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.
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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
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.
The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.
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.
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.
{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.
In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.
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.
This book explains how the meanings of the symbols of logic are determined by the rules that govern them.
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.
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.
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.
Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

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