Towards the Knowledge in Coalgebraic Model of IDS

In the last decades linear logic became a useful logical system for various usage in computer science. Its ability to handle resources and its competence to describe dynamics of processes predetermine it for describing behaviour of programs and program systems. Linear logic can be apprehended as a multiplicative and additive extension of usual logic. We show the possibilities how these fragments can be enriched to describe behaviour and to achieve knowledge on an example of simplified Intrusion Detection System (IDS). We construct Kripke model over a coalgebra of modal linear logic for pursuing observable behaviour of IDS. Using the same Kripke frame we show how knowledge and belief in the terms of epistemic linear logic can be achieved.

[1]  J. Benthem.  Games in dynamic epistemic logic , 2001 .

[2]  Frans Voorbraak,et al.  Generalized Kripke Models for Epistemic Logic , 1991, TARK.

[3]  Mehrnoosh Sadrzadeh,et al.  Epistemic Actions as Resources , 2007, J. Log. Comput..

[4]  Jean-Yves Girard.  From foundations to ludics , 2003, Bull. Symb. Log..

[5]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[6]  Mathieu Marion,et al.  Reasoning About Knowledge In Linear Logic: Modalities and Complexity , 2004, Logic, Epistemology, and the Unity of Science.

[7]  Valerie Novitzká,et al.  A Coalgebra as an Intrusion Detection System , 2010 .

[8]  Valerie Novitzká,et al.  Intrusion detection system episteme , 2012, Central European Journal of Computer Science.

[9]  Andrea Masini,et al.  A modal view of linear logic , 1994, Journal of Symbolic Logic.

[10]  Moshe Y. Vardi.  Conference on Theoretical Aspects of Reasoning about Knowledge , 1990 .

[11]  H. Gumm.  Functors for Coalgebras , 2001 .

[12]  Viliam Slodicák,et al.  Some New Approaches in Functional Programming Using Algebras and Coalgebras , 2011, Electron. Notes Theor. Comput. Sci..

[13]  Martin Chovanec,et al.  Distributed Detection System of Security Intrusions Based on Partially Ordered Events and Patterns , 2009, Towards Intelligent Engineering and Information Technology.

[14]  Y. Venema.  A Modal Logic of Quantification and Substitution Yde Venema , 1995 .

[15]  Alexander Kurz,et al.  Coalgebras and Modal Logic , 1998 .

[16]  D. Mihályi.  Duality Between Formal Description of Program Construction and Program Behaviour , 2010 .

[17]  A. Sima Etaner-Uyar,et al.  Distributed Detection of DDoS Attacks During the Intermediate Phase Through Mobile Agents , 2012, Comput. Informatics.

[18]  Paritosh Das.  A Temporal Logic Based Approach to Multi-Agent Intrusion Detection and Prevention , 2011 .

[19]  Jean Goubault-Larrecq,et al.  The Orchids Intrusion Detection Tool , 2005, CAV.

[20]  P. T. Geach,et al.  KNOWLEDGE AND BELIEF: An Introduction to the Logic of the Two Notions , 1963 .

[21]  W. Hoek,et al.  Epistemic logic: a survey , 2002 .

[22]  Corina Cîrstea,et al.  Coalgebraic Epistemic Update Without Change of Model , 2007, CALCO.

[23]  Lujo Bauer,et al.  A Linear Logic of Authorization and Knowledge , 2006, ESORICS.

[24]  J. Girard,et al.  Proofs and types , 1989 .

[25]  Robert Goldblatt.  A Calculus of Terms for Coalgebras of Polynomial Functors , 2001, CMCS.

[26]  Dirk Pattinson,et al.  Semantical Principles in the Modal Logic of Coalgebras , 2001, STACS.

[27]  Norihiro Kamide,et al.  Linear and affine logics with temporal, spatial and epistemic operators , 2006, Theor. Comput. Sci..

[28]  Mehrnoosh Sadrzadeh.  Modal Linear Logic in Higher Order Logic, an experiment in Coq , 2003 .

[29]  Yde Venema,et al.  Uniform Interpolation for Monotone Modal Logic , 2010, Advances in Modal Logic.

[30]  Hai Jin,et al.  Automated Approach to Intrusion Detection in VM-based Dynamic Execution Environment , 2012, Comput. Informatics.

[31]  Viliam Slodičák.  Some useful structures for categorical approach for program behavior , 2010 .

[32]  Lutz Schröder.  Coalgebraic Modal Logic , 2005 .

[33]  Alessandra Palmigiano,et al.  Proof systems for the coalgebraic cover modality , 2008, Advances in Modal Logic.

[34]  Koushik Sen,et al.  A Temporal Logic Based Framework for Intrusion Detection , 2004, FORTE.

[35]  Lawrence S. Moss,et al.  Coalgebraic Logic , 1999, Ann. Pure Appl. Log..

[36]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .