The Logic of Information Structures

1. Front Matter

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2. Introduction

   Pages 1-12

3. Generalizations

   Pages 13-29

4. Intuitionistic minimal and intuitionistic information processing

   Pages 31-44

5. Functional completeness for substructural subsystems of IPL

   Pages 45-58

6. Formulas-as-types for substructural subsystems of IPL

   Pages 59-80

7. Constructive minimal and constructive information processing

   Pages 81-91

8. Functional completeness for substructural subsystems of N

   Pages 93-106

9. The constructive typed λ-calculus λc and formulas-as-types for N−

   Pages 107-121

10. Monoid models and the informational interpretation of substructural propositional logics

    Pages 123-147

11. Back Matter

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This monograph gives a logical treatment of two central aspects of the concept of information, namely information processing and information structure. The structure of information is treated as a topic in model theory, while information processing is seen as an aspect of proof theory. A wide spectrum of substructural subsystems of intuitionistic propositional logic and of Nelson's constructive logic with strong negation is investigated. In particular, the problems of cut-elimination, functional completeness, and coding of proofs with lambda-terms are handled. Finally, an interpretation of these systems in terms of states of information and operations over these states is presented.

• Functional Completeness
• Funktionale Vollständigkeit
• Information Processing
• Information Structures
• Informationsstrukturen
• Informationsverarbeitung
• Intuitionism
• Intuitionismus
• Substructural Logics
• Unterstruktur-Lo
• model theory
• proof
• proof theory

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