## Modal Logic

An Introduction to its Syntax and Semantics

Author: Nino B. Cocchiarella,Max A. Freund

Publisher: Oxford University Press

ISBN: 9780199710638

Category: Mathematics

Page: 288

View: 5874

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.

## Modal Logic

An Introduction

Author: Brian F. Chellas

Publisher: Cambridge University Press

ISBN: 9780521295154

Category: Mathematics

Page: 295

View: 8895

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.

## Modal Logic

Graph. Darst

Author: Patrick Blackburn,Maarten de Rijke,Yde Venema

Publisher: Cambridge University Press

ISBN: 9780521527149

Category: Computers

Page: 554

View: 9689

This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

## Meaning and Necessity

A Study in Semantics and Modal Logic

Author: Rudolf Carnap

Publisher: University of Chicago Press

ISBN: 9780226093475

Category: Philosophy

Page: 258

View: 4263

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence. . . . The chief virtue of the book is its systematic character. From Frege to Quine most philosophical logicians have restricted themselves by piecemeal and local assaults on the problems involved. The book is marked by a genial tolerance. Carnap sees himself as proposing conventions rather than asserting truths. However he provides plenty of matter for argument."—Anthony Quinton, Hibbert Journal

## Type-logical Semantics

Author: Bob Carpenter

Publisher: MIT Press

ISBN: 9780262531498

Category: Language Arts & Disciplines

Page: 575

View: 3809

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.

## Modal Logic

Author: Alexander Chagrov,Michael Zakharyaschev

Publisher: Oxford University Press

ISBN: 0198537794

Category: Mathematics

Page: 605

View: 4797

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators - `like it is necessary' in philosophy, `it is believed' in cognitive science, `it is provable' in mathematics and `it is true after executing a program' in computer science. It is an advanced text which starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantical and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist can use the book as a source of references. For the first time results and methods of many directions in propositional modal logic - from completeness and duality to algorithmic problems - are collected and systematically presented in one volume. Unlike other books, modal logic is treated here as a uniform theory rather than a collection of a few particular systems. It is the only book presenting the theory of superintuitionistic logics.

## Logic in Grammar

Polarity, Free Choice, and Intervention

Author: Gennaro Chierchia

Publisher: Oxford University Press

ISBN: 0199697973

Category: Language Arts & Disciplines

Page: 468

View: 6635

In a fundamental investigation of language and human reasoning, Gennaro Chierchia looks at how syntactic and inferential processes interact through the study of polarity sensitive and free choice items. He reformulates the semantics of focus and scope and the pragmatics of implicature as part of the recursive semantic system.

## Language and Logics

An Introduction to the Logical Foundations of Language

Author: Howard Gregory

Publisher: Edinburgh University Press

ISBN: 0748691650

Category: Language Arts & Disciplines

Page: 328

View: 6171

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.

## Modality

Author: Paul Portner

Publisher: Oxford University Press

ISBN: 0199292426

Category: Computers

Page: 288

View: 441

This comprehensive review and critical synthesis of research on modality focuses on formal theories within linguistics and related aspects of philosophical logic. It will be welcomed by students of linguistics at graduate level and above, as well as by researchers in philosophy, computational science, and related fields.

## Analyzing meaning

An introduction to semantics and pragmatics

Author: Paul R. Kroeger

Publisher: Language Science Press

ISBN: 3961100349

Category: Language Arts & Disciplines

Page: 502

View: 4773

{This book provides an introduction to the study of meaning in human language, from a linguistic perspective. It covers a fairly broad range of topics, including lexical semantics, compositional semantics, and pragmatics. The chapters are organized into six units: (1) Foundational concepts; (2) Word meanings; (3) Implicature (including indirect speech acts); (4) Compositional semantics; (5) Modals, conditionals, and causation; (6) Tense & aspect. Most of the chapters include exercises which can be used for class discussion and/or homework assignments, and each chapter contains references for additional reading on the topics covered. As the title indicates, this book is truly an INTRODUCTION: it provides a solid foundation which will prepare students to take more advanced and specialized courses in semantics and/or pragmatics. It is also intended as a reference for fieldworkers doing primary research on under-documented languages, to help them write grammatical descriptions that deal carefully and clearly with semantic issues. The approach adopted here is largely descriptive and non-formal (or, in some places, semi-formal), although some basic logical notation is introduced. The book is written at level which should be appropriate for advanced undergraduate or beginning graduate students. It presupposes some previous coursework in linguistics, but does not presuppose any background in formal logic or set theory.

## Intensional and Higher-Order Modal Logic

Author: Daniel Gallin

Publisher: Elsevier

ISBN: 148327473X

Category: Mathematics

Page: 158

View: 1273

North-Holland Mathematics Studies, 19: Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics focuses on an approach to the problem of providing a precise account of natural language syntax and semantics, including the set-theoretic semantical methods, Boolean models, and two-sorted type theory. The book first offers information on intensional logic and alternative formulations of intensional logic. Topics include two-sorted type theory, normal forms, extensions and intensional logic, modal T-logic, persistence in intensional logic, generalized completeness of intensional logic, and natural language and intensional logic. The text then examines higher-order modal logic and algebraic semantics. Discussions focus on Cohen's independence results, topological models of MLp, modal independence results, Boolean models of MLp, relative strength of intensional logic and MLp, propositional operators, modal predicate logic, and propositions in MLp. The monograph is a valuable reference for mathematicians and researchers interested in intensional and higher-order modal logic.

## The Logic of Categorial Grammars

A deductive account of natural language syntax and semantics

Author: Richard Moot,Christian Retore

Publisher: Springer

ISBN: 3642315550

Category: Mathematics

Page: 300

View: 6055

This book is intended for students in computer science, formal linguistics, mathematical logic and to colleagues interested in categorial grammars and their logical foundations. These lecture notes present categorial grammars as deductive systems, in the approach called parsing-as-deduction, and the book includes detailed proofs of their main properties. The papers are organized in topical sections on AB grammars, Lambek’s syntactic calculus, Lambek calculus and montague grammar, non-associative Lambek calculus, multimodal Lambek calculus, Lambek calculus, linear logic and proof nets and proof nets for the multimodal Lambek calculus.

## Introduction to Symbolic Logic and Its Applications

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 048614349X

Category: Mathematics

Page: 272

View: 4404

Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.

Author: Frank Wolter

Publisher: World Scientific

ISBN: 9812776478

Category: Modality

Page: 424

View: 877

Advances in Modal Logic is a unique forum for presenting the latest results and new directions of research in modal logic. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics.Volume 3 presents substantial advances in the relational model theory and the algorithmic treatment of modal logics. It contains invited and contributed papers from the third conference on OC Advances in Modal LogicOCO, held at the University of Leipzig (Germany) in October 2000. It includes papers on dynamic logic, description logic, hybrid logic, epistemic logic, combinations of modal logics, tense logic, action logic, provability logic, and modal predicate logic."

## Modal Logic for Philosophers

Author: James W. Garson

Publisher: Cambridge University Press

ISBN: 1107512301

Category: Philosophy

Page: N.A

View: 8988

This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout.

An Introduction to Modal and Many-valued Logic

Author: J. C. Beall,Bas C. Van Fraassen

Publisher: Oxford University Press, USA

ISBN: 9780199259878

Category: Philosophy

Page: 233

View: 900

"The book opens up topics to debate, suitable for an intermediate course in logic. Each chapter contains innovative features that guide us through the subject: exercises to give students hands-on experience, examples to demonstrate the application of concepts, and lists of further reading."--Jacket.

## Short Introduction to Modal Logic

Author: Grigori Mints

Publisher: Center for the Study of Language (CSLI)

ISBN: 9780937073759

Category: Mathematics

Page: 91

View: 7764

Modal Logic can be characterized as the logic of necessity and possibility, of 'must be' and 'may be'. A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of the subject and provides philosophical motivations to show the point of the formal work. The coverage is self-contained, including a summary of the necessary aspects of classical logic which it presupposes. A set of exercises is included in the final chapter.

## Modal Logics and Philosophy

Author: Rod Girle

Publisher: Routledge

ISBN: 1317492161

Category: Philosophy

Page: 240

View: 9745

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission.

## Philosophy of Logic

Author: N.A

Publisher: Elsevier

ISBN: 9780080466637

Category: Mathematics

Page: 1218

View: 9264

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

## An Introduction to the Philosophy of Science

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 0486140865

Category: Science

Page: 336

View: 6217

Stimulating, thought-provoking text by one of the 20th century's most creative philosophers makes accessible such topics as probability, measurement and quantitative language, causality and determinism, theoretical laws and concepts, more.