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: 6321

DOWNLOAD NOW »

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.
Release

The Logic of Sortals

A Conceptualist Approach

Author: Max A. Freund

Publisher: Springer

ISBN: 3030182789

Category: Philosophy

Page: 160

View: 1929

DOWNLOAD NOW »

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions (such as sortal identity and first-order sortal quantification) are characterized. Most of these logics are intensional in nature and possess, in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches.
Release

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: 8552

DOWNLOAD NOW »

"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
Release

Structured Meanings

The Semantics of Propositional Attitudes

Author: M. J. Cresswell

Publisher: MIT Press

ISBN: 9780262031080

Category: Psychology

Page: 202

View: 1269

DOWNLOAD NOW »

M. J. Cresswell is a logician and philosopher of language who has been a major continuing influence on the growth and development of formal semantics over the past 15 years or more. This book is the outgrowth of years of work on propositional attitudes, the hardest problem in semantics. In it, he traces the problem to the foundations of semantics and solves it by distinguishing between the result of the composition of the simple parts of complex expressions and structure consisting of the uncomposed parts. Cresswell explains the basis of the great intuitive appeal of structured meanings, and why previous attempts, from Carnap's notion of intensional isomorphism on, to use them to solve the propositional attitudes problem have been unsuccessful. His own formalization is integrated into a model-theoretic framework which is capable of incorporating and extending all the insights obtained from Montague's semantics. M. J. Cresswell is Professor of Philosophy, Victoria University of Wellington, New Zealand. He is the author of Logics and Languages, in which he developed an alternative version of Montague Grammar, as well as many articles on possible-worlds semantics; and coauthor with G. E. Hughes of An Introduction to Modal Logic and A Companion to Modal Logic, the standard works in the field. A Bradford Book.
Release

Logic in Linguistics

Author: Jens Allwood,Gunnar-Gunnar Andersson,Lars-Gunnar Andersson,Osten Dahl

Publisher: Cambridge University Press

ISBN: 9780521291743

Category: Language Arts & Disciplines

Page: 185

View: 3838

DOWNLOAD NOW »

An elementary introduction to formal logic, particularly intended for linguists and others interested in languages. Concepts and theories developed within formal logic for the study of artificial languages have for some time been fruitfully applied to the study of natural languages and some knowledge of them is necessary for students of linguists (especially semantics). With this need in mind the authors offer a clear, succinct and basic introduction to set theory, inference, propositional and predicate logic, deduction, modal and intensional logic, and various concomitant extensions of these. There is a discussion too of the relation between linguistics and logical analysis and between logic and natural language. The authors see increasing scope for co-operation between logicians and linguistics in studying the structure of language, and it is the overall aim of the book to promote this co-operation.
Release

Handbook of Modal Logic

Author: Patrick Blackburn,Johan F.A.K. van Benthem,Frank Wolter

Publisher: Elsevier

ISBN: 9780080466668

Category: Mathematics

Page: 1260

View: 1157

DOWNLOAD NOW »

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth
Release

Meaning and Grammar

An Introduction to Semantics

Author: Gennaro Chierchia,Sally McConnell-Ginet

Publisher: MIT Press

ISBN: 9780262531641

Category: Language Arts & Disciplines

Page: 573

View: 2921

DOWNLOAD NOW »

This self-contained introduction to natural language semanticsaddresses the major theoretical questions in the field. This self-contained introduction to natural language semantics addresses the major theoretical questions in the field. The authors introduce the systematic study of linguistic meaning through a sequence of formal tools and their linguistic applications. Starting with propositional connectives and truth conditions, the book moves to quantification and binding, intensionality and tense, and so on. To set their approach in a broader perspective, the authors also explore the interaction of meaning with context and use (the semantics-pragmatics interface) and address some of the foundational questions, especially in connection with cognition in general. They also introduce a few of the most accessible and interesting ideas from recent research to give the reader a bit of the flavor of current work in semantics. The organization of this new edition is modular; after the introductory chapters, the remaining material can be covered in flexible order. The book presupposes no background in formal logic (an appendix introduces the basic notions of set theory) and only a minimal acquaintance with linguistics. This edition includes a substantial amount of completely new material and has been not only updated but redesigned throughout to enhance its user-friendliness.
Release

What Logics Mean

From Proof Theory to Model-Theoretic Semantics

Author: James W. Garson

Publisher: Cambridge University Press

ISBN: 110703910X

Category: Language Arts & Disciplines

Page: 302

View: 4060

DOWNLOAD NOW »

This book explains how the meanings of the symbols of logic are determined by the rules that govern them.
Release

Logic for Applications

Author: Anil Nerode,Richard A. Shore

Publisher: Springer Science & Business Media

ISBN: 1461206499

Category: Computers

Page: 456

View: 1518

DOWNLOAD NOW »

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Release