## 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: 5247

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.

## Symbolic Logic

Syntax, Semantics, and Proof

Author: David W. Agler

Publisher: Rowman & Littlefield

ISBN: 1442217421

Category: Mathematics

Page: 375

View: 6162

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

## 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: 4562

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

## Multi-Dimensional Modal Logic

Author: Maarten Marx,Yde Venema

Publisher: Springer Science & Business Media

ISBN: 9780792343455

Category: Philosophy

Page: 239

View: 4095

Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.) This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.

## Recent Advances in the Syntax and Semantics of Tense, Aspect and Modality

Author: Louis de Saussure,Jacques Moeschler,Genoveva Puskás

Publisher: Walter de Gruyter

ISBN: 3110198762

Category: Language Arts & Disciplines

Page: 253

View: 9787

It is a fact that tense, aspect and modality together form one of the most recurring and active areas of research in contemporary syntax and semantics, as well as in other disciplines of linguistics. A large number of syntactic and semantic phenomena are concerned by the temporal-aspectual-modal level of representation: information about time, aspect and modality is part of virtually all sentences; inflexion is quite widely considered as the core of syntactic projections. Because of this very crucial situation and role in the sentence structure, temporal-aspectual and modal information concerns virtually any part of the sentence and this information has scope over the whole characterization of the eventuality denoted by the sentence. This book is an up-to-date milestone for the studies of temporality and language, in particular regarding syntax and semantics, but with incidental hints to pragmatics and theories of human natural language understanding. Through this very tight selection of 15 papers (originally delivered during the 6th Chronos colloquium), tenses, aspect and modality are investigated both at the descriptive and theoretical levels, involving many different Indo-European and non-Indo-European languages. The volume sheds light on a wide array of phenomena that remained too little explored until now. These include the following: modal subordination in Japanese, epistemic modals in Dutch and English in Free Indirect Speech contexts, aspectual readings of idioms, adverb-licensing with the German perfect, French imperfective past compared with English progressive past, infinitival perfect in English, Adult Root Infinitives, economy constraints on temporal subordinations, future modality, past interpretation of present tense in embedded clauses, and time without tenses in Mandarin and Navajo. The book is of interest to scholars and advanced students in the fields of linguistics (general linguistics, semantics, syntax) as well as philosophy and logic.

## Introduction to Montague Semantics

Author: D. R. Dowty,R. Wall,S. Peters

Publisher: Springer Science & Business Media

ISBN: 9400990650

Category: Language Arts & Disciplines

Page: 316

View: 6775

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.

## Investigations of the Syntax-semantics-pragmatics Interface

Author: Robert D. Van Valin

Publisher: John Benjamins Publishing

ISBN: 9027205728

Category: Language Arts & Disciplines

Page: 484

View: 1267

Investigations of the Syntax-Semantics-Pragmatics Interface presents on-going research in Role and Reference Grammar in a number of critical areas of linguistic theory: verb semantics and argument structure, the nature of syntactic categories and syntactic representation, prosody and syntax, information structure and syntax, and the syntax and semantics of complex sentences. In each of these areas there are important results which not only advance the development of the theory, but also contribute to the broader theoretical discussion. In particular, there are analyses of grammatical phenomena such as transitivity in Kabardian, the verb-less numeral quantifier construction in Japanese, and an unusual kind of complex sentence in Wari' (Chapakuran, Brazil) which not only illustrate the descriptive and explanatory power of the theory, but also present interesting challenges to other approaches. In addition, there are papers looking at the implications and applications of Role and Reference Grammar for neurolinguistic research, parsing and automated text analysis.

## First Steps in Modal Logic

Author: Sally Popkorn

Publisher: Cambridge University Press

ISBN: 9780521464826

Category: Mathematics

Page: 314

View: 5658

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.

## Philosophical Logic

Author: George Englebretsen,Charles Sayward

Publisher: A&C Black

ISBN: 1441119116

Category: Philosophy

Page: 208

View: 5893

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

## Aristotle's Modal Logic

Essence and Entailment in the Organon

Author: Richard Patterson

Publisher: Cambridge University Press

ISBN: 9780521522335

Category: Philosophy

Page: 304

View: 358