Combinators, λ-Terms and Proof Theory
Combinators, λ-Terms and Proof Theory

Author: S. Stenlund

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 186

ISBN-13: 940102913X

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The aim of this monograph is to present some of the basic ideas and results in pure combinatory logic and their applications to some topics in proof theory, and also to present some work of my own. Some of the material in chapter 1 and 3 has already appeared in my notes Introduction to Combinatory Logic. It appears here in revised form since the presen tation in my notes is inaccurate in several respects. I would like to express my gratitude to Stig Kanger for his invalu able advice and encouragement and also for his assistance in a wide variety of matters concerned with my study in Uppsala. I am also in debted to Per Martin-USf for many valuable and instructive conversa tions. As will be seen in chapter 4 and 5, I also owe much to the work of Dag Prawitz and W. W. Tait. My thanks also to Craig McKay who read the manuscript and made valuable suggestions. I want, however, to emphasize that the shortcomings that no doubt can be found, are my sole responsibility. Uppsala, February 1972.

Lambda-Calculus and Combinators
Lambda-Calculus and Combinators

Author: J. Roger Hindley

Publisher: Cambridge University Press

Published: 2008-07-24

Total Pages: 358

ISBN-13: 9780521898850

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Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

Bijective Combinatorics
Bijective Combinatorics

Author: Nicholas Loehr

Publisher: CRC Press

Published: 2011-02-10

Total Pages: 600

ISBN-13: 1439848866

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Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical

Proof Theory
Proof Theory

Author: Katalin Bimbo

Publisher: CRC Press

Published: 2014-08-20

Total Pages: 388

ISBN-13: 1466564660

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Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.

Combinatorics on Words
Combinatorics on Words

Author: Thierry Lecroq

Publisher: Springer Nature

Published: 2021-09-06

Total Pages: 210

ISBN-13: 3030850889

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This book constitutes the refereed proceedings of the 13th International Conference on Combinatorics on Words, WORDS 2021, held virtually in September 2021. The 14 revised full papers presented in this book together with 2 invited talks were carefully reviewed and selected from 18 submissions. WORDS is the main conference series devoted to the mathematical theory of words. In particular, the combinatorial, algebraic and algorithmic aspects of words are emphasized. Motivations may also come from other domains such as theoretical computer science, bioinformatics, digital geometry, symbolic dynamics, numeration systems, text processing, number theory, etc.

Collected Papers on Epistemology, Philosophy of Science and History of Philosophy
Collected Papers on Epistemology, Philosophy of Science and History of Philosophy

Author: W. Stegmüller

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 328

ISBN-13: 940101129X

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These two volumes contain all of my articles published between 1956 and 1975 which might be of interest to readers in the English-speaking world. The first three essays in Vol. 1 deal with historical themes. In each case I as far as possible, meets con have attempted a rational reconstruction which, temporary standards of exactness. In The Problem of Universals Then and Now some ideas of W.V. Quine and N. Goodman are used to create a modern sketch of the history of the debate on universals beginning with Plato and ending with Hao Wang's System L. The second article concerns Kant's Philosophy of Science. By analyzing his position vis-a-vis I. Newton, Christian Wolff, and D. Hume, it is shown that for Kant the very notion of empirical knowledge was beset with a funda mental logical difficulty. In his metaphysics of experience Kant offered a solution differing from all prior as well as subsequent attempts aimed at the problem of establishing a scientific theory. The last of the three historical papers utilizes some concepts of modern logic to give a precise account of Wittgenstein's so-called Picture Theory of Meaning. E. Stenius' interpretation of this theory is taken as an intuitive starting point while an intensional variant of Tarski's concept of a relational system furnishes a technical instrument. The concepts of inodel world and of logical space, together with those of homomorphism and isomorphism be tween model worlds and between logical spaces, form the conceptual basis of the reconstruction.

Handbook of Combinatorics
Handbook of Combinatorics

Author: Ronald L. Graham

Publisher: MIT Press

Published: 2003-03

Total Pages: 1130

ISBN-13: 9780262571722

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Covers combinatorics in graph theory, theoretical computer science, optimization, and convexity theory, plus applications in operations research, electrical engineering, statistical mechanics, chemistry, molecular biology, pure mathematics, and computer science.

A New Kind of Science
A New Kind of Science

Author: Stephen Wolfram

Publisher:

Published: 2002

Total Pages: 1197

ISBN-13: 9780713991161

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This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.