Quantification in Nonclassical Logic

Quantification in Nonclassical Logic
Author: Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
Publsiher: Elsevier
Total Pages: 640
Release: 2009-06-20
ISBN 10: 008093112X
ISBN 13: 9780080931128
Language: EN, FR, DE, ES & NL

Quantification in Nonclassical Logic Book Review:

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

An Introduction to Non Classical Logic

An Introduction to Non Classical Logic
Author: Graham Priest
Publsiher: Cambridge University Press
Total Pages: 329
Release: 2008-04-10
ISBN 10: 9781139469678
ISBN 13: 1139469673
Language: EN, FR, DE, ES & NL

An Introduction to Non Classical Logic Book Review:

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Structural Analysis of Non Classical Logics

Structural Analysis of Non Classical Logics
Author: Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin
Publsiher: Springer
Total Pages: 278
Release: 2015-10-16
ISBN 10: 3662483572
ISBN 13: 9783662483572
Language: EN, FR, DE, ES & NL

Structural Analysis of Non Classical Logics Book Review:

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: (i) structural modeling of certain philosophical issues in the framework of non-classic logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; (ii) conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few.

Labelled Non Classical Logics

Labelled Non Classical Logics
Author: Luca Viganò
Publsiher: Springer Science & Business Media
Total Pages: 292
Release: 2013-04-17
ISBN 10: 1475732082
ISBN 13: 9781475732085
Language: EN, FR, DE, ES & NL

Labelled Non Classical Logics Book Review:

I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.

First Order Modal Logic

First Order Modal Logic
Author: M. Fitting,Richard L. Mendelsohn
Publsiher: Springer Science & Business Media
Total Pages: 287
Release: 1998
ISBN 10: 9780792353355
ISBN 13: 0792353358
Language: EN, FR, DE, ES & NL

First Order Modal Logic Book Review:

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Basic Proof Theory

Basic Proof Theory
Author: A. S. Troelstra,H. Schwichtenberg
Publsiher: Cambridge University Press
Total Pages: 417
Release: 2000-07-27
ISBN 10: 9780521779111
ISBN 13: 0521779111
Language: EN, FR, DE, ES & NL

Basic Proof Theory Book Review:

Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

Philosophy of Logics

Philosophy of Logics
Author: Susan Haack
Publsiher: Cambridge University Press
Total Pages: 276
Release: 1978-07-27
ISBN 10: 9780521293297
ISBN 13: 0521293294
Language: EN, FR, DE, ES & NL

Philosophy of Logics Book Review:

Publisher Description

Quantified Representation of Uncertainty and Imprecision

Quantified Representation of Uncertainty and Imprecision
Author: Dov M. Gabbay,Philippe Smets
Publsiher: Springer Science & Business Media
Total Pages: 477
Release: 2013-11-11
ISBN 10: 9401717354
ISBN 13: 9789401717359
Language: EN, FR, DE, ES & NL

Quantified Representation of Uncertainty and Imprecision Book Review:

We are happy to present the first volume of the Handbook of Defeasible Reasoning and Uncertainty Management Systems. Uncertainty pervades the real world and must therefore be addressed by every system that attempts to represent reality. The representation of uncertainty is a ma jor concern of philosophers, logicians, artificial intelligence researchers and com puter sciencists, psychologists, statisticians, economists and engineers. The present Handbook volumes provide frontline coverage of this area. This Handbook was produced in the style of previous handbook series like the Handbook of Philosoph ical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning. We hope it will answer the needs for adequate representations of uncertainty. This Handbook series grew out of the ESPRIT Basic Research Project DRUMS II, where the acronym is made out of the Handbook series title. This project was financially supported by the European Union and regroups 20 major European research teams working in the general domain of uncertainty. As a fringe benefit of the DRUMS project, the research community was able to create this Hand book series, relying on the DRUMS participants as the core of the authors for the Handbook together with external international experts.

Philosophical Logic

Philosophical Logic
Author: John P. Burgess
Publsiher: Princeton University Press
Total Pages: 168
Release: 2012-08-26
ISBN 10: 0691156336
ISBN 13: 9780691156330
Language: EN, FR, DE, ES & NL

Philosophical Logic Book Review:

Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject. The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.

Logic The Basics

Logic  The Basics
Author: Jc Beall,Shay Allen Logan
Publsiher: Taylor & Francis
Total Pages: 288
Release: 2017-04-20
ISBN 10: 1317528611
ISBN 13: 9781317528616
Language: EN, FR, DE, ES & NL

Logic The Basics Book Review:

Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic (first monadic, then polyadic) · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (solutions available in the encyclopedic online supplement), Logic: The Basics is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic.

Cognition Content and the A Priori

Cognition  Content  and the A Priori
Author: Robert Hanna
Publsiher: OUP Oxford
Total Pages: 464
Release: 2015-10-08
ISBN 10: 0191025593
ISBN 13: 9780191025594
Language: EN, FR, DE, ES & NL

Cognition Content and the A Priori Book Review:

In Cognition, Content, and the A Priori, Robert Hanna works out a unified contemporary Kantian theory of rational human cognition and knowledge. Along the way, he provides accounts of (i) intentionality and its contents, including non-conceptual content and conceptual content, (ii) sense perception and perceptual knowledge, including perceptual self-knowledge, (iii) the analytic-synthetic distinction, (iv) the nature of logic, and (v) a priori truth and knowledge in mathematics, logic, and philosophy. This book is specifically intended to reach out to two very different audiences: contemporary analytic philosophers of mind and knowledge on the one hand, and contemporary Kantian philosophers or Kant-scholars on the other. At the same time, it is also riding the crest of a wave of exciting and even revolutionary emerging new trends and new work in the philosophy of mind and epistemology, with a special concentration on the philosophy of perception. What is revolutionary in this new wave are its strong emphases on action, on cognitive phenomenology, on disjunctivist direct realism, on embodiment, and on sense perception as a primitive and proto-rational capacity for cognizing the world. Cognition, Content, and the A Priori makes a fundamental contribution to this philosophical revolution by giving it a specifically contemporary Kantian twist, and by pushing these new lines of investigation radically further.

Philosophical Logic

Philosophical Logic
Author: George Englebretsen,Charles Sayward
Publsiher: A&C Black
Total Pages: 208
Release: 2011-03-24
ISBN 10: 1441119116
ISBN 13: 9781441119117
Language: EN, FR, DE, ES & NL

Philosophical Logic Book Review:

Introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols.

The Many Valued and Nonmonotonic Turn in Logic

The Many Valued and Nonmonotonic Turn in Logic
Author: Dov M. Gabbay,John Woods
Publsiher: Elsevier
Total Pages: 690
Release: 2007-08-13
ISBN 10: 9780080549392
ISBN 13: 008054939X
Language: EN, FR, DE, ES & NL

The Many Valued and Nonmonotonic Turn in Logic Book Review:

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity , it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity , limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs. The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. Detailed and comprehensive chapters covering the entire range of modal logic. Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Mathematical Methods in Interdisciplinary Sciences

Mathematical Methods in Interdisciplinary Sciences
Author: Snehashish Chakraverty
Publsiher: John Wiley & Sons
Total Pages: 464
Release: 2020-07-15
ISBN 10: 1119585503
ISBN 13: 9781119585503
Language: EN, FR, DE, ES & NL

Mathematical Methods in Interdisciplinary Sciences Book Review:

Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Three Views of Logic

Three Views of Logic
Author: Donald W. Loveland,Richard E. Hodel,S. G. Sterrett
Publsiher: Princeton University Press
Total Pages: 344
Release: 2014-01-26
ISBN 10: 140084875X
ISBN 13: 9781400848751
Language: EN, FR, DE, ES & NL

Three Views of Logic Book Review:

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Logic Methodology and Philosophy of Science IX

Logic  Methodology and Philosophy of Science IX
Author: D. Prawitz,B. Skyrms,D. Westerståhl
Publsiher: Elsevier
Total Pages: 988
Release: 1995-01-10
ISBN 10: 0080544959
ISBN 13: 9780080544953
Language: EN, FR, DE, ES & NL

Logic Methodology and Philosophy of Science IX Book Review:

This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.

Essays on Non classical Logic

Essays on Non classical Logic
Author: Heinrich Wansing
Publsiher: World Scientific
Total Pages: 262
Release: 2001
ISBN 10: 9812799745
ISBN 13: 9789812799746
Language: EN, FR, DE, ES & NL

Essays on Non classical Logic Book Review:

This book covers a broad range of up-to-date issues in non-classical logic that are of interest not only to philosophical and mathematical logicians but also to computer scientists and researchers in artificial intelligence. The problems addressed range from methodological issues in paraconsistent and deontic logic to the revision theory of truth and infinite Turing machines. The book identifies a number of important current trends in contemporary non-classical logic. Among them are dialogical and substructural logic, the classification of concepts of negation, truthmaker theory, and mathematical and foundational aspects of modal and temporal logic. Contents: Fine-Grained Theories of Time (P Blackburn); Revision Sequences and Computers with an Infinite Amount of Time (B LAwe); On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics (S Rahman); Truthmakers, Entailment and Necessity (S Read); Global Definability in Basic Modal Logic (M de Rijke & H Sturm); Ackermann's Implication for Typefree Logic (K Robering); Why Dialogical Logic? (H Rckert); Semantics for Constructive Negations (Y Shramko); Recent Trends in Paraconsistent Logic (M Urchs); Obligations, Authorities, and History Dependence (H Wansing). Readership: Graduate students and researchers in philosophical logic and mathematical logic, as well as computer scientists in artificial intelligence."

Towards Non Being

Towards Non Being
Author: Graham Priest
Publsiher: Oxford University Press on Demand
Total Pages: 190
Release: 2005-05-19
ISBN 10: 0199262543
ISBN 13: 9780199262540
Language: EN, FR, DE, ES & NL

Towards Non Being Book Review:

Towards Non-Being presents an account of the semantics of intentional language - verbs such as 'believes', 'fears', 'seeks', 'imagines'. Graham Priest's account tackles problems concerning intentional states which are often brushed under the carpet in discussions of intentionality, such as their failure to be closed under deducibility. Drawing on the work of the late Richard Routley (Sylvan), it proceeds in terms of objects that may be either existent or non-existent, atworlds that may be either possible or impossible. Since Russell, non-existent objects have had a bad press in Western philosophy; Priest mounts a full-scale defence. In the process, he offers an account of both fictional and mathematical objects as non-existent.The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy or fiction, the philosophy of mathematics, or cognitive representation in AI.

Philosophy of Logic

Philosophy of Logic
Author: Anonim
Publsiher: Elsevier
Total Pages: 1218
Release: 2006-11-29
ISBN 10: 9780080466637
ISBN 13: 008046663X
Language: EN, FR, DE, ES & NL

Philosophy of Logic Book Review:

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

Doubt Truth to be a Liar

Doubt Truth to be a Liar
Author: Graham Priest
Publsiher: Oxford University Press
Total Pages: 226
Release: 2006
ISBN 10: 0199263280
ISBN 13: 9780199263288
Language: EN, FR, DE, ES & NL

Doubt Truth to be a Liar Book Review:

"The book is required reading for anyone who wishes to understand dialetheism; (especially) for anyone who wishes to continue to endorse the old Aristotelian orthodoxy; and, more generally, for anyone who wishes to understand the role that contradiction plays in our thinking."--BOOK JACKET.