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Description Introduction to Higher-Order Categorical Logic: 7 (Cambridge Studies in Advanced Mathematics)

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines.

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INTRODUCTION TO HIGHER ORDER CATEGORICAL LOGIC (Cambridge ~ (Cambridge University Press, 1986.) INTRODUCTION TO HIGHER ORDER CATEGORICAL LOGIC (Cambridge Studies in Advanced Mathematics 7) - Pitts - 1987 - Bulletin of the London Mathematical Society - Wiley Online Library

Introduction to Higher-Order Categorical Logic - J. Lambek ~ Introduction to Higher-Order Categorical Logic Volume 7 of Cambridge Studies in Advanced Mathematics, ISSN 0950-6330 Introduction to Higher Order Categorical Logic, Joachim Lambek: Authors: J..

Introduction to Higher-Order Categorical Logic / J. Lambek ~ Introduction to Higher-Order Categorical Logic J. Lambek , P.J. Scott In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory.

1 Cartesian Closed Categories as Models of Typed -Calculus ~ Introduction to higher order Categorical Logic. No. 7 in Cambridge Studies in Advanced Mathematics. Cambridge Univ. Press, 1986. [3] M.H. S˝rensen and P. Urzyczyn. Lectures on the Curry-Howard Isomorphism, vol. 149 of Studies in Logic and the Foundations of Mathematics. Elsevier Science Inc., New York, NY, USA, 2006. [4] G. Winskel.

A categorical manifesto† / Mathematical - Cambridge Core ~ Lambek, J. and Scott, P. (1986) Introduction to Higher Order Categorical Logic. Cambridge Studies in Advanced Mathematics , Volume 7, Cambridge University Press . MacLane , S. ( 1948 ) Duality for groups .

CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS ~ CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS EDITORIAL BOARD B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK Lectures in Logic and Set Theory Volume 2 This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can

Logic for Applications - Anil Nerode, Richard Shore ~ Page 426 - Lambek, J. and Scott, PJ Introduction to Higher Order Categorical Logic. Cambridge Studies in Advanced Mathematics, vol. 7, Cambridge University Press, 1986. [15] Landin, PJ "A correspondence between ALGOL 60 and Church's lambda notation". ‎

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(PDF) The Synthetic Plotkin Powerdomain / Wesley Phoa ~ J. Lambek, From λ-calculus to cartesian closed categories, in: Hindley & Seldin. J. Lambek and P.J. Scott, Introduction to higher order categorical logic, Cambridge stud- ies in advanced mathematics 7, Cambridge University Press, 1986. M. Makkai and G. Reyes, First order categorical logic, Lecture notes in Mathematics 611, Springer, 1977.

Prática - USP ~ [2] F. Borceux , ``Handbook of Categorical Algebra 3: Categories of Sheaves'', Encyclopedia of Mathematics and its Apllications n.52, Cambridge University Press, 1994. [3] R.I. Goldblatt. ``Topoi: the categorical analysis of logic'', Studies in Logic and the Foundations of Math. Vol 98, North Holland, 1979.

Introduction to Turing categories - ScienceDirect ~ The pdf version has active hyperreferences and is therefore the preferred version for reading online. . Introduction to Higher Order Categorical Logic, Cambridge Studies in Advanced Mathematics, vol. 7, Cambridge University Press (1986) Google Scholar

The algebra of recursive graph - Cambridge Core ~ Introduction to Higher Order Categorical Logic, Cambridge Studies in Advanced Mathematics, volume 7, Cambridge University Press. Launchbury , J. ( 1993 ). A natural semantics for lazy evaluation.

What is a categorical model of Intuitionistic Linear Logic ~ Introduction to higher order categorical logic, volume 7 of Cambridge studies in advanced mathematics. Cambridge University Press, 1987. Cambridge University Press, 1987. Google Scholar

Quantum Number Theory / SpringerLink ~ This paper shows that a theory of numbers can be developed within the framework of typed quantum logic. First, the core system of typed quantum logic is stated precisely, on which a theory of numbers is to be built. Second, under a minimal additional assumption about natural number objects, a step-by-step description of quantum real numbersis provided.

Canonicity and Bi-Approximation in Non-Classical Logics - CORE ~ (1994). Handbook of Categorical Algebra 3, volume 52 of Encyclopedia of Mathematics and its Applications. (1985). Heyting Algebra I, Duality Theory. (1986). Introduction to higher order categorical logic, volume 7 of Cambridge studies in advanced mathematics. (2002). Introduction to Lattices and Order. (2000). Introduction to Process Algebra .

Cambridge Studies in Advanced Mathematics Series by M ~ The Cambridge Studies in Advanced Mathematics is a series of books each of which aims to introduce the reader to an active area of mathematical research. All topics in pure mathematics are covered, and treatments are suitable for graduate students, and experts from other branches of mathematics, seeking access to research topics.

proof-theoretic analysis of the classical propositional ~ Abstract. The matrix method, due to Bibel and Andrews, is a proof procedure designed for automated theorem-proving. We show that underlying this method is a fu

computational trinitarianism in nLab ~ Joachim Lambek, Phil Scott, Introduction to Higher Order Categorical Logic, Cambridge Studies in Advanced Mathematics Vol. 7. Cambridge University Press, 1986. See also at History of categorical semantics of linear type theory for more on this. A exposition of the relation between the three concepts is in

epdf.pub_lectures-in-logic-and-set-theory-set-theory.pdf ~ Unformatted text preview: CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS EDITORIAL BOARD B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK Lectures in Logic and Set Theory Volume 2 This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning .

30+ Category Theory ideas / category theory, mathematics ~ Cambridge Studies in Advanced Mathematics: Introduction to Higher Order Categorical Logic (Series #7) (Paperback) In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory.

(PDF) Category Theory: The Language of Mathematics ~ A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.

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Cambridge Mathematical Textbooks (16 books) Kindle Edition ~ From Book 1: This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time.

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