An Introduction to Non-Classical Logic

From If to Is

Author: Graham Priest

Publisher: Cambridge University Press

ISBN: 9781139469678

Category: Science

Page: N.A

View: 3597

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.

Classical and Nonclassical Logics

An Introduction to the Mathematics of Propositions

Author: Eric Schechter

Publisher: Princeton University Press

ISBN: 9780691122793

Category: Mathematics

Page: 507

View: 833

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Einführung in die mathematische Logik

Klassische Prädikatenlogik

Author: Hans Hermes

Publisher: Springer-Verlag

ISBN: 3322996425

Category: Technology & Engineering

Page: 208

View: 7912

Das vorliegende, 1963 in erster Auflage erschienene Buch ist aus Vorlesungen hervorgegangen. Es soll eine Einführung in die klassische zweiwertige Prädikaten logik geben. Die Beschränkung auf die klassische Logik soll nicht besagen, daß diese Logik prinzipiell einen Vorzug vor anderen, nichtklassischen Logiken besitzt. Die klassische Logik empfiehlt sich jedoch als Einführung in die Logik wegen ihrer Einfachheit und als Fundament für die Anwendung deshalb, weil sie der klassischen Mathematik und damit den darauf aufgebauten exakten Wissenschaften zugrunde liegt. Das Buch wendet sich primär an Studierende der Mathematik, die in den An fängervorlesungen bereits einige grundlegende mathematische Begriffe, wie den Gruppenbegriff, kennengelernt haben. Der Leser soll dazu geführt werden, daß er die Vorteile einer Formalisierung einsieht. Der übergang von der Umgangssprache zu einer formalisierten Sprache, welcher erfahrungsgemäß gewisse Schwierigkeiten bereitet, wird eingehend besprochen und eingeübt. Die Analyse desmathemati schen Umgangs mit den grundlegenden mathematischen Strukturen führt in zwangloser Weise zum semantisch begründeten Folgerungsbegriff.

Einführung in die Modallogik

Author: G.E. Hughes,Max J. Cresswell

Publisher: Walter de Gruyter

ISBN: 3110830027

Category: Philosophy

Page: 350

View: 2901

An Introduction to Non-Classical Logic, From If to Is

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467264709

Category: Education

Page: 50

View: 9587

Facts101 is your complete guide to An Introduction to Non-Classical Logic, From If to Is. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Logik für Dummies

Author: Mark Zegarelli

Publisher: John Wiley & Sons

ISBN: 3527687262

Category: Mathematics

Page: 351

View: 1640

Logik ist die Basis der Wissenschaft, aber auch eine Br?cke zwischen Wissenschaft und Alltag, denn die Grundlagen sind einfach logisch. Doch so einfach sie auf den ersten Blick scheint, so anspruchsvoll ist sie im Detail. "Logik kompakt f?r Dummies" f?hrt Sie systematisch und so einfach wie m?glich in dieses Teilgebiet von Mathematik und Philosophie ein. Dabei arbeitet Mark Zegarelli mit anschaulichen Beispielen und schafft es so, dieses abstrakte Thema nicht nur verst?ndlich zu erkl?ren, sondern auch Wert und Nutzen der Logik aufzuzeigen.

Kripke’s Worlds

An Introduction to Modal Logics via Tableaux

Author: Olivier Gasquet,Andreas Herzig,Bilal Said,François Schwarzentruber

Publisher: Springer Science & Business Media

ISBN: 3764385049

Category: Mathematics

Page: 198

View: 8888

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language.

An Introduction to Many-Valued and Fuzzy Logic

Semantics, Algebras, and Derivation Systems

Author: Merrie Bergmann

Publisher: Cambridge University Press

ISBN: 1139468782

Category: Mathematics

Page: N.A

View: 6299

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

Schicksal, Zeit und Sprache

Über Willensfreiheit

Author: David Foster Wallace

Publisher: Suhrkamp Verlag

ISBN: 3518789503

Category: Philosophy

Page: 207

View: 5873

Können wir die Zukunft durch unser Handeln beeinflussen? Oder ist sie von Gott, vom Schicksal oder von Naturgesetzen vorherbestimmt? Diese Frage beschäftigt Philosophen seit der Antike. 1985 nahm sich ein Student vor, sie ein für allemal zu lösen – David Foster Wallace. Er jongliert souverän mit modallogischen Formeln und Diagrammen und führt exzentrische Beispiele ins Feld, die direkt seinen Erzählungen entsprungen sein könnten: Terroristen, Stabhochspringer, Tennisspieler ohne Schläger. Neben dem posthum erschienenen Aufsatz enthält der Band eine biografische Skizze über Foster Wallace’ Studentenzeit und eine kurze Einführung in die Modallogik.

Einführung in die Mathematische Logik

Ein Lehrbuch

Author: Wolfgang Rautenberg

Publisher: Springer-Verlag

ISBN: 3322915182

Category: Mathematics

Page: 256

View: 3611

Dieses Lehrbuch enthält über den Stoff einer einsemestrigen Einführungsvorlesung hinaus auch Material für eine Vorlesung über Logik für Informatiker (speziell logisches Programmieren), sowie in begrenztem Maße auch Basismaterial für eine Fortsetzung der Einführung in die Spezialrichtungen Modelltheorie, Rekursionstheorie und Beweistheorie. Für eine gekürzte Einführung in die Mathematische Logik kombiniert mit einer Einführung in die Mengenlehre empfiehlt sich für den logischen Teil der Stoff der ersten drei Kapitel. Unabhängig von Vorlesungskonzepten ist das Buch auch zum Selbststudium geeignet. Für einen Großteil der Übungen gibt es Lösungshinweise. Außer einer gewissen Schulung im mathematischen Schließen sind spezielle Vorkenntnisse nicht erforderlich; lediglich für Teile der Modelltheorie wären algebraische Grundkenntnisse wünschenswert. Die Verzeichnisse (Stichwörter, Symbole, Literatur) sind ausführlich und kommen der selbständigen Erarbeitung des Stoffes sehr entgegen. Das Buch ist inhaltsreich und flüssig geschrieben. Aus der Literatur bekannte Beweise wurden oft erheblich vereinfacht. Auch werden viele interessante Details präsentiert, die in der Lehrbuchliteratur nur schwer zu finden sind. Beispiele: Fragmente der 1. Stufe (etwa der Birkhoffsche Vollständigkeitssatz) und die Solovayschen Vollständigkeitssätze über Selbstreferenz. Die Gödelschen Unvollständigkeitssätze und ihr Umfeld werden besonders ausführlich behandelt. Nur gelegentlich werden weiterführende Betrachtungen angestellt, die mit Verweisen auf entsprechende Literaturstellen abschließen.

An Introduction to Paraconsistent Logics

Author: Manuel Bremer

Publisher: Peter Lang Pub Incorporated

ISBN: 9783631534137

Category: Technology & Engineering

Page: 249

View: 5062

This book gives an overview of paraconsistent logics - that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed.

Einführung in die Geometrie und Topologie

Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 4796

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

Lectures on Logic and Computation

ESSLLI 2010, Copenhagen, Denmark, August 2010, ESSLLI 2011, Ljubljana, Slovenia, August 2011, Selected Lecture Notes

Author: Nick Bezhanishvili,Valentin Goranko

Publisher: Springer

ISBN: 3642314856

Category: Computers

Page: 265

View: 5586

The European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The main focus of ESSLLI is on the interface between linguistics, logic and computation. ESSLLI offers foundational, introductory and advanced courses, as well as workshops, covering a wide variety of topics within the three areas of interest: Language and Computation, Language and Logic, and Logic and Computation. During two weeks, around 50 courses and 10 workshops are offered to the attendants, each of 1.5 hours per day during a five days week, with up to seven parallel sessions. ESSLLI also includes a student session (papers and posters by students only, 1.5 hour per day during the two weeks) and four evening lectures by senior scientists in the covered areas. The 6 course notes were carefully reviewed and selected. The papers are organized in topical sections on computational complexity, multi-agant systems, natural language processing, strategies in games and formal semantics.

The Blackwell Guide to Philosophical Logic

Author: Lou Goble

Publisher: Wiley-Blackwell

ISBN: 9780631206934

Category: Philosophy

Page: 522

View: 5083

This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts.

Language and Logics

An Introduction to the Logical Foundations of Language

Author: Howard Gregory

Publisher: N.A

ISBN: 9780748691630

Category:

Page: 384

View: 5133

Taking linguistics students beyond the classical forms often taught in introductory courses, Language and Logics offers a comprehensive introduction to the wide variety of useful non-classical logics that are commonly used in research. Including a brief review of classical logic and its major assumptions, this textbook provides a guided tour of modal, many valued and substructural logics. The textbook starts from simple and intuitive concepts, clearly explaining the logics of language for linguistics students who have little previous knowledge of logic or mathematics. Issues are presented and discussed clearly before going on to introduce symbolic notation. While not avoiding technical detail, the book focuses throughout on helping students develop an intuitive understanding of the field, with particular attention to conceptual questions and to the tailoring of logical systems to thinking about different applications in linguistics and beyond. This is an ideal introductory volume for advanced undergraduates and beginning postgraduate students in linguistics, and for those specializing in semantics.

An Introduction to Classical Islamic Philosophy

Author: Oliver Leaman

Publisher: Cambridge University Press

ISBN: 9780521797573

Category: Philosophy

Page: 253

View: 8006

Islamic philosophy is a unique and fascinating form of thought, and particular interest lies in its classical (Greek-influenced) period, when many of the ideas of Greek philosophy were used to explore the issues and theoretical problems which arise in trying to understand the Qur'an and Islamic practice. In this revised and expanded 2001 edition of his classic introductory work, Oliver Leaman examines the distinctive features of Classical Islamic philosophy and offers detailed accounts of major individual thinkers. In contrast to many previous studies that have treated this subject as only of historical interest, he offers analysis of the key arguments within Islamic philosophy so that the reader can engage with them and assess their strengths and weaknesses. His book will interest a wide range of readers in philosophy, religious studies and Islamic studies.

Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 9710

Goal-Directed Proof Theory

Author: Dov M. Gabbay,N. Olivetti

Publisher: Springer Science & Business Media

ISBN: 9401717133

Category: Philosophy

Page: 268

View: 4041

Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.

Neural-Symbolic Cognitive Reasoning

Author: Artur S. D'Avila Garcez,Luís C. Lamb,Dov M. Gabbay

Publisher: Springer Science & Business Media

ISBN: 3540732454

Category: Computers

Page: 197

View: 5165

This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.