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Combinatory Logic: Pure, Applied and Typed (Discrete Mathematics and Its Applications) [Hardcover]

Katalin Bimbó
5.0 out of 5 stars  See all reviews (1 customer review)

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Book Description

July 27, 2011 1439800006 978-1439800003 1

Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.

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Editorial Reviews


For beginners, it is a compact introduction, including exercises, to the classical syntactic theory of combinators with some pointers to their models and their relation with λ-calculus. More advanced readers may find in the book much information on the connections between combinators and non-classical and substructural logics that are now a prominent topic in several areas, from philosophical logic to theoretical computer science, information that is mostly scattered through the research literature.

One of the commendable aspects of the book is its extensive and up-to-date bibliography, which deals with CL and other relevant topics in logic; it will surely aid many readers who may need to brush up on background information in the course of their study.
—Computing Reviews, 2012

About the Author

Katalin Bimbo is an assistant professor in the Department of Philosophy at the University of Alberta in Edmonton, Canada.

Product Details

  • Series: Discrete Mathematics and Its Applications
  • Hardcover: 357 pages
  • Publisher: Chapman and Hall/CRC; 1 edition (July 27, 2011)
  • Language: English
  • ISBN-10: 1439800006
  • ISBN-13: 978-1439800003
  • Product Dimensions: 6.3 x 9.5 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,589,800 in Books (See Top 100 in Books)

More About the Author

Katalin Bimbó is a logician. She works at the University of Alberta in Canada. Earlier, she held academic positions at other universities including Indiana University Bloomington (USA), Victoria University of Wellington (New Zealand) and the Australian National University (Australia).

Katalin Bimbó's main research interests are in the field of nonclassical logics such as combinatory logic, relevance logics, modal logics, substructural and structurally free logics. She solved (with J. Michael Dunn) a long-open problem concerning the decidability of the logic of implicational ticket entailment -- using sequent calculi. Her research spans the semantics and the proof theory of classical and nonclassical logics.

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1 of 1 people found the following review helpful
5.0 out of 5 stars looks nice September 23, 2011
Format:Hardcover|Verified Purchase
Table of contents:
1. elements of combinatory logic
2. main theorems
3. recursive functions and arithmetic
4. connections to lambda-calculi
5. (in)equational combinatory logic
6. models
7. dual and symmetric combinatory logics
8. applied combinatory logic
9. typed combinatory logic

I have just skimmed through the book. It seems to be written in a very clear style, explaining the rationale behind the study of combo logic and its historical roots.

The author is interested in applying combo logic to the study of linear / substructural logics, whereas I'm interested in the untyped aspect of illative logic.

Ch 7 deals with duality, ie, where f(n) is the function f applied to the number n, it can be dually encoded as the number n applied to f. This is new to me.

Ch 8 deals briefly with illative combo logic.

My library doesn't have this book, so I bought it and keep it as a reference.
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