The Elements Of Mathematical Semantics

Author : Maurice V. Aldridge
Publisher : Walter de Gruyter
Page : 277 pages
File Size : 41,6 Mb
Release : 2011-06-01
Category : Language Arts & Disciplines
ISBN : 9783110871432

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The Elements of Mathematical Semantics by Maurice V. Aldridge Pdf

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.

Author : Yoad Winter
Publisher : Edinburgh University Press
Page : 272 pages
File Size : 44,7 Mb
Release : 2016-04-08
Category : Language Arts & Disciplines
ISBN : 9780748677771

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Elements of Formal Semantics by Yoad Winter Pdf

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.

Author : Jerzy Słupecki,Ludwik Borkowski
Publisher : Pergamon
Page : 372 pages
File Size : 40,5 Mb
Release : 1967
Category : Mathematics
ISBN : UCAL:B4396227

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Elements of Mathematical Logic and Set Theory by Jerzy Słupecki,Ludwik Borkowski Pdf

Author : Pascal Hitzler,Anthony Seda
Publisher : CRC Press
Page : 305 pages
File Size : 45,6 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781439829622

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Mathematical Aspects of Logic Programming Semantics by Pascal Hitzler,Anthony Seda Pdf

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 : Michal Walicki
Publisher : World Scientific Publishing Company
Page : 304 pages
File Size : 40,9 Mb
Release : 2016-08-12
Category : Mathematics
ISBN : 9789814719988

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Introduction To Mathematical Logic (Extended Edition) by Michal Walicki Pdf

This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.

Author : T. Streicher
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461204336

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Semantics of Type Theory by T. Streicher Pdf

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.

Author : Paul C. Rosenbloom
Publisher : Courier Dover Publications
Page : 0 pages
File Size : 44,6 Mb
Release : 2005
Category : Logic, Symbolic and mathematical
ISBN : 0486446174

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The Elements of Mathematical Logic by Paul C. Rosenbloom Pdf

An excellent introduction to mathematical logic, this book provides readers with a sound knowledge of the most important approaches to the subject, stressing the use of logical methods in attacking nontrivial problems. Its chapters cover the logic of classes (including a section on the structure and representation of Boolean algebras, which are applied in the following chapters to the study of deductive systems), the logic of propositions, the logic of propositional functions (summarizing the methods of Russell, Quine, Zermelo, Curry, and Church for the construction of such logics), and the general syntax of language, with a brief introduction that also illustrates applications to so-called undecidability and incompleteness theorems. Other topics include the simple proof of the completeness of the theory of combinations, Church's theorem on the recursive unsolvability of the decision problem for the restricted function calculus, and the demonstrable properties of a formal system as a criterion for its acceptability.

Author : Alberto Peruzzi,Silvano Zipoli Caiani
Publisher : Springer Nature
Page : 191 pages
File Size : 45,7 Mb
Release : 2020-09-14
Category : Philosophy
ISBN : 9783030518219

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Structures Mères: Semantics, Mathematics, and Cognitive Science by Alberto Peruzzi,Silvano Zipoli Caiani Pdf

This book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for future research on this topic.

Author : Casper Storm Hansen
Publisher : Springer Nature
Page : 259 pages
File Size : 54,9 Mb
Release : 2021-11-04
Category : Mathematics
ISBN : 9783030885342

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Founding Mathematics on Semantic Conventions by Casper Storm Hansen Pdf

This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches.

Author : Vladimir Fomichov A.
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 45,9 Mb
Release : 2009-12-01
Category : Science
ISBN : 9780387729268

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Semantics-Oriented Natural Language Processing by Vladimir Fomichov A. Pdf

Gluecklich, die wissen, dass hinter allen Sprachen das Unsaegliche steht. Those are happy who know that behind all languages there is something unsaid Rainer Maria Rilke This book shows in a new way that a solution to a fundamental problem from one scienti?c ?eld can help to ?nd the solutions to important problems emerged in several other ?elds of science and technology. In modern science, the term “Natural Language” denotes the collection of all such languages that every language is used as a primary means of communication by people belonging to any country or any region. So Natural Language (NL) includes, in particular, the English, Russian, and German languages. The applied computer systems processing natural language printed or written texts (NL-texts) or oral speech with respect to the fact that the words are associated with some meanings are called semantics-oriented natural language processing s- tems (NLPSs). On one hand, this book is a snapshot of the current stage of a research p- gram started many years ago and called Integral Formal Semantics (IFS) of NL. The goal of this program has been to develop the formal models and methods he- ing to overcome the dif?culties of logical character associated with the engineering of semantics-oriented NLPSs. The designers of such systems of arbitrary kinds will ?nd in this book the formal means and algorithms being of great help in their work.

Author : Eric Snyder
Publisher : Cambridge University Press
Page : 75 pages
File Size : 51,9 Mb
Release : 2021-05-31
Category : Science
ISBN : 1108456251

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Semantics and the Ontology of Number by Eric Snyder Pdf

What are the meanings of number expressions, and what can they tell us about questions of central importance to the philosophy of mathematics, specifically 'Do numbers exist?' This Element attempts to shed light on this question by outlining a recent debate between substantivalists and adjectivalists regarding the semantic function of number words in numerical statements. After highlighting their motivations and challenges, I develop a comprehensive polymorphic semantics for number expressions. I argue that accounting for the numerous meanings and how they are related leads to a strengthened argument for realism, one which renders familiar forms of nominalism highly implausible.

Author : Michael Main,Austin Melton,Michael Mislove,David Schmidt
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 41,7 Mb
Release : 1988-03-09
Category : Mathematics
ISBN : 3540190201

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Mathematical Foundations of Programming Language Semantics by Michael Main,Austin Melton,Michael Mislove,David Schmidt Pdf

This volume is the proceedings of the 3rd Workshop on the Mathematical Foundations of Programming Language Semantics held at Tulane University, New Orleans, Louisiana, April 8-10, 1987. The 1st Workshop was at Kansas State University, Manhattan, Kansas in April, 1985 (see LNCS 239), and the 2nd Workshop with a limited number of participants was at Kansas State in April, 1986. It was the intention of the organizers that the 3rd Workshop survey as many areas of the Mathematical Foundations of Programming Language Semantics as reasonably possible. The Workshop attracted 49 submitted papers, from which 28 papers were chosen for presentation. The papers ranged in subject from category theory and Lambda-calculus to the structure theory of domains and power domains, to implementation issues surrounding semantics.

Author : Stephen Brookes
Publisher : Springer Science & Business Media
Page : 664 pages
File Size : 49,7 Mb
Release : 1994-05-20
Category : Computers
ISBN : 3540580271

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Mathematical Foundations of Programming Semantics by Stephen Brookes Pdf

This volume is the proceedings of the Ninth International Conference on the Mathematical Foundations of Programming Semantics, held in New Orleans in April 1993. The focus of the conference series is the semantics of programming languages and the mathematics which supports the study of the semantics. The semantics is basically denotation. The mathematics may be classified as category theory, lattice theory, or logic. Recent conferences and workshops have increasingly emphasized applications of the semantics and mathematics. The study of the semantics develops with the mathematics and the mathematics is inspired by the applications in semantics. The volume presents current research in denotational semantics and applications of category theory, logic, and lattice theory to semantics.

Author : Barbara B.H. Partee,A.G. ter Meulen,R. Wall
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Language Arts & Disciplines
ISBN : 9789400922136

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Mathematical Methods in Linguistics by Barbara B.H. Partee,A.G. ter Meulen,R. Wall Pdf

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

Author : Marisa Venturini Zilli
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 53,8 Mb
Release : 1987-10-07
Category : Computers
ISBN : 3540184198

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Mathematical Models for the Semantics of Parallelism by Marisa Venturini Zilli Pdf

The papers collected in this volume are most of the material presented at the Advanced School on Mathematical Models for the Semantics of Parallelism, held in Rome, September 24- October 1, 1986. The need for a comprehensive and clear presentation of the several semantical approaches to parallelism motivated the stress on mathematical models, by means of which comparisons among different approaches can also be performed in a perspicuous way.