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Modal Logic

Modal Logic Author Nino B. Cocchiarella
ISBN-10 0199710635
Release 2008-08-04
Pages 288
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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

Modal Logic Author Brian F. Chellas
ISBN-10 0521295157
Release 1980
Pages 295
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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.

Meaning and Necessity

Meaning and Necessity Author Rudolf Carnap
ISBN-10 0226093476
Release 1988-02-15
Pages 258
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"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

Modal Logic

Modal Logic Author Patrick Blackburn
ISBN-10 0521527147
Release 2002-08-22
Pages 554
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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.

First Order Modal Logic

First Order Modal Logic Author M. Fitting
ISBN-10 9789401152921
Release 2012-12-06
Pages 292
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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.

Type logical Semantics

Type logical Semantics Author Bob Carpenter
ISBN-10 0262531496
Release 1997
Pages 575
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The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.

First Steps in Modal Logic

First Steps in Modal Logic Author Sally Popkorn
ISBN-10 052146482X
Release 1994-12-08
Pages 314
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This is a graduate-level text for a first course in propositional modal logic. It is written from the semantical point of view rather than the more usual proof theoretic approach, and the book covers all basic material including the propositional languages, the semantics and correspondence results, and proof systems and completeness results--as well as some topics not usually covered in a modal logic course, such as bisimulation. Important features of the book are the many exercises and extensive set of solutions that are included.

Modal Logic for Philosophers

Modal Logic for Philosophers Author James W. Garson
ISBN-10 9781107512306
Release 2013-11-25
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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.

Intensional and Higher Order Modal Logic

Intensional and Higher Order Modal Logic Author Daniel Gallin
ISBN-10 9781483274737
Release 2016-06-03
Pages 158
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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.

A New Introduction to Modal Logic

A New Introduction to Modal Logic Author M.J. Cresswell
ISBN-10 9781134800278
Release 2012-08-06
Pages 432
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This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic. A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.

Modal Logic for Open Minds

Modal Logic for Open Minds Author Johan van Benthem
ISBN-10 NWU:35556040094005
Release 2010
Pages 381
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In this work, the author provides an introduction to the field of modal logic, outlining its major ideas and emploring the numerous ways in which various academic fields have adopted it.

Philosophy of Logic

Philosophy of Logic Author
ISBN-10 008046663X
Release 2006-11-29
Pages 1218
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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

Language and Logics

Language and Logics Author Howard Gregory
ISBN-10 9780748691654
Release 2015-07-08
Pages 328
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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
ISBN-10 9780199292424
Release 2009-01-22
Pages 288
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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.

Introduction to Montague Semantics

Introduction to Montague Semantics Author D. R. Dowty
ISBN-10 9789400990654
Release 2012-12-06
Pages 316
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In this book we hope to acquaint the reader with the fundamentals of truth conditional model-theoretic semantics, and in particular with a version of this developed by Richard Montague in a series of papers published during the 1960's and early 1970's. In many ways the paper 'The Proper Treatment of Quantification in Ordinary English' (commonly abbreviated PTQ) represents the culmination of Montague's efforts to apply the techniques developed within mathematical logic to the semantics of natural languages, and indeed it is the system outlined there that people generally have in mind when they refer to "Montague Grammar". (We prefer the term "Montague Semantics" inasmuch as a grammar, as conceived of in current linguistics, would contain at least a phonological component, a morphological component, and other subsystems which are either lacking entirely or present only in a very rudi mentary state in the PTQ system. ) Montague's work has attracted increasing attention in recent years among linguists and philosophers since it offers the hope that semantics can be characterized with the same formal rigor and explicitness that transformational approaches have brought to syntax. Whether this hope can be fully realized remains to be seen, but it is clear nonetheless that Montague semantics has already established itself as a productive para digm, leading to new areas of inquiry and suggesting new ways of conceiving of theories of natural language. Unfortunately, Montague's papers are tersely written and very difficult to follow unless one has a considerable background in logical semantics.

Handbook of Logic and Language

Handbook of Logic and Language Author Johan F.A.K. van Benthem
ISBN-10 0444537279
Release 2010-12-17
Pages 1168
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The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. Completely revised and updated - includes over 25% new material Discusses the interface between logic and language Many of the authors are creators or active developers of the theories

Time and Modality

Time and Modality Author Jacqueline Guéron
ISBN-10 9781402083549
Release 2008-07-27
Pages 296
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Here is a unique work of reference. Not only does it unite studies which explore the syntax and semantics of tense or modality, but it is the first book of its kind to embrace the interaction of tense and modality within a coherent generative model.