The Elements of Mathematical Semantics

for the logical expressions, and if the translations are precise, then, in an important degree, we have the semantics for the natural-language expressions also. The logic which Montague employs, besides being intensional, is both modal ...

Author: Maurice V. Aldridge

Publisher: Walter de Gruyter

ISBN: 9783110871432

Category: Language Arts & Disciplines

Page: 272

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TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.
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The Elements of Mathematical Semantics

The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science.

Author: Maurice Vincent Aldridge

Publisher: Walter de Gruyter

ISBN: 3110129574

Category: Language Arts & Disciplines

Page: 261

View: 184

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TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks, as well as studies that provide new insights by approaching language from an interdisciplinary perspective. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.
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Elements of Formal Semantics

Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning.

Author: Yoad Winter

Publisher: Edinburgh University Press

ISBN: 9780748677771

Category: Language Arts & Disciplines

Page: 272

View: 709

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Introducing some of the foundational concepts, principles and techniques in the formal semantics of natural language, Elements of Formal Semantics outlines the mathematical principles that underlie linguistic meaning. Making use of a wide range of concrete English examples, the book presents the most useful tools and concepts of formal semantics in an accessible style and includes a variety of practical exercises so that readers can learn to utilise these tools effectively. For readers with an elementary background in set theory and linguistics or with an interest in mathematical modelling, this fascinating study is an ideal introduction to natural language semantics. Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning.
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The Alternative Mathematical Model of Linguistic Semantics and Pragmatics

In opposition to the classical set theory of natural language, Novák's highly original monograph offers a theory based on alternative and fuzzy sets.

Author: Vilém Novák

Publisher: Springer Science & Business Media

ISBN: 9781489923172

Category: Language Arts & Disciplines

Page: 204

View: 886

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In opposition to the classical set theory of natural language, Novák's highly original monograph offers a theory based on alternative and fuzzy sets. This new approach is firmly grounded in semantics and pragmatics, and accounts for the vagueness inherent in natural language-filling a large gap in our current knowledge. The theory will foster fruitful debate among researchers in linguistics and artificial intellegence.
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Semantics of Type Theory

Typing plays an important role in software development.

Author: T. Streicher

Publisher: Springer Science & Business Media

ISBN: 9781461204336

Category: Computers

Page: 299

View: 239

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Typing plays an important role in software development. Types can be consid ered as weak specifications of programs and checking that a program is of a certain type provides a verification that a program satisfies such a weak speci fication. By translating a problem specification into a proposition in constructive logic, one can go one step further: the effectiveness and unifonnity of a con structive proof allows us to extract a program from a proof of this proposition. Thus by the "proposition-as-types" paradigm one obtains types whose elements are considered as proofs. Each of these proofs contains a program correct w.r.t. the given problem specification. This opens the way for a coherent approach to the derivation of provably correct programs. These features have led to a "typeful" programming style where the classi cal typing concepts such as records or (static) arrays are enhanced by polymor phic and dependent types in such a way that the types themselves get a complex mathematical structure. Systems such as Coquand and Huet's Calculus of Con structions are calculi for computing within extended type systems and provide a basis for a deduction oriented mathematical foundation of programming. On the other hand, the computational power and the expressive (impred icativity !) of these systems makes it difficult to define appropriate semantics.
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Data Analytics and Management in Data Intensive Domains

Semantic annotation of mathematical texts based on Mocassin and OntoMathPRO ontologies. • The MathLang Document Rhetorical (DRa) Ontology [45] enables one to interpret the elements of document structure using mathematical rhetorical ...

Author: Leonid Kalinichenko

Publisher: Springer

ISBN: 9783319571355

Category: Computers

Page: 281

View: 423

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This book constitutes the refereed proceedings of the 28th International Conference on Data Analytics and Management in Data Intensive Domains, DAMDID/RCDL 2016, held in Ershovo, Moscow, Russia, in October 2016. The 16 revised full papers presented together with one invited talk and two keynote papers were carefully reviewed and selected from 57 submissions. The papers are organized in topical sections on semantic modeling in data intensive domains; knowledge and learning management; text mining; data infrastructures in astrophysics; data analysis; research infrastructures; position paper.
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Intelligent Computer Mathematics

The structure of PMML markup reflects the two-dimensional layout of the mathematical expression. Elements that form semantic units are encapsulated in <mrow> elements, which are comparable to <div> elements in HTML.

Author: Herman Geuvers

Publisher: Springer

ISBN: 9783319620756

Category: Computers

Page: 375

View: 713

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This book constitutes the refereed proceedings of the 10th International Conference on Intelligent Computer Mathematics, CICM 2017, held in Edinburgh, Scotland, in July 2017. The 22 full papers and 3 abstracts of invited papers presented were carefully reviewed and selected from a total of 40 submissions. The papers are organized in three tracks: the Calculemus track examining the integration of symbolic computation and mechanized reasoning; the Digital Mathematics Libraries track dealing with math-aware technologies, standards, algorithms, and processes; the Mathematical Knowledge Management track being concerned with all aspects of managing mathematical knowledge, in informal, semi-formal, and formal settings. An additional track Systems and Projects contains descriptions of systems and relevant projects, both of which are key to a research topic where theory and practice interact on explicitly represented knowledge.
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Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration

Subterms that are not yet enclosed in an mrow or one of the grouping operators listed in [36, table 3.1.3.2] MUST be grouped using the invisible mrow element. 3. For services that need access to the semantics of mathematical expressions ...

Author: C. Lange

Publisher: IOS Press

ISBN: 9781614993452

Category: Computers

Page: 610

View: 411

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Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows. The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contributions of existing knowledge collections of the Web of Data.
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Mathematical Foundation of Programming Semantics

When a collection of Insk informations is of interest , for every one of which there is a more semantic representation and a ... From I one can learn , inter alia , the following : a ) what Synt Infk - s ( i.e. elements of < Synt Inf ...

Author: Austin Melton

Publisher: Springer Science & Business Media

ISBN: 3540168168

Category: Computers

Page: 395

View: 344

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Röntgenbefund und die sich in ihm widerspiegelnde pathologische Anatomie sind neben dem klinischen Bild die wichtigsten Säulen, auf denen die Diagnostik von Knochengeschwülsten und geschwulstähnlichen Läsionen beruht. Radiologen und Pathologen stellen in diesem Buch Klinik, Radiologie und Histolgie der verschiedenen Knochenläsionen am Gliedmaßen- und Achsenskelett umfassend und synoptisch dar. Das umfangreiche Material resultiert aus einer fünfzehnjährigen interdisziplinären Zusammenarbeit. In einem einleitenden Kapitel werden die verschiedenen radiologischen (konventionelles Röntgenbild, CT, Kernspintomographie, Angiographie, transkutane Biopsie) und histologischen Untersuchungstechniken und ihre Wertigkeit beschrieben. Der radiologischen Befundungsmethodik von Knochengeschwülsten u.a. mit Hilfe der Lodwick-Graduierung und einem neueren Staging-System für Knochengeschwülste werden eigene Kapitel gewidmet. Im speziellen Teil des Buches erfolgt die Darstellung der einzelnen benignen und malignen Knochengeschwülste in einer systematischen Untergliederung in ihre Häufigkeit, Lokalisation, Alters- und Geschlechtsprädilektion, Klinik und Prognose, Histologie, Radiologie und Differentialdiagnose. Besonders die unter den Knochengeschwülsten und tumorähnlichen Läsionen häufig vorkommenenden Entitäten sind mit einem umfassenden Bildmaterial ausgestattet, um dem breiten Spektrum ihrer Morphologie gerecht zu werden. Durch das Verständnis klinischer, radiologischer und pathologisch-anatomischer Befunde werden Diagnostik und Therapie der Skelettläsionen sehr erleichtert. Die synoptische Art der Darstellung macht dieses Buch für alle Disziplinen, die sich mit Knochentumoren befassen, zu einem idealen Nachschlagewerk.
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Semantics

The book has been divided into two volumes. The current one is the first volume which highlights the advances in theories and mathematical models in the domain of Semantics. This volume has been divided into four sections and ten chapters.

Author: Muhammad Tanvir Afzal

Publisher: BoD – Books on Demand

ISBN: 9789535105350

Category: Computers

Page: 298

View: 585

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The current book is a nice blend of number of great ideas, theories, mathematical models, and practical systems in the domain of Semantics. The book has been divided into two volumes. The current one is the first volume which highlights the advances in theories and mathematical models in the domain of Semantics. This volume has been divided into four sections and ten chapters. The sections include: 1) Background, 2) Queries, Predicates, and Semantic Cache, 3) Algorithms and Logic Programming, and 4) Semantic Web and Interfaces. Authors across the World have contributed to debate on state-of-the-art systems, theories, mathematical models in the domain of Semantics. Subsequently, new theories, mathematical models, and systems have been proposed, developed, and evaluated.
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The Prague bulletin of mathematical linguistics

This is a slightly different kind of semantic theory : neither a model - theoretic , nor a settheoretic ... so the elements of the picture often loom even in theories which are otherwise developed from different perspectives .

Author:

Publisher:

ISBN: IND:30000085314460

Category: Mathematical linguistics

Page:

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OMDoc An Open Markup Format for Mathematical Documents version 1 2

The attribute type can be used to specify the mathematical type of the number, e.g. complex, real, or integer. ... The m:semantics element provides a way to annotate Content-MathML elements with arbitrary information.

Author: Michael Kohlhase

Publisher: Springer Science & Business Media

ISBN: 9783540378976

Category: Computers

Page: 428

View: 728

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Open Mathematical Documents (OMDoc) is a content markup scheme for mathematical documents including articles, textbooks, interactive books, and courses. OMDoc also serves as the content language for agent communication of mathematical services and a mathematical software bus. This book documents OMDoc version 1.2, the final and mature release of OMDoc 1. The system has been validated in varied applications, and features modularized language design, OPENMATH and MATHML for the representation of mathematical objects.
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Mathematical Knowledge Management

Most MathML content elements allow the definitionURL attribute whose value is a reference to another document that gives more precise semantics to the element it applies to. In the figure the definitionURL attribute is supposed to point ...

Author: Andrea Asperti

Publisher: Springer Science & Business Media

ISBN: 9783540364696

Category: Computers

Page: 230

View: 464

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This book constitutes the refereed proceedings of the Second International Conference on Mathematical Knowledge Management, MKM 2003, held in Betinoro, Italy, in February 2003. The 16 revised full papers presented together with an invited paper were carefully reviewed and selected for presentation. Among the topics addressed are digitization, representation, formalization, proof assistants, distributed libraries of mathematics, NAG library, LaTeX, MathML, mathematics markup, theorem description, query languages for mathematical metadata, mathematical information retrieval, XML-based mathematical knowledge processing, semantic Web, mathematical content management, formalized mathematics repositories, theorem proving, and proof theory.
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Logic and Information

In this provocative and ground-breaking book, Professor Keith Devlin argues that to obtain a deeper understanding of the nature of intelligence and knowledge acquisition we must broaden our concept of logic.

Author: Keith Devlin

Publisher: Cambridge University Press

ISBN: 0521499712

Category: Computers

Page: 307

View: 880

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Paperback edition of ground-breaking new theory of information processing.
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Mathematical Knowledge Management

The main difference lies in the ontological layer, which allows authors of MMiSS documents to create new structural elements or semantic relations by inheriting the predefined ones. Our import and export facility for OMDoc supports ...

Author: Michael Kohlhase

Publisher: Springer Science & Business Media

ISBN: 9783540314301

Category: Computers

Page: 403

View: 291

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This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Mathematical Knowledge Management, MKM 2005, held in Bremen, Germany in July 2005.The 26 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 38 submissions. The papers in this volume cover the whole area of mathematical knowledge management. Topics range from foundations and the representational and document-structure aspects of mathematical knowledge, over process questions like authoring, migration, and consistency management by automated theorem proving to applications in e-learning and case studies.
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A Proposed Software Description Language for Representing Program Logic in XML

Syntax alone is not enough to specify a programming language, and without the specification of semantics a program ... Denotational semantics, which are also called mathematical semantics, assign meanings to language elements by mapping ...

Author: Khaled Mahmoud

Publisher: GRIN Verlag

ISBN: 9783656369684

Category: Computers

Page: 125

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Master's Thesis from the year 2012 in the subject Computer Science - Applied, grade: none, , course: Information Technology , language: English, abstract: This thesis proposes a software description language to represent the source code of C++, Java, and VB.NET in the Extensible Markup Language. The similarity of semantics between these languages enables representing the source code in a form such that both, the source code and logic can be easily shared and reused between these languages. By performing semantic and syntactic comparison between C++, Java and VB.NET, the proposed language has been designed to include the similar and identical features and language constructs. For every adopted language construct, a corresponding construct in the proposed language has been developed. The validity of the proposed language has been investigated and proved theoretically by conducting a semantic comparison between the three languages and experimentally by developing applications to convert source code from Java into the proposed language and from the proposed language into VB.NET. Validation cases have been designed to include various programs such as sorting, searching and also to include the most used programming constructs in the three languages. Source code of the validation cases have been converted from Java into the proposed language, and from the proposed language into VB.NET. Java and VB.NET programs of the validation cases have been executed and results compared. The results were identical for all conducted experiments. The proposed language has some major benefits in the conversion between programming languages as an intermediary language. It may also be used in the integration between systems as it enables sharing of programming logic at runtime. Existing integration technologies only enable the sharing of data between various systems. This thesis is not concerned with adapting programming languages libraries and functions. Future work may extend the proposed language to adapt different features such as pointers and multiple-inheritance into the proposed language.
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H lderlin s Ars poetica

Herdan, Gustav, Type-Token Mathematics: A Textbook of Mathematical Linguistics (Janua linguarum, Series Maior, No. 4.) ('S-Gravenhage, Mouton & Co., ... Rosenbloom, Paul, The Elements of Mathematical Logic (New York, Dover 642 BIBLIOGRAPHY.

Author: Emery Edward George

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783111342566

Category: Language Arts & Disciplines

Page: 699

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Sets Functions and Logic

Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience.

Author: Keith Devlin

Publisher: CRC Press

ISBN: 9780203498736

Category: Mathematics

Page: 160

View: 698

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Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
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The Formal Semantics of Programming Languages

It provides the mathematical basis for our subsequent work on denotational semantics . ... construct ( like a command , or an expression ) is given a meaning by assigning to it an element in a “ domain " of possible meanings .

Author: Glynn Winskel

Publisher: MIT Press

ISBN: 0262731037

Category: Computers

Page: 384

View: 689

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The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.
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