Secrecy logic : protoalgebraic S - secrecy logics

• Autorzy: Voutsadakis G.
• Języki publikacji: EN

Abstrakty

EN

In recent work the notion of a secrecy logic S over a given deductive system S was introduced. Secrecy logics capture the essential features of structures that are used in performing secrecy-preserving reasoning in practical applications. More precisely, they model knowledge bases that consist of information, part of which is considered known to the user and part of which is to remain secret from the user. S-secrecy structures serve as the models of secrecy logics. Several of the universal algebraic and model theoretic properties of the class of S-secrecy structures of a given S-secrecy logic have already been studied. In this paper, our goal is to show how techniques from the theory of abstract algebraic logic may be used to analyze the structure of a secrecy logic and draw conclusions about its algebraic character. In particular, the notion of a protoalgebraic S-secrecy logic is introduced and several characterizing properties are provided. The relationship between protoalgebraic S-secrecy logics and the protoalgebraicity of their underlying deductive systems is also investigated.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2012
• Tom: Vol. 47
• Strony: 3--28
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Voutsadakis G.

• Department of Computer Science, Iowa State University, Ames, IA 50011, U.S.A., and School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, U.S.A.,

Bibliografia

• 1] J. Bao, G. Slutzki, and V. Honavar, Privacy-Preserving Reasoniong on the Semantic Web, Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence 2007, pp. 791–797.
• [2] J. Biskup, For Unknown Secrecies Refusal is Better Than Lying, Data and Knowledge Engineering 33 (2000), pp. 1–23.
• [3] J. Biskup and P.A. Bonatti, Lying Versus Refusal for Known Potential Secrets, Data and Knowledge Engineering 38 (2001), pp. 199–222.
• [4] J. Biskup and P.A. Bonatti, Controlled Query Evaluation for Known Policies by Combining Lying and Refusal, Annals of Mathematics and Artificial Intelligence 40(2004), pp. 37–62.
• [5] J. Biskup and P. Bonatti, Controlled Query Evaluation for Enforcing Confidentiality in Complete Information Systems, International Journal of Information Security 3(2004), pp. 14–27.
• [6] W.J. Blok and D. Pigozzi, Protoalgebraic Logics, Studia Logica 45 (1986), pp. 337–369.
• [7] W.J. Blok and D. Pigozzi, Algebraizable Logics, Memoirs of the American Mathematical Society 77, No. 396 (1989).
• [8] W.J. Blok and D. Pigozzi, Algebraic Semantics for Universal Horn Logic Without Equality, in: Universal Algebra and Quasigroup Theory, A. Romanowska and J.D.H.Smith, Eds., Heldermann Verlag, Berlin 1992
• [9] P.A. Bonatti, S. Kraus, and V.S. Subrahmanian, Foundations of Secure Deductive Databases, IEEE Transactions of Knowledge and Data Engineering 7:3 (1995), pp. 406–422.
• [10] D. Calvanese, G. De Giacomo, M. Lenzerini, and R. Rosati, View-Based Query Answering over Description Logic Ontologies, Proceedings of the 11th International Conference of Knowledge Representation and Reasoning, KR 2008, pp. 242–251.
• [11] B. Cuenca Grau and I. Horrocks, Privacy-Preserving Query Answering in Logic-Based Information Systems, 18th European Conference on Artificial Intelligence,ECAI 2008, pp. 40–44.
• [12] J. Czelakowski, Protoalgebraic Logics, Trends in Logic-Studia Logica Library 10,Kluwer, Dordrecht, 2001.
• [13] J.M. Font and R. Jansana, A General Algebraic Semantics for Sentential Logics,Lecture Notes in Logic 332: 7 (1996), Springer-Verlag, Berlin Heidelberg, 1996
• [14] J.M. Font, R. Jansana, and D. Pigozzi, A Survey of Abstract Algebraic Logic, Studia Logica 74:1/2 (2003), pp. 13–97.
• [15] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove, and D.S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.
• [16] G.L. Sicherman, W. de Jonge, and R.P. van de Riet, Answering Queries Without Revealing Secrets, ACM Transactions on Database Systems 8:1 (1983), pp. 41–59.
• [17] P. Stouppa and T. Studer, A Formal Model of Data Privacy, 6th International Andrei Ershov Memorial Conference, Perspectives of Systems Informatics, PSI 2006, pp. 400–408.
• [18] P. Stouppa and T. Studer, Data Privacy for ALC Knowledge Bases, Logical Foundations of Computer Science, LFCS 2009, pp. 409–421.
• [19] G. Voutsadakis, Secrecy Logic: S-Secrecy Structures, Turkish Journal of Mathematics 35:1 (2011), pp. 1–28.