Joachim Lambek The Interplay Of Mathematics Logic And Linguistics
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Joachim Lambek The Interplay Of Mathematics Logic And Linguistics
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Author : Claudia Casadio
language : en
Publisher: Springer Nature
Release Date : 2021-03-20
Joachim Lambek The Interplay Of Mathematics Logic And Linguistics written by Claudia Casadio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-20 with Philosophy categories.
This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.
Introduction To Higher Order Categorical Logic
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Author : J. Lambek
language : en
Publisher: Cambridge University Press
Release Date : 1988-03-25
Introduction To Higher Order Categorical Logic written by J. Lambek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-25 with Mathematics categories.
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Logic Language Information And Computation
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Author : Alexandra Silva
language : en
Publisher: Springer Nature
Release Date : 2021-10-05
Logic Language Information And Computation written by Alexandra Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-05 with Philosophy categories.
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.
New Perspectives In Algebra Topology And Categories
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Author : Maria Manuel Clementino
language : en
Publisher: Springer Nature
Release Date : 2021-10-16
New Perspectives In Algebra Topology And Categories written by Maria Manuel Clementino and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-16 with Mathematics categories.
This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of « roadmap » and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as « self-contained » chapters, the authors have tried to coordinate the texts in order to make them complementary. The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds d’Appui à l’Internationalisation of the Université catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.
Toposes Triples And Theories
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Author : M. Barr
language : en
Publisher: Springer
Release Date : 2013-06-09
Toposes Triples And Theories written by M. Barr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-09 with Mathematics categories.
As its title suggests, this book is an introduction to three ideas and the connections between them. Before describing the content of the book in detail, we describe each concept briefly. More extensive introductory descriptions of each concept are in the introductions and notes to Chapters 2, 3 and 4. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. In that sense, a topos is a generalized set theory. However, it originated with Grothendieck and Giraud as an abstraction of the of the category of sheaves of sets on a topological space. Later, properties Lawvere and Tierney introduced a more general id~a which they called "elementary topos" (because their axioms did not quantify over sets), and they and other mathematicians developed the idea that a theory in the sense of mathematical logic can be regarded as a topos, perhaps after a process of completion. The concept of triple originated (under the name "standard construc in Godement's book on sheaf theory for the purpose of computing tions") sheaf cohomology. Then Peter Huber discovered that triples capture much of the information of adjoint pairs. Later Linton discovered that triples gave an equivalent approach to Lawverc's theory of equational theories (or rather the infinite generalizations of that theory). Finally, triples have turned out to be a very important tool for deriving various properties of toposes.
Types And Programming Languages
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Author : Benjamin C. Pierce
language : en
Publisher: MIT Press
Release Date : 2002-01-04
Types And Programming Languages written by Benjamin C. Pierce and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-04 with Computers categories.
A comprehensive introduction to type systems and programming languages. A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems—and of programming languages from a type-theoretic perspective—has important applications in software engineering, language design, high-performance compilers, and security. This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.
The Syntactic Process
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Author : Mark Steedman
language : en
Publisher: MIT Press
Release Date : 2000
The Syntactic Process written by Mark Steedman and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Language Arts & Disciplines categories.
In this book Mark Steedman argues that the surface syntax of natural languages maps spoken and written forms directly to a compositional semantic representation that includes predicate-argument structure, quantification, and information structure, without constructing any intervening structural representation. His purpose is to construct a principled theory of natural grammar that is directly compatible with both explanatory linguistic accounts of a number of problematic syntactic phenomena and a straightforward computational account of the way sentences are mapped onto representations of meaning. The radical nature of Steedman's proposal stems from his claim that much of the apparent complexity of syntax, prosody, and processing follows from the lexical specification of the grammar and from the involvement of a small number of universal rule-types for combining predicates and arguments. These syntactic operations are related to the combinators of Combinatory Logic, engendering a much freer definition of derivational constituency than is traditionally assumed. This property allows Combinatory Categorial Grammar to capture elegantly the structure and interpretation of coordination and intonation contour in English as well as some well-known interactions between word order, coordination, and relativization across a number of other languages. It also allows more direct compatibility with incremental semantic interpretation during parsing. The book covers topics in formal linguistics, intonational phonology, computational linguistics, and experimental psycholinguistics, presenting them as an integrated theory of the language faculty in a form accessible to readers from any of those fields.
Information Arts
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Author : Stephen Wilson
language : en
Publisher: MIT Press
Release Date : 2003-02-28
Information Arts written by Stephen Wilson and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-28 with Social Science categories.
An introduction to the work and ideas of artists who use—and even influence—science and technology. A new breed of contemporary artist engages science and technology—not just to adopt the vocabulary and gizmos, but to explore and comment on the content, agendas, and possibilities. Indeed, proposes Stephen Wilson, the role of the artist is not only to interpret and to spread scientific knowledge, but to be an active partner in determining the direction of research. Years ago, C. P. Snow wrote about the "two cultures" of science and the humanities; these developments may finally help to change the outlook of those who view science and technology as separate from the general culture. In this rich compendium, Wilson offers the first comprehensive survey of international artists who incorporate concepts and research from mathematics, the physical sciences, biology, kinetics, telecommunications, and experimental digital systems such as artificial intelligence and ubiquitous computing. In addition to visual documentation and statements by the artists, Wilson examines relevant art-theoretical writings and explores emerging scientific and technological research likely to be culturally significant in the future. He also provides lists of resources including organizations, publications, conferences, museums, research centers, and Web sites.
Picturing Quantum Processes
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Author : Bob Coecke
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-16
Picturing Quantum Processes written by Bob Coecke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Computers categories.
Quantum phenomena are explained through the language of diagrams, setting out an innovative visual method of presenting complex scientific theories. Focusing on physical intuition over mathematical formalism, and packed with exercises, this unique book is accessible to students and researchers across scientific disciplines, from undergraduate to Ph.D. level.
Foundations Of Software Science And Computation Structures
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Author : Jean Goubault-Larrecq
language : en
Publisher:
Release Date : 2020-10-09
Foundations Of Software Science And Computation Structures written by Jean Goubault-Larrecq and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-09 with Computers categories.
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.