The Logic of Information Structures

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.

Inhalt
Generalizations.- Intuitionistic minimal and intuitionistic information processing.- Functional completeness for substructural subsystems of IPL.- Formulas-as-types for substructural subsystems of IPL.- Constructive minimal and constructive information processing.- Functional completeness for substructural subsystems of N.- The constructive typed ?-calculus ?c and formulas-as-types for N?.- Monoid models and the informational interpretation of substructural propositional logics.