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Foundations of Mathematical Logic
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Perspectives on the History of Mathematical Logic
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.
Practical Haskell
Get a practical, hands-on introduction to the Haskell language, its libraries and environment, and to the functional programming paradigm that is fast growing in importance in the software industry. This book contains excellent coverage of the Haskell ecosystem and supporting tools, include Cabal and Stack for managing projects, HUnit and QuickCheck for software testing, the Spock framework for developing web applications, Persistent and Esqueleto for database access, and parallel and distributed programming libraries. You’ll see how functional programming is gathering momentum, allowing you to express yourself in a more concise way, reducing boilerplate, and increasing the safety of your ...
Combinatory Logic
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Haskell Programming
A balance of flexible and inflexible qualities make Haskell a fascinating programming language to learn and use. First, the Haskell programming language is not named after Eddie Haskell, the sneaky double-dealing neighbor kid in the ancient TV sitcom, Leave It To Beaver. Haskell is named after Haskell Brooks Curry, an American mathematician and logician. If you don't know, logicians create models to describe and define human reasoning, for example, problems in mathematics, computer science, and philosophy. Haskell's main work was in combinatory logic, a notation designed to eliminate the need for variables in mathematical logic. Combinatory logic captures many key features of computation and...
First Order Mathematical Logic
"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. I...
Combinatory Linguistics
The book examines to what extent the mediating relation between constituents and their semantics can arise from combinatory knowledge of words. It traces the roots of Combinatory Categorial Grammar, and uses the theory to promote a Humean question in linguistics and cognitive science: Why do we see limited constituency and dependency in natural languages, despite their diversity and potential infinity? A potential answer is that constituents and dependencies might have arisen from a single resource: adjacency. The combinatory formulation of adjacency constrains possible grammars.
Crime, Shame and Reintegration
Crime, Shame and Reintegration is a contribution to general criminological theory. Its approach is as relevant to professional burglary as to episodic delinquency or white collar crime. Braithwaite argues that some societies have higher crime rates than others because of their different processes of shaming wrongdoing. Shaming can be counterproductive, making crime problems worse. But when shaming is done within a cultural context of respect for the offender, it can be an extraordinarily powerful, efficient and just form of social control. Braithwaite identifies the social conditions for such successful shaming. If his theory is right, radically different criminal justice policies are needed - a shift away from punitive social control toward greater emphasis on moralizing social control. This book will be of interest not only to criminologists and sociologists, but to those in law, public administration and politics who are concerned with social policy and social issues.
Lectures on the Curry-Howard Isomorphism
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance,...
Self-Efficacy in Changing Societies
The volume addresses important issues of human adaptation and change.
