Secrecy logic: S-secrecy structures

Authors : George VOUTSADAKIS

Pages : 1-27

View : 13 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let S = \lan L,\vdashS\ran be a deductive system. An S-secrecy logic is a quadruple K = \lan FmLinsert ignore into journalissuearticles values(V);,K,B,S\ran, where FmLinsert ignore into journalissuearticles values(V); is the algebra of L-formulas, K,B are S-theories, with B \subseteq K and S \subseteq K such that S \cap B = \emptyset. K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible insert ignore into journalissuearticles values(or browsable); part of the knowledge base and S is a secret set, a set of sensitive or private information that the knowledge base aims at concealing from its users. To provide models for this context, the notion of an S-secrecy structure is introduced. It is a quadruple A = \lan A,KA,BA,SA\ran, consisting of an L-algebra A, two S-filters KA,BA on A, with BA \subseteq KA, and a subset SA \subseteq KA, such that SA\cap BA = \emptyset. Several model theoretic/universal algebraic and categorical properties of the class of S-secrecy structures, endowed with secrecy homomorphisms, are studied relating to various universal algebraic and categorical constructs.
Keywords : Secrecy preserving reasoning, abstract algebraic logic, logical matrices, protoalgebraic logics, first order structures, homomorphism theorems, regular categories, subdirect products, subdirectly irreducible structures