The Logic of Information Structures [Paperback]

This monograph gives a logical treatment of two centralaspects of the concept of information, namely informationprocessing and information structure. The structure ofinformation is treated as a topic in model theory, whileinformation processing is seen as an aspect of proof theory.A wide spectrum of substructural subsystems ofintuitionistic propositional logic and of Nelson'sconstructive logic with strong negation is investigated. Inparticular, the problems of cut-elimination, functionalcompleteness, and coding of proofs with lambda-terms arehandled. Finally, an interpretation of these systems interms of states of information and operations over thesestates is presented.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.Springer Book Archives