Article

A qualitative framework for Shannon information theories

Author:

Gerard AllweinAuthors Info & Claims

NSPW '04: Proceedings of the 2004 workshop on New security paradigms

Pages 23 - 31

https://doi.org/10.1145/1065907.1066030

Published: 20 September 2004 Publication History

Abstract

This paper presents a new paradigm for information theory which is a synthesis of Barwise-Seligman's qualitative theory and Shannon's quantitative theory. The new paradigm is best viewed as a meta-theory for Shannon information theories and allows different probability theories, and sub-sequently, new Shannon information theories, to work within a common framework. The resulting Shannon theories conform to a qualitative structure and decorate it with measures of information. This approach is useful for analyzing assurance problems where there the analysis must contend with incomplete and even contradictory information. In particular, the mathematical constructs of the theory allow one to use just about any logic which admits a companion measure theory.

References

[1]

E. W. Adams. A Primer of Probability Logic. CSLI Publications, 1998.

[2]

G. Allwein. Probability theory for classifications i: the classical case. Technical report, U.S. Naval Research Laboratory, 2004.

[3]

G. Allwein. Probability theory for classifications ii: the general case. Technical report, U.S. Naval Research Laboratory, 2004.

[4]

M. Barr. *-Autonomous Categories. Springer-Verlag, 1979. Lecture Notes in Mathematics 752.

[5]

J. Barwise and J. Seligman. Information Flow: The Logic of Distributed Systems. Cambridge University Press, 1997. Cambridge Tracts in Theoretical Computer Science 44.

Digital Library

[6]

F. I. Dretske. Knowledge and the Flow of Information. CSLI Publications, 1999.

[7]

A. Kolmogorov. Foundations of Probability. Chelsea Publishing Company, New York, 1956. Second English Edition.

[8]

P. Mateus, A. Sernadas, and C. Sernadas. Precategories for combining probabilistic automata. Electronic Notes in Theoretical Computer Science, 29, 1999.

[9]

I. S. Moskowitz, L. Chang, and R. E. Newman. Capacity is the wrong paradigm. In Proc. New Security Paradigms Workshop, Sept. 23-26, pages 114--126. ACM Press, 2002.

Digital Library

[10]

I. S. Moskowitz, R. E. Newman, D. P. Crepeau, and A. R. Miller. Covert channels and anonymizing networks. In Proceedings of WPES 2003, pages 79--93. ACM Press, 2003.

Digital Library

[11]

R. Nelson. What is a secret and what does that have to do with computer security. In Proceedings NSPW, Rhode Island, pages 74--79, 1994.

Digital Library

[12]

P. Roeper and H. Leblanc. Probability Theory and Probability Logic. University of Toronto Press, 1999.

[13]

C. E. Shannon. The lattice theory of information. IRE Transactions Information Theory, (1):180--183, 1950.

[14]

C. E. Shannon. Communication Theory of Secrecy Systems, pages 84--143. University of Illinois Press, 1993.

[15]

C. E. Shannon and W. Weaver. The Mathematical Theory of Communication. University of Illinois Press, 1949.

Digital Library

Cited By

Mares E(2024)Logic and Information10.1017/9781009466745Online publication date: 20-May-2024
https://doi.org/10.1017/9781009466745
Fields CGlazebrook JMarcianò A(2024)Communication Protocols and QECCs from the Perspective of TQFT, Part I: Constructing LOCC Protocols and QECCs from TQFTsFortschritte der Physik10.1002/prop.202400049Online publication date: 23-Jul-2024
https://doi.org/10.1002/prop.202400049
Fields CGlazebrook J(2020)Do Process-1 simulations generate the epistemic feelings that drive Process-2 decision making?Cognitive Processing10.1007/s10339-020-00981-921:4(533-553)Online publication date: 30-Jun-2020
https://doi.org/10.1007/s10339-020-00981-9
Show More Cited By

Recommendations

Kolmogorov Complexity and Information Theory.With an Interpretation in Terms of Questions and Answers

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy, ...
Spatial information in phased‐array radar

In this study, the application of information theory to describe radar measurement problems is investigated. In Shannon's information theory, mutual information is used to quantify the reduction in the a priori uncertainty of the transmitted message. ...
Shannon Information Model in E-commerce Information Analysis
JCAI '09: Proceedings of the 2009 International Joint Conference on Artificial Intelligence

The concept of shannon information entropy is introduced to area of E-Commerce. Sorting of significance of attributes in database based on entropy is proposed to discover information value on E-Commerce information analysis. The information entropy is ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

NSPW '04: Proceedings of the 2004 workshop on New security paradigms

September 2004

124 pages

ISBN:1595930760

DOI:10.1145/1065907

Conference Chair:
Victor Raskin

Copyright © 2004 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGSAC: ACM Special Interest Group on Security, Audit, and Control
San Diego Super Computing Ctr: San Diego Super Computing Ctr
James Madison University
ACSA: Applied Computing Security Assoc
NSA: The National Security Agency

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 September 2004

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Acceptance Rates

Overall Acceptance Rate 98 of 265 submissions, 37%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

5
Total Citations
View Citations
669
Total Downloads

Downloads (Last 12 months)7
Downloads (Last 6 weeks)0

Reflects downloads up to 08 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Mares E(2024)Logic and Information10.1017/9781009466745Online publication date: 20-May-2024
https://doi.org/10.1017/9781009466745
Fields CGlazebrook JMarcianò A(2024)Communication Protocols and QECCs from the Perspective of TQFT, Part I: Constructing LOCC Protocols and QECCs from TQFTsFortschritte der Physik10.1002/prop.202400049Online publication date: 23-Jul-2024
https://doi.org/10.1002/prop.202400049
Fields CGlazebrook J(2020)Do Process-1 simulations generate the epistemic feelings that drive Process-2 decision making?Cognitive Processing10.1007/s10339-020-00981-921:4(533-553)Online publication date: 30-Jun-2020
https://doi.org/10.1007/s10339-020-00981-9
Lawless WMittu RSofge D(2018)Cyber-(in)Security, Context and Theory: Proactive Cyber-DefensesComputational Context10.1201/9780429453151-14(293-326)Online publication date: 7-Dec-2018
https://doi.org/10.1201/9780429453151-14
Russell SMoskowitz IRaglin A(2017)Human Information Interaction, Artificial Intelligence, and ErrorsAutonomy and Artificial Intelligence: A Threat or Savior?10.1007/978-3-319-59719-5_4(71-101)Online publication date: 26-Aug-2017
https://doi.org/10.1007/978-3-319-59719-5_4
Allwein GHarrison W(2016)Distributed Modal LogicJ. Michael Dunn on Information Based Logics10.1007/978-3-319-29300-4_16(331-362)Online publication date: 1-Apr-2016
https://doi.org/10.1007/978-3-319-29300-4_16

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten