Substructural Logics

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Substructural logics comprise a family of nonclassical logics that arose in response to problems in theoretical computer science, mathematical linguistics, and category theory. They include intuitionist logic, relevant logic, BCK logic, linear logic, and Lambeck's calculus of synthetic categories. This book brings together new papers by some of the most eminent authorities in these various traditions in order to provide a unified view of the field. This important volume—the first to bring together the disparate strands of work in substructural logics—will be welcomed by student and professional logicians, theoretical computer scientists, theoretical linguists, philosophers, and mathematicians working in category theory and universal algebra.

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Product Details

  • ISBN-13: 9780198537779
  • Publisher: Oxford University Press, USA
  • Publication date: 4/28/1994
  • Series: Studies in Logic and Computation Series
  • Pages: 400
  • Product dimensions: 6.37 (w) x 9.50 (h) x 1.06 (d)

Meet the Author

Universitat Tubingen

Mathematical Institute, Belgrade

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Table of Contents

A Historical Introduction to Substructural Logics 1
Life in the Undistributed Middle 31
Theorems in Classical Logic are Instances of Theorems in Condensed BCI Logic 43
Partial Gaggles Applied to Logics with Restricted Structural Rules 63
A General Theory of Structured Consequence Relations 109
Decidability and Interpolation for a First-Order Relevance Logic 153
Logic without Structural Rules (Another Look at Cut Elimination) 179
From Categorial Grammar to Bilinear Logic 207
The Semantics of Entailment 0 239
Semantics for Substructural Logics 259
The Semantics of Pretopologies 293
Lambda-Terms with Functional Symbols and Decidability in Certain Closed Categories 309
Tutorial on Linear Logic 327
The Landscape of Deduction 357
Index 377
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