Secrecy logic: S-secrecy structures

Let S = < L, proves(S)> be a deductive system. An S-secrecy logic is a quadruple K = < Fm-L(V),K,B, S >, where Fm-L(V) is the algebra of L-formulas, K,B are S-theories, with B subset of K and S subset of K such that S boolean AND B = theta. K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible (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 = < A, K-A, B-A, S-A >, consisting of an L-algebra A, two S-filters K-A, B-A on A, with B-A subset of K-A, and a subset S-A subset of K-A, such that S-A boolean AND B-A = theta. 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.