Eliminating The Universe: Logical Properties Of Natural Language

Eliminating The Universe: Logical Properties Of Natural Language PDF Author: Edward L Keenan
Publisher: World Scientific
ISBN: 9814719854
Category : Mathematics
Languages : en
Pages : 183

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Book Description
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'.

Eliminating The Universe: Logical Properties Of Natural Language

Eliminating The Universe: Logical Properties Of Natural Language PDF Author: Edward L Keenan
Publisher: World Scientific
ISBN: 9814719854
Category : Mathematics
Languages : en
Pages : 183

Get Book Here

Book Description
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'.

Natural Language Semantics

Natural Language Semantics PDF Author: Brendan S. Gillon
Publisher: MIT Press
ISBN: 0262350777
Category : Language Arts & Disciplines
Languages : en
Pages : 731

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Book Description
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.

Systemic Functional Insights on Language and Linguistics

Systemic Functional Insights on Language and Linguistics PDF Author: Christian M.I.M. Matthiessen
Publisher: Springer Nature
ISBN: 9811687137
Category : Language Arts & Disciplines
Languages : en
Pages : 328

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Book Description
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.

Eliminating the Universe

Eliminating the Universe PDF Author: Edward Louis Keenan
Publisher:
ISBN: 9789814719841
Category : LANGUAGE ARTS & DISCIPLINES
Languages : en
Pages : 168

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Book Description


Boolean Semantics for Natural Language

Boolean Semantics for Natural Language PDF Author: Edward L. Keenan
Publisher: Springer Science & Business Media
ISBN: 9400964048
Category : Language Arts & Disciplines
Languages : en
Pages : 399

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Book Description
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.

Quantifiers in Language and Logic

Quantifiers in Language and Logic PDF Author: Stanley Peters
Publisher: OUP Oxford
ISBN: 0191516236
Category : Philosophy
Languages : en
Pages : 550

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Book Description
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.

The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory

The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory PDF Author: Christopher Michael Langan
Publisher: Mega Foundation Press
ISBN: 0971916225
Category : Philosophy
Languages : en
Pages : 94

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Book Description
Paperback version of the 2002 paper published in the journal Progress in Information, Complexity, and Design (PCID). ABSTRACT Inasmuch as science is observational or perceptual in nature, the goal of providing a scientific model and mechanism for the evolution of complex systems ultimately requires a supporting theory of reality of which perception itself is the model (or theory-to-universe mapping). Where information is the abstract currency of perception, such a theory must incorporate the theory of information while extending the information concept to incorporate reflexive self-processing in order to achieve an intrinsic (self-contained) description of reality. This extension is associated with a limiting formulation of model theory identifying mental and physical reality, resulting in a reflexively self-generating, self-modeling theory of reality identical to its universe on the syntactic level. By the nature of its derivation, this theory, the Cognitive Theoretic Model of the Universe or CTMU, can be regarded as a supertautological reality-theoretic extension of logic. Uniting the theory of reality with an advanced form of computational language theory, the CTMU describes reality as a Self Configuring Self-Processing Language or SCSPL, a reflexive intrinsic language characterized not only by self-reference and recursive self-definition, but full self-configuration and self-execution (reflexive read-write functionality). SCSPL reality embodies a dual-aspect monism consisting of infocognition, self-transducing information residing in self-recognizing SCSPL elements called syntactic operators. The CTMU identifies itself with the structure of these operators and thus with the distributive syntax of its self-modeling SCSPL universe, including the reflexive grammar by which the universe refines itself from unbound telesis or UBT, a primordial realm of infocognitive potential free of informational constraint. Under the guidance of a limiting (intrinsic) form of anthropic principle called the Telic Principle, SCSPL evolves by telic recursion, jointly configuring syntax and state while maximizing a generalized self-selection parameter and adjusting on the fly to freely-changing internal conditions. SCSPL relates space, time and object by means of conspansive duality and conspansion, an SCSPL-grammatical process featuring an alternation between dual phases of existence associated with design and actualization and related to the familiar wave-particle duality of quantum mechanics. By distributing the design phase of reality over the actualization phase, conspansive spacetime also provides a distributed mechanism for Intelligent Design, adjoining to the restrictive principle of natural selection a basic means of generating information and complexity. Addressing physical evolution on not only the biological but cosmic level, the CTMU addresses the most evident deficiencies and paradoxes associated with conventional discrete and continuum models of reality, including temporal directionality and accelerating cosmic expansion, while preserving virtually all of the major benefits of current scientific and mathematical paradigms.

Model Generation for Natural Language Interpretation and Analysis

Model Generation for Natural Language Interpretation and Analysis PDF Author: Karsten Konrad
Publisher: Springer
ISBN: 3540246401
Category : Computers
Languages : en
Pages : 176

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Book Description
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.

Current Topics in Logic and Analytic Philosophy

Current Topics in Logic and Analytic Philosophy PDF Author: Concha Martínez
Publisher: Univ Santiago de Compostela
ISBN: 8497508114
Category : Analysis (Philosophy)
Languages : en
Pages : 289

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Book Description


Logical Structures for Representation of Knowledge and Uncertainty

Logical Structures for Representation of Knowledge and Uncertainty PDF Author: Ellen Hisdal
Publisher: Physica
ISBN: 3790818879
Category : Mathematics
Languages : en
Pages : 440

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Book Description
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).