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 Bimbó
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.

An Introduction to Mathematical Logic and Type Theory

Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9789401599344
Release Date: 2013-04-17
Genre: Mathematics

In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Logic for Computer Science

Author: Jean H. Gallier
Publisher: Courier Dover Publications
ISBN: 9780486780825
Release Date: 2015-06-18
Genre: Computers

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

First Order Logic and Automated Theorem Proving

Author: Melvin Fitting
Publisher: Springer Science & Business Media
ISBN: 9781468403572
Release Date: 2012-12-06
Genre: Mathematics

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

The Temporal Logic of Reactive and Concurrent Systems

Author: Zohar Manna
Publisher: Springer Science & Business Media
ISBN: 9781461209317
Release Date: 2012-12-06
Genre: Computers

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.

The Description Logic Handbook

Author: Franz Baader
Publisher: Cambridge University Press
ISBN: 0521781760
Release Date: 2003-01-09
Genre: Computers

Description Logics are a family of knowledge representation languages that have been studied extensively in Artificial Intelligence over the last two decades. They are embodied in several knowledge-based systems and are used to develop various real-life applications. The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically-oriented readers, to those with more practically-oriented interests who need a sound and modern understanding of knowledge representation systems based on Description Logics. The chapters are written by some of the most prominent researchers in the field, introducing the basic technical material before taking the reader to the current state of the subject, and including comprehensive guides to the literature. In sum, the book will serve as a unique reference for the subject, and can also be used for self-study or in conjunction with Knowledge Representation and Artificial Intelligence courses.

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.

In Contradiction

Author: Graham Priest
Publisher: Oxford University Press
ISBN: 9780199263295
Release Date: 2006-02-16
Genre: Language Arts & Disciplines

Priest advocates and defends the view that there are true contradictions (dialetheism), a perspective that flies in the face of orthodoxy in Western philosophy since Aristole and remains at the centre of philosophical debate. This edition contains the author's reflections on developments since 1987.

Paraconsistent logic

Author: Graham Priest
Publisher: Philosophia Verlag Gmbh
ISBN: UCAL:B4410730
Release Date: 1989
Genre: Philosophy

Proceedings of the First International Scientific Conference Intelligent Information Technologies for Industry IITI 16

Author: Ajith Abraham
Publisher: Springer
ISBN: 9783319336091
Release Date: 2016-05-10
Genre: Computers

This volume of Advances in Intelligent Systems and Computing contains papers presented in the main track of IITI 2016, the First International Conference on Intelligent Information Technologies for Industry held in May 16-21 in Sochi, Russia. The conference was jointly co-organized by Rostov State Transport University (Russia) and VŠB – Technical University of Ostrava (Czech Republic) with the participation of Russian Association for Artificial Intelligence (RAAI) and Russian Association for Fuzzy Systems and Soft Computing (RAFSSC). The volume is devoted to practical models and industrial applications related to intelligent information systems. The conference has been a meeting point for researchers and practitioners to enable the implementation of advanced information technologies into various industries. Nevertheless, some theoretical talks concerning the-state-of-the-art in intelligent systems and soft computing are included in the proceedings as well.

Automated Reasoning

Author: Robert Stephen Boyer
Publisher: Springer Science & Business Media
ISBN: 9789401134880
Release Date: 2012-12-06
Genre: Computers

These essays have been written to honor W. W. Bledsoe, a scientist who has contributed to such diverse fields as mathematics, systems analysis, pattern recognition, biology, artificial intelligence, and automated reasoning. The first essay provides a sketch of his life, emphasizing his scientific contributions. The diversity of the fields to which Bledsoe has contributed is reflected in the range of the other essays, which are original scientific contributions by some of his many friends and colleagues. Bledsoe is a founding father of the field of automated reasoning, and a majority of the essays are on that topic. These essays are collected together here not only to acknowledge Bledsoe's manifold and substantial scientific contributions but also to express our appreciation for the great care and energy that he has devoted to nurturing many of the scientists working in those scientific fields he has helped found. Robert S. Boyer Austin February, 1991 ix Acknow ledgements Thanks to Larry Wos, editor of the Journal of Automated Reasoning, and Derek Middleton and Martin Scrivener, Kluwer Academic editors, for sup porting the idea of initiating this collection of essays. Thanks to A. Michael Ballantyne and Michael Spivak, for help with lffi.TWC, especially in identifying many formatting problems and providing fixes.