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Author : Alfred Tarski
Publisher : Hackett Publishing
ISBN 13 : 9780915144761
Total Pages : 542 pages
Book Rating : 4.1/5 (447 download)
Download or read book Logic, Semantics, Metamathematics written by Alfred Tarski and published by Hackett Publishing. This book was released on 1983-01-01 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bob Carpenter
Publisher : MIT Press
ISBN 13 : 9780262531498
Total Pages : 616 pages
Book Rating : 4.5/5 (314 download)
Download or read book Type-Logical Semantics written by Bob Carpenter and published by MIT Press. This book was released on 1998-07-24 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar. It also contains a great deal of original work on categorial grammar and its application to natural-language semantics. The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language. The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, coordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book contains more mathematical development than is usually found in texts on natural language; an appendix includes the basic mathematical concepts used throughout the book.
Author : David W. Agler
Publisher : Rowman & Littlefield
ISBN 13 : 1442217421
Total Pages : 397 pages
Book Rating : 4.4/5 (422 download)
Download or read book Symbolic Logic written by David W. Agler and published by Rowman & Littlefield. This book was released on 2013 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Symbolic Logic: Syntax, Semantics, and Proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems, propositional and predicate 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. This text makes this often confounding topic much more accessible with step-by-step example proofs, chapter glossaries of key terms, hundreds of homework problems and solutions for practice, and suggested further readings.
Author : Theodore Hailperin
Publisher : Rowman & Littlefield
ISBN 13 : 1611460107
Total Pages : 124 pages
Book Rating : 4.6/5 (114 download)
Download or read book Logic with a Probability Semantics written by Theodore Hailperin and published by Rowman & Littlefield. This book was released on 2011 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word "sentential" in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ("no," "and," "or," etc.) but not including quantifiers ("for all," "there is"). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion basedon taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, notentities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion-the suppositional-in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for anyprobability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language. The chapter concludes by showing the Borel's early denumerableprobability concept (1909) can be justified by its being, in essence, close to Hailperin's probability result applied to denumerable language. The final chapter introduces the notion of conditional-probability to a language having quantifiers of the kind
Author : Nick Riemer
Publisher : Cambridge University Press
ISBN 13 : 0521851920
Total Pages : 477 pages
Book Rating : 4.5/5 (218 download)
Download or read book Introducing Semantics written by Nick Riemer and published by Cambridge University Press. This book was released on 2010-03-25 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the study of meaning in language for undergraduate students.
Author : Kisno
Publisher : LLC Publishing
ISBN 13 : 6029126350
Total Pages : 106 pages
Book Rating : 4.0/5 (291 download)
Download or read book Semantics: A View to Logic of Language written by Kisno and published by LLC Publishing. This book was released on with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: I see semantics as one branch of linguistics, which is the study of language: as an area of study parallel to, and interacting with, those syntax and phonology, which deal respectively with the formal patterns of language, and the way in which these are translated into sounds. While syntax and phonology study the structure of expressive possibilities in language, semantics study the meanings that can be expressed. It may convincingly be claimed that viewing semantics as a component discipline of linguistics is the most fruitful and exciting point of departure at the present time. The book of this kind cannot attempt an overall survey of the field of semantics or at least, if it does, it will end up as a superficial compendium of what others have thought about meaning. The only sensible course is to give evidence that linguistics does exist in our life and it is hypocritical not to acknowledge that linguistics is difficult to understand due to its scientificity. Semantics is a non-fiction science through its unique approach to find the meaning of language not by guessing or judging something subjectively. The strength of the integrated view is that it makes possible a transfer to semantics of techniques of analysis which have proved successful with other aspects of language. It has to be conceded that the primary appeal of semantics is an intellectual one, similar in some respects to that of mathematics or any pure science. Only after seeking understanding for understanding’s sake can one acquire the wisdom which consists in using that understanding for good ends.
Author : Pascal Hitzler
Publisher : CRC Press
ISBN 13 : 1000218724
Total Pages : 323 pages
Book Rating : 4.0/5 (2 download)
Download or read book Mathematical Aspects of Logic Programming Semantics written by Pascal Hitzler and published by CRC Press. This book was released on 2016-04-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.
Author : Andrew M. Pitts
Publisher : Cambridge University Press
ISBN 13 : 0521580579
Total Pages : 375 pages
Book Rating : 4.5/5 (215 download)
Download or read book Semantics and Logics of Computation written by Andrew M. Pitts and published by Cambridge University Press. This book was released on 1997-01-30 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to present modern developments in semantics and logics of computation in a way that is accessible to graduate students. The book is based on a summer school at the Isaac Newton Institute and consists of a sequence of linked lecture course by international authorities in the area. The whole set have been edited to form a coherent introduction to these topics, most of which have not been presented pedagogically before.
Author : Rudolf Carnap
Publisher : University of Chicago Press
ISBN 13 : 0226093476
Total Pages : 266 pages
Book Rating : 4.2/5 (26 download)
Download or read book Meaning and Necessity written by Rudolf Carnap and published by University of Chicago Press. This book was released on 1988-02-15 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Author : John N. Martin
Publisher : Routledge
ISBN 13 : 1351249185
Total Pages : 253 pages
Book Rating : 4.3/5 (512 download)
Download or read book The Cartesian Semantics of the Port Royal Logic written by John N. Martin and published by Routledge. This book was released on 2019-11-04 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l’Art de penser, 1662-1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes’ metaphysics. The Logic’s authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book’s central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea’s defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic’s metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.
Author : David J. Pym
Publisher : Springer Science & Business Media
ISBN 13 : 9401700915
Total Pages : 323 pages
Book Rating : 4.4/5 (17 download)
Download or read book The Semantics and Proof Theory of the Logic of Bunched Implications written by David J. Pym and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Author : Eric Pacuit
Publisher : Springer
ISBN 13 : 3319671499
Total Pages : 165 pages
Book Rating : 4.3/5 (196 download)
Download or read book Neighborhood Semantics for Modal Logic written by Eric Pacuit and published by Springer. This book was released on 2017-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.
Author : Nino B. Cocchiarella
Publisher : Oxford University Press
ISBN 13 : 0190451203
Total Pages : 288 pages
Book Rating : 4.1/5 (94 download)
Download or read book Modal Logic written by Nino B. Cocchiarella and published by Oxford University Press. This book was released on 2008-08-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Tero Tulenheimo
Publisher : Springer
ISBN 13 : 3319531190
Total Pages : 217 pages
Book Rating : 4.3/5 (195 download)
Download or read book Objects and Modalities written by Tero Tulenheimo and published by Springer. This book was released on 2017-03-14 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs.
Author : Brendan S. Gillon
Publisher : MIT Press
ISBN 13 : 0262039206
Total Pages : 731 pages
Book Rating : 4.2/5 (62 download)
Download or read book Natural Language Semantics written by Brendan S. Gillon and published by MIT Press. This book was released on 2019-03-12 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.
Author : Marie Duží
Publisher : Springer Science & Business Media
ISBN 13 : 9048188121
Total Pages : 562 pages
Book Rating : 4.0/5 (481 download)
Download or read book Procedural Semantics for Hyperintensional Logic written by Marie Duží and published by Springer Science & Business Media. This book was released on 2010-07-01 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.
Author : Dale Jacquette
Publisher : Routledge
ISBN 13 : 1317546547
Total Pages : 321 pages
Book Rating : 4.3/5 (175 download)
Download or read book Logic and How it Gets That Way written by Dale Jacquette and published by Routledge. This book was released on 2014-09-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic.
