
Category : Philosophy
ISBN : 9783030712587

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Arnon Avron on Semantics and Proof Theory of Non-Classical Logics by Ofer Arieli,Anna Zamansky Pdf

This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.