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An Introduction to Substructural Logics
 
 

An Introduction to Substructural Logics [Paperback]

Greg Restall (Author)

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Book Description

041521534X 978-0415215343 February 3, 2000 First Edition
This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:
* Proof Theory
* Propositional Structures
* Frames
* Decidability
* Coda
Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

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Editorial Reviews

Review

Greg Lestall offers a comprehensive introduction to substructural logics, some examples of which are relevant logics, linear logic, the Lambek calculus, and Lukasiewicz's many-valued logics. Restall discusses the question of what distinguishes these logics from classical logic; what motivates the creation of these logics; how theorums in the Lambek calculus are proved; what rules the Lambek calculus reinterprets or drops; what kinds of semantics can be given for these kinds of logics; and whether these logics are decidable. In every case Restall's book does a good job of presenting answers to these questions..
Teaching Philosophy

About the Author

Greg Restall, Macquarie University

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Greg Restall teaches and researches in Logic and Philosophy at the University of Melbourne. He's likes the way his work oscillates between the discursive and the technical. When proving a theorem is too difficult, there's always handwaving. When coming up with a good explanation for something doesn't work, we can retreat into technicalities. Greg blogs at consequently.org.

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Inside This Book (learn more)
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
substructural logics, consecution system, strong excluded middle, split negation, canonical accessibility relations, following consecutions, antecedent regularity, lattice connectives, intensional connectives, extensional conjunction, double negation introduction, positive modality, modal confusion, closure frame, generated subframe, positive modalities, consequent position, prime theory, poset categories, prime theories, connective rules, finite model property, premise combination, natural deduction system, intuitionistic linear logic
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Practice, Left Push, Left Pop, Pair Extension Theorem, Slice Lemma, Curry's Lemma, Entailment Volume
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