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.
Author(s): Heinrich Wansing (auth.)
Series: Lecture Notes in Computer Science 681 : Lecture Notes in Artificial Intelligence
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1993
Language: English
Pages: 168
Tags: Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations
Introduction....Pages 1-12
Generalizations....Pages 13-29
Intuitionistic minimal and intuitionistic information processing....Pages 31-44
Functional completeness for substructural subsystems of IPL ....Pages 45-58
Formulas-as-types for substructural subsystems of IPL ....Pages 59-80
Constructive minimal and constructive information processing....Pages 81-91
Functional completeness for substructural subsystems of N....Pages 93-106
The constructive typed λ-calculus λ c and formulas-as-types for N − ....Pages 107-121
Monoid models and the informational interpretation of substructural propositional logics....Pages 123-147
