Handbook of Logic in Computer Science Volume 5: Logic and Algebraic Methods

, by Abramsky, S.; Gabbay, Dov. M.; Maibaum, T. S. E.

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ISBN: 9780198537816 | 0198537816
Cover: Hardcover
Copyright: 4/5/2001

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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 toany serious worker in the areas.

List of contributors

xvii

Martin-Lof's type theory

(38)

B. Nordstrom

K. Petersson

J. M. Smith

Introduction

(3)

Different formulations of type theory

(1)

Implementations

(1)

Propositions as sets

(3)

Semantics and formal rules

(9)

Types

(2)

Hypothetical judgements

(3)

Function types

(2)

The type Set

(1)

Definitions

(1)

Propositional logic

(3)

Set theory

(13)

The set of Boolean values

(1)

The empty set

(1)

The set of natural numbers

(2)

The set of functions (Cartesian product of a family of sets)

(3)

Propositional equality

(2)

The set of lists

(1)

Disjoint union of two sets

(1)

Disjoint union of a family of sets

(1)

The set of small sets

(2)

The ALF series of interactive editors for type theory

(7)

Categorial logic

(84)

Andrew M. Pitts

Introduction

(3)

Equational logic

(7)

Syntactic considerations

(1)

Categorical semantics

(3)

Internal languages

(2)

Categorical datatypes

(17)

Disjoint union types

(5)

Product types

(3)

Function types

(2)

Inductive types

(3)

Computation types

(2)

Theories as categories

(10)

Change of category

(1)

Clasifying category of a theory

(5)

Theory--category correspondence

(2)

Theories with datatypes

(2)

Predicate logic

(23)

Formulas and sequents

(1)

Hyperdoctrines

(4)

Satisfaction

(2)

Propositional connectives

(5)

Quantification

(4)

Equality

(4)

Completeness

(3)

Dependent types

100

(23)

Syntactic considerations

101

(6)

Classifying category of a theory

107

(2)

Type-categories

109

(5)

Categorical semantics

114

(5)

Dependent products

119

(4)

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Handbook of Logic in Computer Science Volume 5: Logic and Algebraic Methods

Summary

Table of Contents

Supplemental Materials