Modal Logic

Modal Logic

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.

Author: Nino B. Cocchiarella

Publisher: Oxford University Press

ISBN: 9780190451202

Category: Philosophy

Page: 288

View: 123

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.
Categories: Philosophy

Meaning and Necessity

Meaning and Necessity

"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.

Author: Rudolf Carnap

Publisher: University of Chicago Press

ISBN: 0226093476

Category: Philosophy

Page: 258

View: 571

"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
Categories: Philosophy

Logic in Linguistics

Logic in Linguistics

The authors offer a clear, succinct and basic introduction to set theory and formal logic for linguists.

Author: Jens Allwood

Publisher: Cambridge University Press

ISBN: 0521291747

Category: Language Arts & Disciplines

Page: 185

View: 101

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.
Categories: Language Arts & Disciplines

The Logic of Sortals

The Logic of Sortals

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 ...

Author: Max A. Freund

Publisher: Springer

ISBN: 9783030182786

Category: Philosophy

Page: 160

View: 889

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.
Categories: Philosophy

Logic for Applications

Logic for Applications

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.

Author: Anil Nerode

Publisher: Springer Science & Business Media

ISBN: 9781461206491

Category: Computers

Page: 456

View: 668

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.
Categories: Computers

The Logic of Provability

The Logic of Provability

Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Author: George Boolos

Publisher: Cambridge University Press

ISBN: 0521483255

Category: Philosophy

Page: 275

View: 913

Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.
Categories: Philosophy

Type logical Semantics

Type logical Semantics

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

Author: Bob Carpenter

Publisher: MIT Press

ISBN: 0262531496

Category: Language Arts & Disciplines

Page: 575

View: 716

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.
Categories: Language Arts & Disciplines

Logics for Computer Science

Logics for Computer Science

Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics.

Author: Anita Wasilewska

Publisher: Springer

ISBN: 9783319925912

Category: Computers

Page: 535

View: 781

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.
Categories: Computers

Structured Meanings

Structured Meanings

This book is the outgrowth of years of work on propositional attitudes, the hardest problem in semantics.

Author: M. J. Cresswell

Publisher: MIT Press

ISBN: 0262031086

Category: Psychology

Page: 202

View: 296

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.
Categories: Psychology

Modality

Modality

This comprehensive review and critical synthesis of research on modality focuses on formal theories within linguistics and related aspects of philosophical logic.

Author: Paul Portner

Publisher: Oxford University Press

ISBN: 9780199292424

Category: Computers

Page: 288

View: 486

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.
Categories: Computers

Computer Science Logic

Computer Science Logic

2 Modal Dependence Logic We will Only briefly introduce the syntax and
semantics of modal dependence logic here. For a more profound overview
consult Väänänen's introduction 17 or Sevenster's analysis 15, which includes a
 ...

Author: Anuj Dawar

Publisher: Springer

ISBN: 9783642152054

Category: Computers

Page: 548

View: 264

Annotation. This volume constitutes the refereed proceedings of the 24th International Workshop on Computer Science Logic, CSL 2010, held in Brno, Czech Republic, in August 2010. The 33 full papers presented together with 7 invited talks, were carefully reviewed and selected from 103 submissions. Topics covered include automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and games, modal and temporal logic, model checking, decision procedures, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, verification and program analysis, linear logic, higher-order logic, and nonmonotonic reasoning.
Categories: Computers

Modalities and Multimodalities

Modalities and Multimodalities

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 ...

Author: Walter Carnielli

Publisher: Springer Science & Business Media

ISBN: 9781402085901

Category: Philosophy

Page: 304

View: 730

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.
Categories: Philosophy

Multi Dimensional Modal Logic

Multi Dimensional Modal Logic

5.6.2 MODALIZING ORDINARY FIRST-ORDER LOGIC We motivated the
introduction of the similarity types CMLn and MLRn in section 5.1 , by ... The first
and easiest solution would be to adapt the first-order syntax to the modal
semantics.

Author: Maarten Marx

Publisher: Springer Science & Business Media

ISBN: 079234345X

Category: Philosophy

Page: 239

View: 588

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.
Categories: Philosophy

Proof Theory of Modal Logic

Proof Theory of Modal Logic

EWA ORLOWSKA RELATIONAL PROOF SYSTEMS FOR MODAL LOGIC'S 1
INTRODUCTION The purpose of this paper ... formalism the three basic
components of any propositional logical system: syntax, semantics and deduction
apparatus.

Author: Heinrich Wansing

Publisher: Springer Science & Business Media

ISBN: 9789401727983

Category: Philosophy

Page: 318

View: 326

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Categories: Philosophy

Investigations of the Syntax semantics pragmatics Interface

Investigations of the Syntax semantics pragmatics Interface

We outline the characteristics of modality drawing on previous work on modality
and modal logic, and relate this to ... Introduction In this paper we give a brief
overview of the present treatment of modality in rrg within the operator projection.

Author: Robert D. Van Valin

Publisher: John Benjamins Publishing

ISBN: 9789027205728

Category: Language Arts & Disciplines

Page: 484

View: 398

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.
Categories: Language Arts & Disciplines

What Logics Mean

What Logics Mean

Modal. logic. This chapter is an introduction to the natural semantics for modal
logics. A pleasing result is that the basic ... 16.1 Natural semantics for the modal
logic K Let us introduce the (unary) operator □ (for necessity) to the syntax with
the ...

Author: James W. Garson

Publisher: Cambridge University Press

ISBN: 9781107039100

Category: Language Arts & Disciplines

Page: 302

View: 544

This book explains how the meanings of the symbols of logic are determined by the rules that govern them.
Categories: Language Arts & Disciplines

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

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

Introduction Many languages like Japanese have an elaborate modal system as
well as a set of evidentials, and some ... there are striking analogies that have
already been exploited as in the similarities between tense logic and modal logic.

Author: Louis de Saussure

Publisher: Walter de Gruyter

ISBN: 9783110198768

Category: Language Arts & Disciplines

Page: 253

View: 675

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.
Categories: Language Arts & Disciplines

Aristotle s Modal Logic

Aristotle s Modal Logic

Chapter 1 Introduction 1 . ... Accordingly , one major aim of this study will be to
examine in detail the internal workings of Aristotle ' s modal logichis logic not
just of ... in that the logical system itself must be understood from the start in the
light of basic points of syntax and semantics deriving from Aristotle ' s views on
what ...

Author: Richard Patterson

Publisher: Cambridge University Press

ISBN: 0521522331

Category: Philosophy

Page: 291

View: 375

This 1995 book argues that a proper understanding of Aristotle's modal logic requires an appreciation of its connection to the metaphysics.
Categories: Philosophy

Types Tableaus and G del s God

Types  Tableaus  and G  del   s God

M. Fitting. II MODAL LOGIC Chapter 7 MODAL LOGIC SYNTAX AND
SEMANTICS 1. Introduction The 7: MODAL LOGIC, SYNTAX AND SEMANTICS 1
Introduction.

Author: M. Fitting

Publisher: Springer Science & Business Media

ISBN: 1402006047

Category: Philosophy

Page: 181

View: 868

Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.
Categories: Philosophy

Perspectives of Systems Informatics

Perspectives of Systems Informatics

Being the complex algebraic-coalgebraic semantics, these logics have
interesting decidability properties. ... 1 Introduction The success of Process
Algebras [2] in modelling a wide class of concurrent and distributed systems ...
The dual nature of these calculi—algebraic»equational syntax versus
coalgebraic operational semantics, makes them particularly appropriate for a
modal logic-based approach.

Author: Edmund Clarke

Publisher: Springer

ISBN: 9783642297090

Category: Computers

Page: 411

View: 909

This book contains thoroughly refereed and revised papers from the 8th International Andrei Ershov Memorial Conference on Perspectives of System Informatics, PSI 2011, held in Akademgorodok, Novosibirsk, Russia, in June/July 2011. The 18 revised full papers and 10 revised short papers presented were carefully reviewed and selected from 60 submissions. The volume also contains 5 invited papers covering a range of hot topics in computer science and informatics. The papers are organized in topical sections on foundations of program and system development and analysis, partial evaluation, mixed computation, abstract interpretation, compiler construction, computer models and algorithms for bioinformatics, programming methodology and software engineering, information technologies, knowledge-based systems, and knowledge engineering.
Categories: Computers