J Michael Dunn On Information Based Logics

Author : Katalin Bimbo
Publisher : Springer
Page : 436 pages
File Size : 42,9 Mb
Release : 2016-04-02
Category : Philosophy
ISBN : 9783319293004

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J. Michael Dunn on Information Based Logics by Katalin Bimbo Pdf

This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.

Author : J. Michael Dunn
Publisher : Unknown
Page : 144 pages
File Size : 50,7 Mb
Release : 2019-10-30
Category : Mathematics
ISBN : 1848903189

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The Algebra of Intensional Logics by J. Michael Dunn Pdf

J. Michael Dunn's PhD dissertation occupies a unique place in the development of the algebraic approach to logic. In The Algebra of Intensional Logics, Dunn introduced De Morgan monoids, a class of algebras in which the algebra of R (the logic of relevant implication) is free. This is an example where a logic's algebra is neither a Boolean algebra with further operations, nor a residuated distributive lattice. De Morgan monoids served as a paradigm example for the algebraization of other relevance logics, including E, the logic of entailment and R-Mingle (RM), the extension of R with the mingle axiom. De Morgan monoids extend De Morgan lattices, which algebraize the logic of first-degree entailments that is a common fragment of R and E. Dunn studied the role of the four-element De Morgan algebra D in the representation of De Morgan lattices, and from this he derived a completeness theorem for first-degree entailments. He also showed that every De Morgan lattice can be embedded into a 2-product of Boolean algebras, and proved related results about De Morgan lattices in which negation has no fixed point. Dunn also developed an informal interpretation for first-degree entailments utilizing the notion of aboutness, which was motivated by the representation of De Morgan lattices by sets. Dunn made preeminent contributions to several areas of relevance logic in his career spanning more than half a century. In proof theory, he developed sequent calculuses for positive relevance logics and a tableaux system for first-degree entailments; in semantics, he developed a binary relational semantics for the logic RM. The use of algebras remained a central theme in Dunn's work from the proof of the admissibility of the rule called γ to his theory of generalized Galois logics (or ``gaggles''), in which the residuals of arbitrary operations are considered. The representation of gaggles---utilizing relational structures---gave a new framework for relational semantics for relevance and for so-called substructural logics, and led to an information-based interpretation of them.

Author : Katalin Bimbó
Publisher : Unknown
Page : 472 pages
File Size : 50,5 Mb
Release : 2022-05-19
Category : Electronic
ISBN : 1848903952

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Relevance Logics and Other Tools for Reasoning. Essays in Honor of J. Michael Dunn by Katalin Bimbó Pdf

This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's career spanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers in this volume touch upon topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimbó was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada.

Author : Hitoshi Omori,Heinrich Wansing
Publisher : Springer Nature
Page : 324 pages
File Size : 49,6 Mb
Release : 2020-01-01
Category : Philosophy
ISBN : 9783030311360

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New Essays on Belnap-Dunn Logic by Hitoshi Omori,Heinrich Wansing Pdf

This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn. Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing. This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.

Author : Alan Ross Anderson,Nuel D. Belnap Jr.,J. Michael Dunn
Publisher : Princeton University Press
Page : 778 pages
File Size : 49,7 Mb
Release : 2017-03-14
Category : Philosophy
ISBN : 9781400887071

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Entailment, Vol. II by Alan Ross Anderson,Nuel D. Belnap Jr.,J. Michael Dunn Pdf

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : J. Michael Dunn,Gary Hardegree
Publisher : OUP Oxford
Page : 490 pages
File Size : 47,9 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 : Alexandra Silva,Renata Wassermann,Ruy de Queiroz
Publisher : Springer Nature
Page : 435 pages
File Size : 48,8 Mb
Release : 2021-10-05
Category : Philosophy
ISBN : 9783030888534

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Logic, Language, Information, and Computation by Alexandra Silva,Renata Wassermann,Ruy de Queiroz Pdf

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.

Author : George Metcalfe
Publisher : Springer Nature
Page : 309 pages
File Size : 42,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031626876

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Logic, Language, Information, and Computation by George Metcalfe Pdf

Author : Ivo Düntsch,Edwin Mares
Publisher : Springer Nature
Page : 591 pages
File Size : 55,9 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 : Elizabeth Black,Sanjay Modgil,Nir Oren
Publisher : Springer
Page : 227 pages
File Size : 41,8 Mb
Release : 2018-03-05
Category : Computers
ISBN : 9783319755533

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Theory and Applications of Formal Argumentation by Elizabeth Black,Sanjay Modgil,Nir Oren Pdf

This book constitutes the refereed proceedings of the 4th International Workshop on the Theory and Applications of Formal Argumentation, TAFA 2017, held in Melbourne, VIC, Australia, in August 2017. The workshop was co-located with International Joint Conference on Artifi cial Intelligence(IJCAI 2017). The 15 revised full papers presented were carefully reviewed and selected from 20 submissions. The workshops covers the subjects such as non-monotonic reasoning, decision making, inter-agent communication, the semantic web, grid applications, ontologies, recommender systems, machine learning, neural networks, trust computing, normative systems, social choice theory, judgement aggregation and game theory, and law and medicine.

Author : Federico L. G. Faroldi,Frederik Van De Putte
Publisher : Springer Nature
Page : 796 pages
File Size : 42,8 Mb
Release : 2023-11-25
Category : Philosophy
ISBN : 9783031294150

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Kit Fine on Truthmakers, Relevance, and Non-classical Logic by Federico L. G. Faroldi,Frederik Van De Putte Pdf

This book explores some of Kit Fine's outstanding contributions to logic, philosophy of language, philosophy of mathematics, and metaphysics, among others. Contributing authors address in-depth issues about truthmaker semantics, counterfactual conditionals, grounding, vagueness, non-classical consequence relations, and arbitrary objects, offering critical reflections and novel research contributions. Each chapter is accompanied by an extensive commentary, in which Kit Fine offers detailed responses to the ideas and themes raised by the contributors. The book includes a brief autobiography and exhaustive list of his publications to this date. This book is of interest to logicians of all stripes and to analytic philosophers more generally.

Author : Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada
Publisher : Springer
Page : 694 pages
File Size : 41,9 Mb
Release : 2017-09-01
Category : Mathematics
ISBN : 9783662556658

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Logic, Rationality, and Interaction by Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada Pdf

This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning.

Author : Can Başkent,Thomas Macaulay Ferguson
Publisher : Springer Nature
Page : 704 pages
File Size : 47,8 Mb
Release : 2020-01-01
Category : Philosophy
ISBN : 9783030253653

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Graham Priest on Dialetheism and Paraconsistency by Can Başkent,Thomas Macaulay Ferguson Pdf

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .

Author : Janusz Czelakowski
Publisher : Springer
Page : 454 pages
File Size : 48,6 Mb
Release : 2018-03-20
Category : Philosophy
ISBN : 9783319747729

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by Janusz Czelakowski Pdf

This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.

Author : Ofer Arieli,Anna Zamansky
Publisher : Springer Nature
Page : 369 pages
File Size : 43,8 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.