The Logic of Information StructuresThis 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. |
Contents
Introduction | 1 |
Intuitionistic minimal and intuitionistic information processing | 31 |
Bibliography | 149 |
Copyright | |
1 other sections not shown
Other editions - View all
Common terms and phrases
A₁ AISPL application of cut b₁ b₂ BHK interpretation Categorial Grammar Chapter characterized clause connectives consider constructive negation COSPL cut-elimination deductive Definition denote Došen ELIM empty sequence encoding equivalent F(A₁ finite formula functional completeness FV(M fvos Gentzen Heredity higher-level homomorphism implicational logic implies induction hypothesis inductively defined information pieces information processing information structures informational interpretation instantiations interderivable interpolation intuitionistic logic ISPL Kripke frame Kripke model Kutschera L-formula Lambek Calculus Lemma Logic of Information M₁ monoid model MSPL N₁ notion occurrences operations P₁ pieces of information pr(II premise PROOF By induction proof of Theorem proof-theoretic PROOFISPL propositional logic propositional variable provable prove refutability resp S₁ sequence of types sequent calculus slomos structural inference rules structural rules subformula substructural logics substructural subsystems syntactic T₁ T₂ valid variable of type X₁ Y₁