Download or read book Eliminating The Universe Logical Properties Of Natural Language written by Keenan Edward L and published by World Scientific. This book was released on 2018-07-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book synthesizes the author's work (1980s-2015) on the logical expressive power of natural language. It extends the tools and concepts of model theory as used in (higher order) predicate logic to the study of natural language semantics. It focuses on boolean structure, generalized quantification (separated from variable binding), covering some cases of anaphora. Different categories — predicates, adjective, quantifiers — are modeled by non-isomorphic boolean lattices.Of empirical linguistic interest is the expressibility of many natural classes of quantifiers defined in terms of their logical (automorphism invariant) properties. Some of these correlate with classes used syntactically in generative grammar. In other cases we find general (possibly universal) constraints on possible quantifier denotations in natural language.Also of novel logical interest are entailment paradigms that depend on relations between pairs or triples of generalized quantifier denoting expressions, ones that are in some cases inherently vague. In addition we note novel binary quantifiers that lie beyond the 'Frege boundary' in that they are provably not identical to any iterated application of unary quantifiers.Of philosophical interest is the existence of models which make the same sentences true as standard models but which lack a universe and hence, seemingly, a notion of 'reference'. Moreover, these models generalize to ones in which we can represent (some) intensional expressions without the use of novel ontological objects, such as 'possible worlds' or 'propositions'.

Download or read book Eliminating the Universe written by Edward Louis Keenan and published by . This book was released on 2016 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Systemic Functional Insights on Language and Linguistics written by Christian M.I.M. Matthiessen and published by Springer Nature. This book was released on 2022-04-05 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a collection of 10 interviews with Christian M.I.M. Matthiessen, who is a key figure in Systemic Functional Linguistics (SFL) and has collaborated closely with M.A.K. Halliday since the 1980s. As noted by Professor Chang Chenguang, Editor of the M.A.K. Halliday Library Functional Linguistics Series, “this collection of interviews serves as an important reference for scholars and students of SFL. It provides a unique perspective on the theoretical development and future outlooks of SFL, as well as Matthiessen’s own interpretations of the theory. It also enriches our understanding of SFL and is a very useful addition to the series.” Written in an engaging dialogic format, the book paints a vivid picture of SFL thriving among the landscape of general linguistics and of SFL as an important tool now being applied in various areas.

Download or read book Quantifiers in Language and Logic written by Stanley Peters and published by OUP Oxford. This book was released on 2006-04-27 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.

Download or read book Boolean Semantics for Natural Language written by Edward L. Keenan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 1978, one of the authors of this book was sitting in on a course in logic for linguists given by the other author. In attempting to present some of Montague's insights in an elementary way (hopefully avoid ing the notation which many find difficult at first), the authors began dis cussions aimed towards the construction of a simple model-theoretical semantic apparatus which could be applied directly to a small English-like language and used to illustrate the methods of formal logical interpretation. In these discussions two points impressed themselves on us. First, our task could be simplified by using boolean algebras and boolean homomorphisms in the models; and second, the boolean approach we were developing had much more widespread relevance to the logical structure of English than we first thought. During the summer and fall of 1978 we continued work on the system, proving the more fundamental theorems (including what we have come to call the Justification Theorem) and outlining the way in which an intensional interpretation scheme could be developed which made use of the boolean approach (which was originally strictly extensional). We presented our findings in a monograph (Keenan and Faltz, 1978) which the UCLA Linguistics Department kindly published as part of their series called Occa sional Papers in Linguistics; one of the authors also presented the system at a colloquium held at the Winter Meeting of the Linguistic Society of America in December 1978.

Download or read book Model Generation for Natural Language Interpretation and Analysis written by Karsten Konrad and published by Springer. This book was released on 2004-01-26 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical theorem proving has undergone an impressive development during the last two decades, resulting in a variety of powerful systems for applications in mathematical deduction and knowledge processing. Natural language processing has become a topic of outstanding relevance in information technology, mainly due to the explosive growth of the Web, where by far the largest part of information is encoded in natural language documents. This monograph focuses on the development of inference tools tailored to applications in natural language processing by demonstrating how the model generation paradigm can be used as a framework for the support of specific tasks in natural language interpretation and natural language based inference in a natural way. The book appears at a pivotal moment, when much attention is being paid to the task of adding a semantic layer to the Web, and representation and processing of natural language based semantic information pops up as a primary requirement for further technological progress.

Download or read book Applied Logic How What and Why written by László Pólos and published by Springer Science & Business Media. This book was released on 1995-03-31 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Other methodological issues in the formal studies of natural language are discussed, such as the need for types, modal operators and other logical operators in the formal framework. Further articles address the scope of these methodological issues from other perspectives ranging from cognition to computation.

Download or read book Language Form and Logic written by Peter Ludlow and published by Oxford University Press. This book was released on 2022-02-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.

Download or read book Current Topics in Logic and Analytic Philosophy written by Concha Martínez and published by Univ Santiago de Compostela. This book was released on 2007 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Truth Interpretation and Information written by Jeroen Groenendijk and published by Walter de Gruyter. This book was released on 2013-02-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter

Download or read book The Logic of Natural Language written by Fred Sommers and published by Oxford University Press, USA. This book was released on 1982 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sustained argument for the virtues of a traditional, as opposed to a quantification-theoretical, analysis of the logic of natural language.

Download or read book Logical Structures for Representation of Knowledge and Uncertainty written by Ellen Hisdal and published by Physica. This book was released on 2013-04-17 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the business of science not to create laws, but to discover them. We do not originate the constitution of our own minds, greatly as it may be in our power to modify their character. And as the laws of the human intellect do not depend upon our will, so the forms of science, of (1. 1) which they constitute the basis, are in all essential regards independent of individual choice. George Boole [10, p. llJ 1. 1 Comparison with Traditional Logic The logic of this book is a probability logic built on top of a yes-no or 2-valued logic. It is divided into two parts, part I: BP Logic, and part II: M Logic. 'BP' stands for 'Bayes Postulate'. This postulate says that in the absence of knowl edge concerning a probability distribution over a universe or space one should assume 1 a uniform distribution. 2 The M logic of part II does not make use of Bayes postulate or of any other postulates or axioms. It relies exclusively on purely deductive reasoning following from the definition of probabilities. The M logic goes an important step further than the BP logic in that it can distinguish between certain types of information supply sentences which have the same representation in the BP logic as well as in traditional first order logic, although they clearly have different meanings (see example 6. 1. 2; also comments to the Paris-Rome problem of eqs. (1. 8), (1. 9) below).

Download or read book Quantifiers in Language and Logic written by Stanley Peters and published by Clarendon Press. This book was released on 2006-04-27 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment of meaning. It presents a broad view of the semantics and logic of quantifier expressions in natural languages and, to a slightly lesser extent, in logical languages. The authors progress carefully from a fairly elementary level to considerable depth over the course of sixteen chapters; their book will be invaluable to a broad spectrum of readers, from those with a basicknowledge of linguistic semantics and of first-order logic to those with advanced knowledge of semantics, logic, philosophy of language, and knowledge representation in artificial intelligence.

Download or read book Language Form and Logic written by Peter Ludlow and published by Oxford University Press. This book was released on 2022-02-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena.

Download or read book On Reference written by Andrea Bianchi and published by OUP Oxford. This book was released on 2015-03-05 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the times we open our mouth to communicate, we talk about things. This can happen because (some of) the linguistic expressions we use have semantic properties that connect them to extra-linguistic entities. Thanks to these properties, they may be used by us to refer to things. Or, as we may also say, they themselves refer to things, though in certain cases they do so only relative to a context of use. But how can we characterize the semantic properties in question? What exactly is reference? Philosophers have been trying to answer these questions at least since Plato's Cratylus, but not until the last century, when language occupied center-stage in philosophy, did the problem come to be felt as really pressing. In the last decade of the nineteenth century, Gottlob Frege produced an account of reference that set the stage for the contemporary discussion. Nevertheless, around 1970 a number of powerful arguments against it were produced by Saul Kripke and others. As a result, many philosophers began to look at reference from a new perspective, which highlighted the crucial role played by wordly historical facts that may be unknown to the speakers. This semantic revolution, however, left us with a number of open problems. The eighteen original essays collected in this volume deal with many of these problems, thus contributing to our understanding of the nature of reference, its role in cognition, and the place it should be given in semantic theory.