Abstract
In our paper we investigate the possibilities of modal logics in coalgebras of program systems. We deal with a simplified model of an intrusion detection system. We model an intrusion detection system as a coalgebra and construct its Kripke model of coalgebraic modal linear logic using powerset endofunctor. In this model we present our idea how a fragment of epistemic linear logic can provide knowledge and belief of intrusion attempt.
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References
Gumm H.P., Functors for Coalgebras. Algebr. Univ., 45, 135–147, 2001
Kamide N., Linear and affine logics with temporal, spatial and epistemic operators. Theor. Comput. Sci., 353, 165207, 2006
Kurz A., Coalgebras and Modal Logic. CWI, Amsterdam, Netherlands, 2001
Mihályi D., Novitzká V., a Coalgebra as an Intrusion Detection System, Acta Polytech. Hung., 7, 71–79, 2010
Mihályi D., Novitzká V., Princípy duality medzi konštruovaním a správaním programov, Equilibria, 2010
Moss L.S., Coalgebraic Logic. Ann. Pure Appl. Logic, 96, 1999
Schröder L., Pattinson D., Coalgebraic Modal Logic: Forays Beyond Rank 1. IFIP WG 1.3 meeting, Sierra Nevada, 2008
Schubert Ch., Topo-Bisimulations are Coalgebraic. Rendiconti dell’ Istituto di Matemàtica dell’Universitá di Trieste, 42, 257–270, 2010
Slodičák V., Macko, P., New approaches in functional programming using algebras and coalgebras, In: European Joint Conferrences on Theory and Practice of Software — ETAPS 2011 (March 2011), Workshop on Generative Technologies, Universität des Saarlandes, Saarbrücken, Germany, 1323
Slodičák V., Some useful structures for categorical approach for program behavior, J. Inform. Organ. Sci., 35, 99–109, 2011
Voorbraak F., Generalized Kripke Models For Epistemic Logic. Proceedings of Fourth Conference on Theoretical aspects of reasoning about knowledge, Morgan Kaufmann Publishers Inc. San Francisco, CA, USA, 1992, 214–228
Zouhar M., Základy logiky. Proceedings of Fourth Conference on Theoretical aspects of reasoning about knowledge, Veda SAV, Bratislava, 2008
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Mihályi, D., Novitzká, V. & Ľaľová, M. Intrusion detection system episteme. centr.eur.j.comp.sci. 2, 214–221 (2012). https://doi.org/10.2478/s13537-012-0014-8
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DOI: https://doi.org/10.2478/s13537-012-0014-8