Proof Theory of N4 Paraconsistent Logics

Author: Norihiro Kamide
ISBN: 1848901674
Release Date: 2015-01-20
Genre: Mathematics

The present book is the first monograph ever with a central focus on the proof theory of paraconsistent logics in the vicinity of the four-valued, constructive paraconsistent logic N4 by David Nelson. The volume brings together a number of papers the authors have written separately or jointly on various systems of inconsistency-tolerant logic. The material covers the structural proof theory of N4, its fragments, including first-degree entailment logic, related logics, such as trilattice logics, connexive systems, systems of symmetric and dual paraconsistent logic, and variations of bi-intuitionistic logic, paraconsistent temporal logics, substructural subsystems of N4, such as paraconsistent intuitionistic linear logics, paraconsistent logics based on involutive quantales, and paraconsistent Lambek logics. Although the proof-theory of N4 and N4-related logics is the central theme of the present monograph, models and model-theoretic semantics also play an important role in the presentation. The relational, Kripke-style models that are dealt with provide a motivating and intuitively appealing insight into the logics with respect to which they are shown to be sound and complete. Nevertheless, the emphasis is on Gentzen-style proof systems -in particular sequent calculi of a standard and less standard kind- for paraconsistent logics, and cut-elimination and its consequences are a central topic throughout. A unifying element of the presentation is the repeated application of embedding theorems in order to transfer results from other logics such as intuitionistic logic to the paraconsistent case.

J Michael Dunn on Information Based Logics

Author: Katalin Bimbo
Publisher: Springer
ISBN: 9783319293004
Release Date: 2016-04-02
Genre: Philosophy

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.

Paraconsistent Logic Consistency Contradiction and Negation

Author: Walter Carnielli
Publisher: Springer
ISBN: 9783319332055
Release Date: 2016-06-14
Genre: Philosophy

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.

Constructive Negations and Paraconsistency

Author: Sergei Odintsov
Publisher: Springer Science & Business Media
ISBN: 1402068670
Release Date: 2008-03-19
Genre: Philosophy

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.

Handbook of Paraconsistency

Author: Jean-Yves Béziau
ISBN: 1904987737
Release Date: 2007
Genre: Computers

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.

Categories for the Working Philosopher

Author: Elaine Landry
Publisher: Oxford University Press
ISBN: 9780191065828
Release Date: 2017-11-17
Genre: Philosophy

Often people have wondered why there is no introductory text on category theory aimed at philosophers working in related areas. The answer is simple: what makes categories interesting and significant is their specific use for specific purposes. These uses and purposes, however, vary over many areas, both "pure", e.g., mathematical, foundational and logical, and "applied", e.g., applied to physics, biology and the nature and structure of mathematical models. Borrowing from the title of Saunders Mac Lane's seminal work "Categories for the Working Mathematician", this book aims to bring the concepts of category theory to philosophers working in areas ranging from mathematics to proof theory to computer science to ontology, from to physics to biology to cognition, from mathematical modeling to the structure of scientific theories to the structure of the world. Moreover, it aims to do this in a way that is accessible to non-specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, and in a way that builds on the concepts that are already familiar to philosophers working in these areas.

The Worldwide List of Alternative Theories and Critics

Author: Jean de Climont
Publisher: Editions d Assailly
ISBN: 9782902425174
Release Date: 2016-05-24
Genre: Science

This directory includes the scientists found in the Internet. The scientists of the directory are only those involved in physics (natural philosophy). The list includes 9000 names of scientists, doctors or engineers for more than 50%. Their position is shortly presented together with their proposed alternative theory when applicable. There are more than 1000 such theories, all amazingly very different from one another. Ce répertoire, exclusivement disponible en langue anglaise, inclut les scientifiques, exclusivement dans le domaine de la physique, référencés sur Internet. La liste comporte plus de 9000 noms de scientifiques, docteurs ou ingénieurs à plus de 50%. Elle précise leur position de manière succincte et expose, le cas échéant, les lignes directrices de la solution alternative qu'ils proposent. Il y a ainsi plus de 1000 théories, toutes remarquablement différentes.

How Do Madhyamikas Think

Author: Tom J. F. Tillemans
Publisher: Simon and Schuster
ISBN: 9781614292661
Release Date: 2016-04-12
Genre: Religion

A respected professor of Buddhist philosophy brings readers on a fascinating journey through Buddhism’s most animating ideas. Tom Tillemans, who has studied Buddhist philosophy since the 1970s, excels in bringing analytic and continental philosophy into conversation with thinkers in the Sanskrit and Tibetan traditions. This volume collects his writings on the most rarefied of Buddhist philosophical traditions, the Madhyamaka, and its radical insights into the nature of reality. Tillemans’ approach ranges from retelling the history of ideas, to considering implications of those ideas for practice, to formal appraisal of their proofs. The 12 essays (four of which are being published for the first time) are products of rich and sophisticated debates and dialogues with colleagues in the field.