Reflexive Structures
Reflexive Structures

Author: Luis E. Sanchis

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 243

ISBN-13: 1461238781

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Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.

Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures
Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures

Author: S. Abramsky

Publisher: OUP Oxford

Published: 2001-01-25

Total Pages: 556

ISBN-13: 0191546275

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This handbook volume covers fundamental topics of semantics in logic and computation. The chapters (some monographic in length), were written following years of co-ordination and follow a thematic point of view. The volume brings the reader up to front line research, and is indispensable to any serious worker in the areas.

Constructivism in Mathematics, Vol 2
Constructivism in Mathematics, Vol 2

Author: A.S. Troelstra

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 607

ISBN-13: 008095510X

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Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Theories of Computability
Theories of Computability

Author: Nicholas Pippenger

Publisher: Cambridge University Press

Published: 1997-05-28

Total Pages: 268

ISBN-13: 9780521553803

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A mathematically sophisticated introduction to Turing's theory, Boolean functions, automata, and formal languages.

Tzotzil Clause Structure
Tzotzil Clause Structure

Author: J. Aissen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 312

ISBN-13: 9400937415

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xv NOTES ON THE ORTHOGRAPHY AND CITATIONS xxi LIST OF ABBREVIA TIONS XXIIl CHAPTER 1: GRAMMATICAL NOTES 1 1. Introduction 1 2. Basics 1 3. Major Lexical Classes 2 3. 1. V 3 3. 2. N 3 3. 3. A 5 3. 3. 1. Quantifiers 6 3. 3. 2. Existentials and Locatives 6 4. Minor Lexical Classes 7 4. 1. Clitics 7 4. 1. 1. Clause-proclitic 7 4. 1. 2. S-enclitic 8 4. 1. 3. V-enclitic 8 4. 1. 4. Clause-second 9 4. 2. Directionals 9 4. 3. Particles 11 5. Flagging 11 6. Word Order 12 7. Construction Survey 12 7. 1. Negation 12 13 7. 2. Questions 7. 3. Complement Clauses 14 16 7. 4. Motion cum Purpose 17 7. 5. Topics 7. 6. Prepredicate Position 18 19 Notes CHAPTER 2: THEORETICAL SKETCH 20 20 1. Arcs vii Vlll T ABLE OF CONTENTS 1. 1. Sets of Grammatical Relations 22 1. 2. Stratum 24 Ergative and Absolutive 1. 3. 25 1. 4. 25 Formal Connections between Arcs 2. Sponsor and Erase 26 2. 1. Successors 26 2. 2. Replacers 28 2. 3. Self-Sponsor and Self-Erase 30 3. Ancestral Relations 31 4. Pair Networks 31 Resolution of Overlapping Arcs 32 5. 6. Coordinate Determination 33 7. Rules and Laws 35 8. Word Order 36 9. APG Versions of RG Laws 36 9. 1. Stratal Uniqueness Law 36 9. 2. Chomeur Law and Motivated Chomage Law 36 Relational Succession Law and Host Limitation Law 9. 3.

Types for Proofs and Programs
Types for Proofs and Programs

Author: Paul Callaghan

Publisher: Springer

Published: 2003-08-03

Total Pages: 252

ISBN-13: 3540458425

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This book constitutes the thoroughly refereed post-proceedings of the International Workshop of the TYPES Working Group, TYPES 2000, held in Durham, UK in December 2000. The 15 revised full papers presented were carefully reviewed and selected during two rounds of refereeing and revision. All current issues on type theory and type systems and their applications to programming, systems design, and proof theory are addressed.