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| algebraic methods in philosophical logic: Algebraic Methods in Philosophical Logic J. Michael Dunn, Gary Hardegree, 2001-06-28 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. |
| algebraic methods in philosophical logic: Algebraic Methods in Philosophical Logic J. Michael Dunn, Gary M. Hardegree, 2001 |
| algebraic methods in philosophical logic: Interpolation and Definability Dov M. Gabbay, Larisa Maksimova, 2005-05-12 This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control. |
| algebraic methods in philosophical logic: Algebraic Methods in General Rough Sets A. Mani, Gianpiero Cattaneo, Ivo Düntsch, 2019-01-11 This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value. |
| algebraic methods in philosophical logic: Algebraic Set Theory André Joyal, Ieke Moerdijk, 1995-09-14 This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic. |
| algebraic methods in philosophical logic: An Algebraic Introduction to Mathematical Logic D.W. Barnes, J.M. Mack, 2013-06-29 This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory. |
| algebraic methods in philosophical logic: The Evolution of Logic W. D. Hart, 2010-08-23 Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy. |
| algebraic methods in philosophical logic: Symbolic Logic Gary M. Hardegree, 2011 |
| algebraic methods in philosophical logic: An Investigation of the Laws of Thought George Boole, 1854 |
| algebraic methods in philosophical logic: Ewa Orłowska on Relational Methods in Logic and Computer Science Joanna Golińska-Pilarek, Michał Zawidzki, 2018-12-20 This book is a tribute to Professor Ewa Orłowska, a Polish logician who was celebrating the 60th year of her scientific career in 2017. It offers a collection of contributed papers by different authors and covers the most important areas of her research. Prof. Orłowska made significant contributions to many fields of logic, such as proof theory, algebraic methods in logic and knowledge representation, and her work has been published in 3 monographs and over 100 articles in internationally acclaimed journals and conference proceedings. The book also includes Prof. Orłowska’s autobiography, bibliography and a trialogue between her and the editors of the volume, as well as contributors' biographical notes, and is suitable for scholars and students of logic who are interested in understanding more about Prof. Orłowska’s work. |
| algebraic methods in philosophical logic: Philosophy of Logical Systems Jaroslav Peregrin, 2019-11-11 This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent the new logic only engaged new and more powerful instruments to answer the questions posed by the old one, and to what extent it replaced these questions with new ones. Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic; classifies the various tools which were adopted to build such languages; gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment; discusses what can actually be achieved by relocating the problems of logic from natural language into them; and reaches certain conclusions with respect to the possibilities and limitations of this formal turn of logic. This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard (and not so standard) logical systems that were established during the short history of modern logic. |
| algebraic methods in philosophical logic: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| algebraic methods in philosophical logic: Proof Theory and Algebra in Logic Hiroakira Ono, 2019-08-02 This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic. |
| algebraic methods in philosophical logic: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1927 The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century. |
| algebraic methods in philosophical logic: The Semantics and Proof Theory of the Logic of Bunched Implications David J. Pym, 2013-04-17 This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts. |
| algebraic methods in philosophical logic: Handbook of Philosophical Logic Dov M. Gabbay, Franz Guenthner, 2013-03-09 It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other. |
| algebraic methods in philosophical logic: Hiroakira Ono on Substructural Logics Nikolaos Galatos, Kazushige Terui, 2021-12-13 This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic. |
| algebraic methods in philosophical logic: Philosophy of Logic , 2006-11-29 The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter |
| algebraic methods in philosophical logic: The Mathematics of Metamathematics Helena Rasiowa, Roman Sikorski, 1963 |
| algebraic methods in philosophical logic: Quantum Logic in Algebraic Approach Miklós Rédei, 2013-03-09 This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J. |
| algebraic methods in philosophical logic: Paraconsistent Logic: Consistency, Contradiction and Negation Walter Carnielli, Marcelo Esteban Coniglio, 2016-06-14 This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. |
| algebraic methods in philosophical logic: Introduction to Mathematical Philosophy Bertrand Russell, 2007-04-01 Not to be confused with the philosophy of mathematics, mathematical philosophy is the structured set of rules that govern all existence. Or, in a word: logic. While this branch of philosophy threatens to be an intimidating and abstract subject, it is one that is surprisingly simple and necessarily sensible, particularly at the pen of writer Bertrand Russell, who infuses this work, first published in 1919, with a palpable and genuine desire to assist the reader in understanding the principles he illustrates. Anyone interested in logic and its development and application here will find a comprehensive and accessible account of mathematical philosophy, from the idea of what numbers actually are, through the principles of order, limits, and deduction, and on to infinity. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959). |
| algebraic methods in philosophical logic: Natural Dualities for the Working Algebraist David M. Clark, Brian A. Davey, 1998-11-12 First text in subject; aimed at algebraists, category theorists in mathematics and computer science. |
| algebraic methods in philosophical logic: Logical Options John L. Bell, David DeVidi, Graham Solomon, 2001-03-30 Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work. |
| algebraic methods in philosophical logic: Intermediate Quantities Philip Peterson, 2020-07-24 This title was first published in 2000: Intermediate quantifiers express logical quantities which fall between Aristotle's two quantities of categorical propositions - universal and particular. Few, many and most express the most commonly referred to intermediate quantifiers, but this book argues that an infinite number can be understood through a deeper examination of the logical nature of all intermediate quantifiers. Presenting and analyzing the logical and linguistic features of intermediate quantifiers, in a fashion typical of traditional logic, Philip L. Peterson presents an account integrating the logic and semantics of intermediate quantifiers with the two traditional quantities by traditional methods. Having introduced the basic idea of how to approach the task in the first chapter, with heavy emphasis on the linguistic meanings and ordinary uses of English intermediate quantifier expressions, Peterson then undertakes the task of completely integrating the three basic intermediate quantities into traditional logic in the following chapter. |
| algebraic methods in philosophical logic: Mathematics and Its Logics Geoffrey Hellman, 2021-02-04 The essays in this volume present a sustained case for a healthy pluralism in mathematics and its logics. |
| algebraic methods in philosophical logic: The Structure of Models of Peano Arithmetic Roman Kossak, James Schmerl, 2006-06-29 Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups. |
| algebraic methods in philosophical logic: Philosophical and Mathematical Logic Harrie de Swart, 2018-11-28 This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since if ..., then ... can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo |
| algebraic methods in philosophical logic: Logic and Structure Dirk van Dalen, 2013-11-11 Logic appears in a 'sacred' and in a 'profane' form. The sacred form is dominant in proof theory, the profane form in model theory. The phenomenon is not unfamiliar, one observes this dichotomy also in other areas, e.g. set theory and recursion theory. For one reason or another, such as the discovery of the set theoretical paradoxes (Cantor, Russell), or the definability paradoxes (Richard, Berry), a subject is treated for some time with the utmost awe and diffidence. As a rule, however, sooner or later people start to treat the matter in a more free and easy way. Being raised in the 'sacred' tradition, I was greatly surprised (and some what shocked) when I observed Hartley Rogers teaching recursion theory to mathema ticians as if it were just an ordinary course in, say, linear algebra or algebraic topology. In the course of time I have come to accept his viewpoint as the didac tically sound one: before going into esoteric niceties one should develop a certain feeling for the subject and obtain a reasonable amount of plain working knowledge. For this reason I have adopted the profane attitude in this introductory text, reserving the more sacred approach for advanced courses. Readers who want to know more about the latter aspect of logic are referred to the immortal texts of Hilbert-Bernays or Kleene. |
| algebraic methods in philosophical logic: Plato's Ghost Jeremy Gray, 2008-09-02 Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics. |
| algebraic methods in philosophical logic: The Law of Non-Contradiction Graham Priest, JC Beall, Bradley Armour-Garb, 2006-11-30 The Law of Non-Contradiction-that no contradiction can be true-has been a seemingly unassailable dogma since the work of Aristotle, in Book Gamma of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. One of the editors contributes an introduction which surveys the issues and serves to frame the debate. This collection will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. |
| algebraic methods in philosophical logic: Topological Duality for Distributive Lattices Mai Gehrke, Sam van Gool, 2024-03-07 Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory. |
| algebraic methods in philosophical logic: Inferentialism J. Peregrin, 2014-09-26 In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms. |
| algebraic methods in philosophical logic: Consequence Relations Alex Citkin, Alexei Muravitsky, 2022 An in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, intended for advanced undergraduate and graduate students in mathematics and philosophy, as well as researchers in the field of mathematical and philosophical logic. |
| algebraic methods in philosophical logic: Relational and Algebraic Methods in Computer Science Jules Desharnais, Walter Guttmann, Stef Joosten, 2018-10-22 This book constitutes the proceedings of the 17th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2018, held in Groningen, The Netherlands, in October/November 2018. The 21 full papers and 1 invited paper presented together with 2 invited abstracts and 1 abstract of a tutorial were carefully selected from 31 submissions. The papers are organized in the following topics: Theoretical foundations; reasoning about computations and programs; and applications and tools. |
| algebraic methods in philosophical logic: Formal Theories of Truth J. C. Beall, Michael Glanzberg, David Ripley, 2018 Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth. |
| algebraic methods in philosophical logic: Neural Mechanisms Fabrizio Calzavarini, Marco Viola, 2020-12-02 This volume brings together new papers advancing contemporary debates in foundational, conceptual, and methodological issues in cognitive neuroscience. The different perspectives presented in each chapter have previously been discussed between the authors, as the volume builds on the experience of Neural Mechanisms (NM) Online – webinar series on the philosophy of neuroscience organized by the editors of this volume. The contributed chapters pertain to five core areas in current philosophy of neuroscience. It surveys the novel forms of explanation (and prediction) developed in cognitive neuroscience, and looks at new concepts, methods and techniques used in the field. The book also highlights the metaphysical challenges raised by recent neuroscience and demonstrates the relation between neuroscience and mechanistic philosophy. Finally, the book dives into the issue of neural computations and representations. Assembling contributions from leading philosophers of neuroscience, this work draws upon the expertise of both established scholars and promising early career researchers. |
| algebraic methods in philosophical logic: Mathematics, Logic, and their Philosophies Mojtaba Mojtahedi, Shahid Rahman, Mohammad Saleh Zarepour, 2021-02-09 This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community. |
| algebraic methods in philosophical logic: The Routledge Handbook of Propositions Chris Tillman, Adam Russell Murray, 2022-09-30 Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research. |
| algebraic methods in philosophical logic: New Essays on Belnap-Dunn Logic Hitoshi Omori, Heinrich Wansing, 2020-01-01 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. |
Algebraic Methods in Philosophical Logic - gbv.de
Algebraic Methods in Philosophical Logic J. MICHAEL DUNN and GARY M. HARDEGREE CLARENDON PRESS • OXFORD 2001
AN ALGEBRAIC APPROACH - api.pageplace.de
logic and the theory of Boolean algebras has been known for a long time. One of the turning points in the algebraic study of logic was the introduction by Lindenbaum and Tarski of the …
The algebra of logic - Archive.org
Mathematical Logic is a necessary preliminary to logical Mathematics. “Mathematical Logic” is the name given by. Logic”; and Symbolic Logic is, in essentials, the Logic of Aristotle, given new …
Mathematical Methods in Philosophy - Banff International …
Philosophical logic includes logical systems such as logics of possibility and necessity (alethic modal logic), of time (temporal logic), of knowledge and belief (epistemic and doxastic logic), …
Applying Algebraic Logic to Logic - Springer
In the present paper we define the algebraic counterpart Alg,(C) of a logic C together with the algebraic counterpart Algm(C) of semantical-model theoretical ingredients of C.
Algebra is the Language of Mathematics & Algebraic …
Using algebraic structures to represent and manipulate philosophical concepts and arguments, aiming for greater clarity and precision. The process of formalizing philosophical arguments …
Hajnal Andréka Zalán Gyenis István Németi Ildikó Sain …
logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and …
Algebraic Methods In Philosophical Logic J Michael Dunn(3)
introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) …
Non-classical Logics: Theory, Applications and Tools
Paraconsistent logics are logics which allow contradictory but non-trivial theories. A propositional logic L is paraconsistent (with respect to :) if there are L-formulas A; B, such that A; :A 6`B. …
Algebraic methods in philosophical logic - web.flu.cas.cz
5.3 Algebraic Semantics for Sententia1 Languages 144 5.4 Truth-Value Semantics 146 5.5 Possible Worlds Semantics 148 5.6 Logica1 Matrices and Logical Atlases 152 5.7 …
An Algebraic Approach To Non Classical Logics (book)
Hiroakira Ono,2019-08-02 This book offers a concise introduction to both proof theory and algebraic methods the core of the syntactic and semantic study of logic respectively The …
Logic, and Some Philosophical Remarks on
A few decades ago, the reigning cliche in the philosophy of mathematics was "the three schools": logicism (Frege-Russell-Carnap), formalism (Hilbert), intuitionism (Brouwer).
David Hilbert’s contributions to logical theory - University of …
In the following examination of how model theory, proof theory, and the modern concept of logical completeness each emerged from Hilbert’s thought, one theme recurs as a unifying motif: …
Algebraic Methods In Philosophical Logic J Michael Dunn …
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 …
Logic and Philosophical Methodology - Princeton University
One side of the question of logic and philosophical methodology is that of the application of logic in philosophy. Since logic has traditionally been regarded as a methodological discipline, it is …
Dual Intuitionistic Logic and a Variety of Negations: The Logic …
We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of …
LOGIC IN PHILOSOPHY - Universiteit van Amsterdam
Stanford course 'Logic in Philosophy' (2003D), and it will be the basis for a new textbook in philosophical logic. Our first two themes show how some of the core ideas of pre-modern logic …
Algebraic Logic and Topoi; a Philosophical Holistic Approach
We take a magical tour in algebraic logic and its most novel applica-tions. In algebraic logic we start from classical results on neat embed-dings due to Andre ka, Henkin, N emeti, Monk and …
Refutation systems: an overview and some applications to …
In this paper we provide a concise, but comprehensively referenced overview of the literature on refutation systems and discuss some of their applications to philosophical logics. Consider a …
OXFORD LOGIC GUIDES - Johns Hopkins University
Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. The challenge for me was to make the basic definitions, theorems, …
Book Reviews - sedici.unlp.edu.ar
J. Michael Dunn and Gary M. Hardegree, Algebraic Methods in Philosophical Logic, Oxford Logic Guides, no.41, Clarendon Press, Oxford University Press, Oxford, New York, etc., 2001, pp xv …
Alfred Tarski. Life and Logic - American Mathematical Society
logic at the University of California, Berkeley, that ... rigorous philosophical work in this area. The second major movement that affected, and was affected by, Tarski was the Unity of Science ...
The Mathematics of Logic - Cambridge University Press
Mathematical logic has been in existence as a recognised branch of mathe-matics for over a hundred years. Its methods and theorems have shown their applicability not just to …
The Introduction of Topology into Analytic Philosophy: Two …
logics and certain modal logics as logics of the topological closure operator. Within logic, these ideas have been very influential. Nevertheless, one might protest that these connections fell …
Algebraic Foundations Of Many Valued Reasoning Trends In …
Algebraic Foundations Of Many Valued Reasoning Trends In Logic: Algebraic Foundations of Many-Valued Reasoning R.L. Cignoli,Itala M. d'Ottaviano,Daniele Mundici,2013-03-09 This ...
CHAPTER 11 Introduction to Intuitionistic Logic - Stony Brook …
Introduction to Intuitionistic Logic Intuitionistic logic has developed as a result of certain philosophical views on the foundation of mathematics, known as intuitionism. Intuitionism was …
BOOK SERIES - STUDIA LOGICA LIBRARY - JSTOR
Trends in Logic Editor-in-chief: Heinrich Wansing e-mail: Heinrich.Wansing@rub.de Outstanding Contributions to Logic Editor-in-chief: Sven Ove Hansson e-mail: soh@kth.se Logic in Asia …
Logic and Algebraic Structures in Quantum Computing
Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, ... 978-1-107-03339-9 - Logic …
First Order Predicate Calculus - www.api.orats
Mathematicians First-Order Modal Logic First Order Mathematical Logic Logic and Implication Logic & Natural Language First-Order Dynamic Logic Logic for Philosophy Metalogic Logic for …
BOOK SERIES - STUDIA LOGICA LIBRARY - JSTOR
BOOK SERIES - STUDIA LOGICA LIBRARY Book series founded by Ryszard Wójcicki Studia Logica library consists of three subseries: Trends in Logic Editor-in-chief: Heinrich Wansing
TheGeometrizationofMeaning arXiv:2104.13288v2 [math.LO] …
a preliminary philosophical analysis of the results obtained so far. They concern formalized algebraic theories with axioms in the form of equational laws, theories based on propositional …
Contents of Volume 109 i467 - JSTOR
Joanna Golińska-Pilarek and Michał Zawidzki, (eds.), Ewa Orłowska on Relational Methods in Logic and Computer Science I. Rewitzky 443 ... (Eds.), Recent Trends in Philosophical Logic , …
A Mathematical Introduction to Logic, 2nd Edition - McGill …
CHAPTER ONE Sentential Logic 11 1.0 Informal Remarks on Formal Languages 11 1.1 The Language of Sentential Logic 13 1.2 Truth Assignments 20 1.3 A Parsing Algorithm 29 1.4 …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
Unlocking the Power of Algebraic Methods: A …
Algebraic methods extend to inequalities, which express relationships of "greater than," "less than," "greater than or equal to," and "less than or equal to." Key aspects include: Solving …
Unlocking the Power of Algebraic Methods: A …
Algebraic methods extend to inequalities, which express relationships of "greater than," "less than," "greater than or equal to," and "less than or equal to." Key aspects include: Solving …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
BASIC CONCEPTS OF LOGIC - UMass
1. WHAT IS LOGIC? Logic may be defined as the science of reasoning. However, this is not to suggest that logic is an empirical (i.e., experimental or observational) science like physics, …
Mathematical Logic for Mathematicians, Part I
1.2. THE LANGUAGE OF MATHEMATICS 9 1. ^will denote and. 2. _will denote or. 3. :will denote not. 4. !will denote implies. In order to ignore the nagging question of what constitutes a …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
The general algebraic framework for Mathematical Fuzzy Logic
based fuzzy logics: Methods and algebraic equivalencies. Annals of Pure and Applied Logic, 160:53{81, 2009. [5] Petr Cintula, Christian G. Fermuller, Petr H ajek, and Carles Noguera, …
LOGIC IN PHILOSOPHY - Universiteit van Amsterdam
methods rather than rigid subfields. It is themes and their metamorphoses across subdisciplines that provide the coherence of a field. Here is the worst that can happen. Some atlases of …
Tautologies - Logic Matters
(2)Philosophical remarks about the relation between the technical notions and correspond-ing informal ideas (tautology vs logical truth, tautological entailment vs logical entail-ment). A bit of …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
Introduction to CATEGORY THEORY and CATEGORICAL …
course in basic algebra or topology because algebraic structures like groups, rings, modules etc. and topological spaces serve as the most important source of examples illustrating the …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
An Introduction to Symbolic Logic - old.maa.org
The next key step in this revolution in logic was made by the great German mathematician and philosopher Gottlob Frege. Frege created a powerful and profoundly original symbolic system …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
Quantumlogicandmeaning - arXiv.org
further philosophical justification that would go beyond purely formal semantic methods, our argument justifies Fine’s claim that it is not the classical distributive law that fails in QM: …
Beginning Mathematical Logic: A Study Guide - Logic Matters
undergraduate courses on mathematical logic. And serious logic is taught less and less in philosophy departments too. Yet logic itself remains as exciting and rewarding a subject as it …
Fundamentals of Fuzzy Logics
understanding of the logic, while algebraic semantics may be necessary to establish mathematical properties; for investigating proofs in a logic and defining automated rea-soning methods, …
Lukasiewiczs Logics And Prime Numbers [PDF] - now.acs.org
fatalism and prime numbers What do logic and prime numbers have in common The book adopts truth functional approach to examine functional properties of finite valued Lukasiewicz logics …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
Modal Logic: A Semantic Perspective - Universiteit van …
3.3 Invariance and definability in first-order logic 14 3.4 Invariance and definability in modal logic 15 3.5 Modal logic and first-order logic compared 16 3.6 Bisimulation as a game 18 4 …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
An Introduction To Philosophical Logic 3rd Edition (book)
Philosophical logic is essential for understanding the structure of arguments and evaluating their validity. It helps us identify fallacies, refine our reasoning, and communicate our ideas ...
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
ALGEBRAIC LOGIC - Renyi
2 ALGEBRAIC LOGIC INTRODUCTION Algebraic logic can be divided into two main parts. Part I studies algebras which are relevant to logic(s), e.g. algebras which were obtained from logics …
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Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
12 Going further - Logic Matters
4. Ren´e Cori and Daniel Lascar, Mathematical Logic, A Course with Exer-cises: Part I (OUP, 2000), Chapter 2. And for a higher-level treatment of intuitionistic logic and Heyting algebras, …
TheEvolutionofRoughSets 1970s–1981 - arXiv.org
Theeffectoftheworkbythisgroupresultedinthecreationofanucleusoftheteamthat subsequentlyworkedatWarsawUniversity,mostlywithinthesectionoftheMathematical
en-maneco.modares.ac.ir
Humberstone, L., 2015, Philosophical Applications of Modal Logic, College Publications. Jaquette, D, 2002, A Companion to Philosophical Logic, Blackwell.
The Place and Value of Logic in Louis Couturat’s …
closer look at his work at large, the place and value of logic are not simple problems for Couturat. On one hand, the logic differs from the Greek methods of Aristotelian logic, and yet it has no …
PROVABILITY LOGIC - City University of New York
Handbook of Philosophical Logic, ... ability. Independently, the same notion appeared in an algebraic context in the work of R. Magari and his school in Italy (see [Magari, 1975b]). A dra- …
