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| Author | : J. Barwise |
| Publisher | : Cambridge University Press |
| Total Pages | : 912 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1107168252 |
This book brings together several directions of work in model theory between the late 1950s and early 1980s.
| Author | : Henk Barendregt |
| Publisher | : Cambridge University Press |
| Total Pages | : 969 |
| Release | : 2013-06-20 |
| Genre | : Mathematics |
| ISBN | : 1107276349 |
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
| Author | : Helmut Schwichtenberg |
| Publisher | : Cambridge University Press |
| Total Pages | : 480 |
| Release | : 2011-12-15 |
| Genre | : Mathematics |
| ISBN | : 1139504169 |
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
| Author | : Robert F. Lusch |
| Publisher | : Cambridge University Press |
| Total Pages | : 253 |
| Release | : 2014-01-30 |
| Genre | : Business & Economics |
| ISBN | : 1139952021 |
In 2004, Robert F. Lusch and Stephen L. Vargo published their groundbreaking article on the evolution of marketing theory and practice toward 'service-dominant (S-D) logic', describing the shift from a product-centred view of markets to a service-led model. Now, in this keenly anticipated book, the authors present a thorough primer on the principles and applications of S-D logic. They describe a clear alternative to the dominant worldview of the heavily planned, production-oriented, profit-maximizing firm, presenting a coherent, organizing framework based on ten foundational premises. The foundational premises of S-D logic have much wider implications beyond marketing for the future of the firm, transcending different industries and contexts, and will provide readers with a deeper sense of why the exchange of service is the fundamental basis of all social and economic exchange. This accessible book will appeal to students, as well as to researchers and practitioners.
| Author | : Keith J. Devlin |
| Publisher | : Cambridge University Press |
| Total Pages | : 438 |
| Release | : 2017-03-16 |
| Genre | : Computers |
| ISBN | : 110716835X |
A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.
| Author | : Stephen George Simpson |
| Publisher | : Cambridge University Press |
| Total Pages | : 461 |
| Release | : 2009-05-29 |
| Genre | : Mathematics |
| ISBN | : 052188439X |
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
| Author | : Thomas Drucker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 2009-05-21 |
| Genre | : Mathematics |
| ISBN | : 0817647694 |
This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
| Author | : Gil Sagi |
| Publisher | : Cambridge University Press |
| Total Pages | : 316 |
| Release | : 2021-09-09 |
| Genre | : Mathematics |
| ISBN | : 1108529828 |
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
| Author | : Jon Barwise |
| Publisher | : Cambridge University Press |
| Total Pages | : 409 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1107168333 |
This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.
| Author | : Eugenio G. Omodeo |
| Publisher | : Springer |
| Total Pages | : 283 |
| Release | : 2017-05-11 |
| Genre | : Computers |
| ISBN | : 3319549812 |
This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.
