Paraconsistency In Mathematics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Paraconsistency In Mathematics PDF full book. Access full book title Paraconsistency In Mathematics.
| Author | : Zach Weber |
| Publisher | : Cambridge University Press |
| Total Pages | : 149 |
| Release | : 2022-08-11 |
| Genre | : Science |
| ISBN | : 1009002309 |
Download Paraconsistency in Mathematics Book in PDF, ePub and Kindle
Paraconsistent logic makes it possible to study inconsistent theories in a coherent way. From its modern start in the mid-20th century, paraconsistency was intended for use in mathematics, providing a rigorous framework for describing abstract objects and structures where some contradictions are allowed, without collapse into incoherence. Over the past decades, this initiative has evolved into an area of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element provides a selective introductory survey of this research program, distinguishing between `moderate' and `radical' approaches. The emphasis is on philosophical issues and future challenges.
| Author | : Walter Alexandr Carnielli |
| Publisher | : CRC Press |
| Total Pages | : 576 |
| Release | : 2002-04-10 |
| Genre | : Mathematics |
| ISBN | : 0203910133 |
Download Paraconsistency Book in PDF, ePub and Kindle
This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.
| Author | : Holger Andreas |
| Publisher | : Springer |
| Total Pages | : 221 |
| Release | : 2016-12-02 |
| Genre | : Philosophy |
| ISBN | : 331940220X |
Download Logical Studies of Paraconsistent Reasoning in Science and Mathematics Book in PDF, ePub and Kindle
This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic’s status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency.
| Author | : Koji Tanaka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 2012-07-26 |
| Genre | : Philosophy |
| ISBN | : 9400744382 |
Download Paraconsistency: Logic and Applications Book in PDF, ePub and Kindle
A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.
| Author | : Sergei Odintsov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 241 |
| Release | : 2008-03-19 |
| Genre | : Philosophy |
| ISBN | : 1402068670 |
Download Constructive Negations and Paraconsistency Book in PDF, ePub and Kindle
Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.
| Author | : Walter Alexandr Carnielli |
| Publisher | : CRC Press |
| Total Pages | : 576 |
| Release | : 2019-10-02 |
| Genre | : Inconsistency (Logic) |
| ISBN | : 9781138466906 |
Download Paraconsistency Book in PDF, ePub and Kindle
This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.
| Author | : Jean-Yves Béziau |
| Publisher | : |
| Total Pages | : 532 |
| Release | : 2007 |
| Genre | : Computers |
| ISBN | : |
Download Handbook of Paraconsistency Book in PDF, ePub and Kindle
Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories. Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area. During the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence. This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications. The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.
| Author | : Can Başkent |
| Publisher | : Springer Nature |
| Total Pages | : 704 |
| Release | : 2020-01-01 |
| Genre | : Philosophy |
| ISBN | : 3030253651 |
Download Graham Priest on Dialetheism and Paraconsistency Book in PDF, ePub and Kindle
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 | : Zach Weber |
| Publisher | : Cambridge University Press |
| Total Pages | : 339 |
| Release | : 2021-10-21 |
| Genre | : Mathematics |
| ISBN | : 1108999026 |
Download Paradoxes and Inconsistent Mathematics Book in PDF, ePub and Kindle
Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
| Author | : Arnon Avron |
| Publisher | : |
| Total Pages | : 576 |
| Release | : 2018-05-21 |
| Genre | : |
| ISBN | : 9781848902701 |
Download Theory of Effective Propositional Paraconsistent Logics Book in PDF, ePub and Kindle
Perhaps the most counterintuitive property of classical logic (as well as of its most famous rival, intuitionistic logic) is the fact that it allows the inference of any proposition from a single pair of contradicting statements. A lot of work and efforts have been devoted over the years to develop alternatives to classical logic that do not have this drawback. Those alternatives are nowadays called `paraconsistent systems', and the corresponding research area --- paraconsistent reasoning. The purpose of this book is to provide a comprehensive methodological presentation of the rich mathematical theory that exists by now concerning the most fundamental part of paraconsistent reasoning: propositional (monotonic) logics. Among those logics it mainly concentrates on those which are effective (in the sense that they are decidable, have a concrete semantics, and can be equipped with implementable analytic proof systems). The first part of the book defines in precise terms all the basic notions that are related to paraconsistency, after reviewing all the necessary preliminaries. The other parts describe in detail all of the main approaches to the subject. This includes finite-valued semantics (both truth functional and non-deterministic); logics of formal inconsistency; relevant logics; constructive paraconsistent logics which are based on positive intuitionistic logic; and paraconsistent logics which are based on modal logics. The book covers thousands of paraconsistent logics, each of which is studied both from a semantical and from a proof theoretical points of view. In addition, most of those logics are characterized in terms of minimality or maximality properties that they may have.
