## Introduction to Higher-Order Categorical Logic

**Author**: J. Lambek,P. J. Scott

**Publisher:**Cambridge University Press

**ISBN:**9780521356534

**Category:**Mathematics

**Page:**304

**View:**533

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Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

## Theorem Proving in Higher Order Logics

*22nd International Conference, TPHOLs 2009, Munich, Germany, August 17-20, 2009, Proceedings*

**Author**: Stefan Berghofer,Tobias Nipkow,Christian Urban,Makarius Wenzel

**Publisher:**Springer

**ISBN:**3642033598

**Category:**Computers

**Page:**517

**View:**1583

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This book constitutes the refereed proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics, TPHOLs 200, held in Munich, Germany, in August 2009. The 26 revised full papers presented together with 1 proof pearl, 4 tool presentations, and 3 invited papers were carefully reviewed and selected from 55 submissions. The papers cover all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification such as formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.

## Mathematical Logic and Theoretical Computer Science

**Author**: Kueker

**Publisher:**CRC Press

**ISBN:**9780824777463

**Category:**Mathematics

**Page:**408

**View:**2969

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## Categorical Foundations

*Special Topics in Order, Topology, Algebra, and Sheaf Theory*

**Author**: Maria Cristina Pedicchio,Walter Tholen,G. C. Rota

**Publisher:**Cambridge University Press

**ISBN:**9780521834148

**Category:**Mathematics

**Page:**417

**View:**4974

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The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics.

## Automated Reasoning

*Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings*

**Author**: Ulrich Furbach,Natarajan Shankar

**Publisher:**Springer Science & Business Media

**ISBN:**3540371877

**Category:**Computers

**Page:**688

**View:**6168

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Here are the proceedings of the Third International Joint Conference on Automated Reasoning, IJCAR 2006, held in Seattle, Washington, USA, August 2006. The book presents 41 revised full research papers and 8 revised system descriptions, with 3 invited papers and a summary of a systems competition. The papers are organized in topical sections on proofs, search, higher-order logic, proof theory, proof checking, combination, decision procedures, CASC-J3, rewriting, and description logic.

## Logic for Applications

**Author**: Anil Nerode,Richard Shore

**Publisher:**Springer Science & Business Media

**ISBN:**9780387948935

**Category:**Computers

**Page:**456

**View:**2348

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In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

## Lecture notes in pure and applied mathematics

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**7279

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## International Mathematical News

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**7368

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## Categorical Logic

**Author**: Andrew M. Pitts

**Publisher:**N.A

**ISBN:**N.A

**Category:**Logic, Symbolic and mathematical

**Page:**94

**View:**3273

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Abstract: "This document provides an introduction to the interaction between category theory and mathematical logic which is slanted towards computer scientists."

## Relative category theory and geometric morphisms

*a logical approach*

**Author**: Jonathan Chapman,Frederick Rowbottom

**Publisher:**Oxford University Press, USA

**ISBN:**N.A

**Category:**Mathematics

**Page:**263

**View:**3272

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Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical approach to be taken to topics such as category theory relative to a topos and the relative Giraud theorem. The work is self-contained except that the authors presuppose a familiarity with basic category theory and topos theory. Logicians, set and category theorists, and computer scientist working in the field will find this work essential reading.

## Names and Higher-order Functions

**Author**: Ian David Bede Stark,University of Cambridge. Computer Laboratory

**Publisher:**N.A

**ISBN:**N.A

**Category:**Functional programming (Computer science)

**Page:**140

**View:**3920

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Abstract: "Many functional programming languages rely on the elimination of 'impure' features: assignment to variables, exceptions and even input/output. But some of these are genuinely useful, and it is of real interest to establish how they can be reintroducted [sic] in a controlled way. This dissertation looks in detail at one example of this: the addition to a functional language of dynamically generated names. Names are created fresh, they can be compared with each other and passed around, but that is all. As a very basic example of state, they capture the graduation between private and public, local and global, by their interaction with higher-order functions. The vehicle for this study is the nu-calculus, an extension of the simply-typed lambda calculus. The nu calculus is equivalent to a certain fragment of Standard ML, omitting side- effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higher-order functions can be complex and subtle. Various operational and denotational methods for reasoning about the nu-calculus are developed. These include a computational metalanguage in the style of Moggi, which distinguishes in the type system between values and computations. This leads to categorical models that use a strong monad, and examples are devised based on functor categories. The idea of logical relations is used to derive powerful reasoning methods that capture some of the distinction between private and public names. These techniques are shown to be complete for establishing contextual equivalence between first-order expressions; they are also used to construct a correspondingly abstract categorical model All the work with the nu-calculus extends cleanly to Reduced ML, a larger language that introduces integer references: mutable storage cells that are dynamically allocated. It turns out that the step up is quite simple, and both the computational metalanguage and the simple categorical models can be reused."

## Handbook of Theoretical Computer Science: Formal models and semantics

**Author**: Jan Leeuwen

**Publisher:**Elsevier Science

**ISBN:**9780444880741

**Category:**Computers

**Page:**1280

**View:**9745

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The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing.

## Categories in computer science and logic

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**403

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## Computer Science Logic

*18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 20-24, 2004, Proceedings*

**Author**: Jerzy Marcinkowski

**Publisher:**Springer

**ISBN:**N.A

**Category:**Computer science

**Page:**520

**View:**7953

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This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.

## Constructive Kripke semantics and realizability

**Author**: James Lipton

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**33

**View:**1766

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## Categorical Algebra and its Applications

*Proceedings of a Conference, Held in Louvain-la-Neuve, Belgium, July 26 - August 1, 1987*

**Author**: Francis Borceux

**Publisher:**Springer

**ISBN:**9783540503620

**Category:**Mathematics

**Page:**382

**View:**1582

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Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.

## Subject Guide to Books in Print

*An Index to the Publishers' Trade List Annual*

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**American literature

**Page:**N.A

**View:**8642

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## The Bulletin of Symbolic Logic

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Logic, Symbolic and mathematical

**Page:**N.A

**View:**7143

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## Principia Mathematica.

**Author**: Alfred North Whitehead,Bertrand Russell

**Publisher:**N.A

**ISBN:**N.A

**Category:**Logic, Symbolic and mathematical

**Page:**167

**View:**8470

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